Daily Papers

Multivariate time series is prevalent in many scientific and industrial domains. Modeling multivariate signals is challenging due to their long-range temporal dependencies and intricate interactions--both direct and indirect. To confront these complexities, we introduce a method of representing multivariate signals as nodes in a graph with edges indicating interdependency between them. Specifically, we leverage graph neural networks (GNN) and attention mechanisms to efficiently learn the underlying relationships within the time series data. Moreover, we suggest employing hierarchical signal decompositions running over the graphs to capture multiple spatial dependencies. The effectiveness of our proposed model is evaluated across various real-world benchmark datasets designed for long-term forecasting tasks. The results consistently showcase the superiority of our model, achieving an average 23\% reduction in mean squared error (MSE) compared to existing models.

This paper does not propose any new algorithms but instead outlines various problems in the field of visual generation based on the author's personal understanding. The core of these problems lies in how to decompose visual signals, with all other issues being closely related to this central problem and stemming from unsuitable approaches to signal decomposition. This paper aims to draw researchers' attention to the significance of Visual Signal Decomposition.

Spatial audio quality is a highly multifaceted concept, with many interactions between environmental, geometrical, anatomical, psychological, and contextual considerations. Methods for characterization or evaluation of the geometrical components of spatial audio quality, however, remain scarce, despite being perhaps the least subjective aspect of spatial audio quality to quantify. By considering interchannel time and level differences relative to a reference signal, it is possible to construct a signal model to isolate some of the spatial distortion. By using a combination of least-square optimization and heuristics, we propose a signal decomposition method to isolate the spatial error from a processed signal, in terms of interchannel gain leakages and changes in relative delays. This allows the computation of simple energy-ratio metrics, providing objective measures of spatial and non-spatial signal qualities, with minimal assumptions and no dataset dependency. Experiments demonstrate the robustness of the method against common spatial signal degradation introduced by, e.g., audio compression and music source separation. Implementation is available at https://github.com/karnwatcharasupat/spauq.

In time series forecasting, effectively disentangling intricate temporal patterns is crucial. While recent works endeavor to combine decomposition techniques with deep learning, multiple frequencies may still be mixed in the decomposed components, e.g., trend and seasonal. Furthermore, frequency domain analysis methods, e.g., Fourier and wavelet transforms, have limitations in resolution in the time domain and adaptability. In this paper, we propose D-PAD, a deep-shallow multi-frequency patterns disentangling neural network for time series forecasting. Specifically, a multi-component decomposing (MCD) block is introduced to decompose the series into components with different frequency ranges, corresponding to the "shallow" aspect. A decomposition-reconstruction-decomposition (D-R-D) module is proposed to progressively extract the information of frequencies mixed in the components, corresponding to the "deep" aspect. After that, an interaction and fusion (IF) module is used to further analyze the components. Extensive experiments on seven real-world datasets demonstrate that D-PAD achieves the state-of-the-art performance, outperforming the best baseline by an average of 9.48% and 7.15% in MSE and MAE, respectively.

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.

Learning decompositions of expensive-to-evaluate black-box functions promises to scale Bayesian optimisation (BO) to high-dimensional problems. However, the success of these techniques depends on finding proper decompositions that accurately represent the black-box. While previous works learn those decompositions based on data, we investigate data-independent decomposition sampling rules in this paper. We find that data-driven learners of decompositions can be easily misled towards local decompositions that do not hold globally across the search space. Then, we formally show that a random tree-based decomposition sampler exhibits favourable theoretical guarantees that effectively trade off maximal information gain and functional mismatch between the actual black-box and its surrogate as provided by the decomposition. Those results motivate the development of the random decomposition upper-confidence bound algorithm (RDUCB) that is straightforward to implement - (almost) plug-and-play - and, surprisingly, yields significant empirical gains compared to the previous state-of-the-art on a comprehensive set of benchmarks. We also confirm the plug-and-play nature of our modelling component by integrating our method with HEBO, showing improved practical gains in the highest dimensional tasks from Bayesmark.

Target audio source separation with natural language queries presents a promising paradigm for extracting arbitrary audio events through arbitrary text descriptions. Existing methods mainly face two challenges, the difficulty in jointly modeling acoustic-textual alignment and semantic-aware separation within a blindly-learned single-stage architecture, and the reliance on large-scale accurately-labeled training data to compensate for inefficient cross-modal learning and separation. To address these challenges, we propose a hierarchical decomposition framework, HSM-TSS, that decouples the task into global-local semantic-guided feature separation and structure-preserving acoustic reconstruction. Our approach introduces a dual-stage mechanism for semantic separation, operating on distinct global and local semantic feature spaces. We first perform global-semantic separation through a global semantic feature space aligned with text queries. A Q-Audio architecture is employed to align audio and text modalities, serving as pretrained global-semantic encoders. Conditioned on the predicted global feature, we then perform the second-stage local-semantic separation on AudioMAE features that preserve time-frequency structures, followed by acoustic reconstruction. We also propose an instruction processing pipeline to parse arbitrary text queries into structured operations, extraction or removal, coupled with audio descriptions, enabling flexible sound manipulation. Our method achieves state-of-the-art separation performance with data-efficient training while maintaining superior semantic consistency with queries in complex auditory scenes.

Models for audio source separation usually operate on the magnitude spectrum, which ignores phase information and makes separation performance dependant on hyper-parameters for the spectral front-end. Therefore, we investigate end-to-end source separation in the time-domain, which allows modelling phase information and avoids fixed spectral transformations. Due to high sampling rates for audio, employing a long temporal input context on the sample level is difficult, but required for high quality separation results because of long-range temporal correlations. In this context, we propose the Wave-U-Net, an adaptation of the U-Net to the one-dimensional time domain, which repeatedly resamples feature maps to compute and combine features at different time scales. We introduce further architectural improvements, including an output layer that enforces source additivity, an upsampling technique and a context-aware prediction framework to reduce output artifacts. Experiments for singing voice separation indicate that our architecture yields a performance comparable to a state-of-the-art spectrogram-based U-Net architecture, given the same data. Finally, we reveal a problem with outliers in the currently used SDR evaluation metrics and suggest reporting rank-based statistics to alleviate this problem.

Deep Neural Networks (DNNs) have been a large driver and enabler for AI breakthroughs in recent years. These models have been getting larger in their attempt to become more accurate and tackle new upcoming use-cases, including AR/VR and intelligent assistants. However, the training process of such large models is a costly and time-consuming process, which typically yields a single model to fit all targets. To mitigate this, various techniques have been proposed in the literature, including pruning, sparsification or quantization of the model weights and updates. While able to achieve high compression rates, they often incur computational overheads or accuracy penalties. Alternatively, factorization methods have been leveraged to incorporate low-rank compression in the training process. Similarly, such techniques (e.g.,~SVD) frequently rely on the computationally expensive decomposition of layers and are potentially sub-optimal for non-linear models, such as DNNs. In this work, we take a further step in designing efficient low-rank models and propose Maestro, a framework for trainable low-rank layers. Instead of regularly applying a priori decompositions such as SVD, the low-rank structure is built into the training process through a generalized variant of Ordered Dropout. This method imposes an importance ordering via sampling on the decomposed DNN structure. Our theoretical analysis demonstrates that our method recovers the SVD decomposition of linear mapping on uniformly distributed data and PCA for linear autoencoders. We further apply our technique on DNNs and empirically illustrate that Maestro enables the extraction of lower footprint models that preserve model performance while allowing for graceful accuracy-latency tradeoff for the deployment to devices of different capabilities.

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current decomposition methods -- decomposes neural network parameters into a sum of sparsely used vectors in parameter space. However, the current main method in this framework, Attribution-based Parameter Decomposition (APD), is impractical on account of its computational cost and sensitivity to hyperparameters. In this work, we introduce Stochastic Parameter Decomposition (SPD), a method that is more scalable and robust to hyperparameters than APD, which we demonstrate by decomposing models that are slightly larger and more complex than was possible to decompose with APD. We also show that SPD avoids other issues, such as shrinkage of the learned parameters, and better identifies ground truth mechanisms in toy models. By bridging causal mediation analysis and network decomposition methods, this demonstration opens up new research possibilities in mechanistic interpretability by removing barriers to scaling linear parameter decomposition methods to larger models. We release a library for running SPD and reproducing our experiments at https://github.com/goodfire-ai/spd.

Multivariate long-term and efficient time series forecasting is a key requirement for a variety of practical applications, and there are complex interleaving time dynamics in time series data that require decomposition modeling. Traditional time series decomposition methods are single and rely on fixed rules, which are insufficient for mining the potential information of the series and adapting to the dynamic characteristics of complex series. On the other hand, the Transformer-based models for time series forecasting struggle to effectively model long sequences and intricate dynamic relationships due to their high computational complexity. To overcome these limitations, we introduce KARMA, with an Adaptive Time Channel Decomposition module (ATCD) to dynamically extract trend and seasonal components. It further integrates a Hybrid Frequency-Time Decomposition module (HFTD) to further decompose Series into frequency-domain and time-domain. These components are coupled with multi-scale Mamba-based KarmaBlock to efficiently process global and local information in a coordinated manner. Experiments on eight real-world datasets from diverse domains well demonstrated that KARMA significantly outperforms mainstream baseline methods in both predictive accuracy and computational efficiency. Code and full results are available at this repository: https://github.com/yedadasd/KARMA

Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank approximation and its application in adaptation can sometimes be obscure, leaving practitioners and researchers with questions about its true capabilities and limitations. This paper seeks to clarify low-rank approximation and adaptation by offering a comprehensive guide that reveals their inner workings and explains their utility in a clear and accessible way. Our focus here is to develop a solid intuition for how low-rank approximation and adaptation operate, and why they are so effective. We begin with basic concepts and gradually build up to the mathematical underpinnings, ensuring that readers of all backgrounds can gain a deeper understanding of low-rank approximation and adaptation. We strive to strike a balance between informal explanations and rigorous mathematics, ensuring that both newcomers and experienced experts can benefit from this survey. Additionally, we introduce new low-rank decomposition and adaptation algorithms that have not yet been explored in the field, hoping that future researchers will investigate their potential applicability.

Efficiently capturing the long-range patterns in sequential data sources salient to a given task -- such as classification and generative modeling -- poses a fundamental challenge. Popular approaches in the space tradeoff between the memory burden of brute-force enumeration and comparison, as in transformers, the computational burden of complicated sequential dependencies, as in recurrent neural networks, or the parameter burden of convolutional networks with many or large filters. We instead take inspiration from wavelet-based multiresolution analysis to define a new building block for sequence modeling, which we call a MultiresLayer. The key component of our model is the multiresolution convolution, capturing multiscale trends in the input sequence. Our MultiresConv can be implemented with shared filters across a dilated causal convolution tree. Thus it garners the computational advantages of convolutional networks and the principled theoretical motivation of wavelet decompositions. Our MultiresLayer is straightforward to implement, requires significantly fewer parameters, and maintains at most a O(Nlog N) memory footprint for a length N sequence. Yet, by stacking such layers, our model yields state-of-the-art performance on a number of sequence classification and autoregressive density estimation tasks using CIFAR-10, ListOps, and PTB-XL datasets.

Given a factorization of an image into a sum of linear components, we present a zero-shot method to control each individual component through diffusion model sampling. For example, we can decompose an image into low and high spatial frequencies and condition these components on different text prompts. This produces hybrid images, which change appearance depending on viewing distance. By decomposing an image into three frequency subbands, we can generate hybrid images with three prompts. We also use a decomposition into grayscale and color components to produce images whose appearance changes when they are viewed in grayscale, a phenomena that naturally occurs under dim lighting. And we explore a decomposition by a motion blur kernel, which produces images that change appearance under motion blurring. Our method works by denoising with a composite noise estimate, built from the components of noise estimates conditioned on different prompts. We also show that for certain decompositions, our method recovers prior approaches to compositional generation and spatial control. Finally, we show that we can extend our approach to generate hybrid images from real images. We do this by holding one component fixed and generating the remaining components, effectively solving an inverse problem.

In this study, we examine the efficacy of post-hoc local attribution methods in identifying features with predictive power from irrelevant ones in domains characterized by a low signal-to-noise ratio (SNR), a common scenario in real-world machine learning applications. We developed synthetic datasets encompassing symbolic functional, image, and audio data, incorporating a benchmark on the {\it (Model \(\times\) Attribution\(\times\) Noise Condition)} triplet. By rigorously testing various classic models trained from scratch, we gained valuable insights into the performance of these attribution methods in multiple conditions. Based on these findings, we introduce a novel extension to the notable recursive feature elimination (RFE) algorithm, enhancing its applicability for neural networks. Our experiments highlight its strengths in prediction and feature selection, alongside limitations in scalability. Further details and additional minor findings are included in the appendix, with extensive discussions. The codes and resources are available at https://github.com/geshijoker/ChaosMining/{URL}.

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

In language modeling based music generation, a generated waveform is represented by a sequence of hierarchical token stacks that can be decoded either in an auto-regressive manner or in parallel, depending on the codebook patterns. In particular, flattening the codebooks represents the highest quality decoding strategy, while being notoriously slow. To this end, we propose a novel stack-and-delay style of decoding strategy to improve upon the flat pattern decoding where generation speed is four times faster as opposed to vanilla flat decoding. This brings the inference time close to that of the delay decoding strategy, and allows for faster inference on GPU for small batch sizes. For the same inference efficiency budget as the delay pattern, we show that the proposed approach performs better in objective evaluations, almost closing the gap with the flat pattern in terms of quality. The results are corroborated by subjective evaluations which show that samples generated by the new model are slightly more often preferred to samples generated by the competing model given the same text prompts.

In quantised autoencoders, images are usually split into local patches, each encoded by one token. This representation is redundant in the sense that the same number of tokens is spend per region, regardless of the visual information content in that region. Adaptive discretisation schemes like quadtrees are applied to allocate tokens for patches with varying sizes, but this just varies the region of influence for a token which nevertheless remains a local descriptor. Modern architectures add an attention mechanism to the autoencoder which infuses some degree of global information into the local tokens. Despite the global context, tokens are still associated with a local image region. In contrast, our method is inspired by spectral decompositions which transform an input signal into a superposition of global frequencies. Taking the data-driven perspective, we learn custom basis functions corresponding to the codebook entries in our VQ-VAE setup. Furthermore, a decoder combines these basis functions in a non-linear fashion, going beyond the simple linear superposition of spectral decompositions. We can achieve this global description with an efficient transpose operation between features and channels and demonstrate our performance on compression.

Source separation involves the ill-posed problem of retrieving a set of source signals that have been observed through a mixing operator. Solving this problem requires prior knowledge, which is commonly incorporated by imposing regularity conditions on the source signals, or implicitly learned through supervised or unsupervised methods from existing data. While data-driven methods have shown great promise in source separation, they often require large amounts of data, which rarely exists in planetary space missions. To address this challenge, we propose an unsupervised source separation scheme for domains with limited data access that involves solving an optimization problem in the wavelet scattering covariance representation spacex2014an interpretable, low-dimensional representation of stationary processes. We present a real-data example in which we remove transient, thermally-induced microtiltsx2014known as glitchesx2014from data recorded by a seismometer during NASA's InSight mission on Mars. Thanks to the wavelet scattering covariances' ability to capture non-Gaussian properties of stochastic processes, we are able to separate glitches using only a few glitch-free data snippets.

This paper makes a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian eigendecomposition and singular value decomposition. The other consists of Gaussian elimination and the Gram-Schmidt procedure with various pivoting rules for computing the Cholesky decomposition and QR decomposition respectively. Both families are cast as special cases of a more general class of factorization algorithms. We provide a randomized pivoting rule that applies to this general class (which differs substantially from the usual pivoting rules for Gaussian elimination / Gram-Schmidt) which results in the same linear rate of convergence for each algorithm, irrespective of which factorization it computes. A second important consequence of this randomized pivoting rule is a provable, effective bound on the numerical stability of the Jacobi eigenvalue algorithm, which addresses a longstanding open problem of Demmel and Veseli\'c `92.

This paper considers the problem of undersampled MRI reconstruction. We propose a novel Transformer-based framework for directly processing signal in k-space, going beyond the limitation of regular grids as ConvNets do. We adopt an implicit representation of k-space spectrogram, treating spatial coordinates as inputs, and dynamically query the sparsely sampled points to reconstruct the spectrogram, i.e. learning the inductive bias in k-space. To strike a balance between computational cost and reconstruction quality, we build the decoder with hierarchical structure to generate low-resolution and high-resolution outputs respectively. To validate the effectiveness of our proposed method, we have conducted extensive experiments on two public datasets, and demonstrate superior or comparable performance to state-of-the-art approaches.

Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general framework which unifies many existing GNN models from the view of parameterized decomposition and filtering, and show how it helps to enhance the flexibility of GNNs while alleviating the smoothness and amplification issues of existing models. Essentially, we show that the extensively studied spectral graph convolutions with learnable polynomial filters are constrained variants of this formulation, and releasing these constraints enables our model to express the desired decomposition and filtering simultaneously. Based on this generalized framework, we develop models that are simple in implementation but achieve significant improvements and computational efficiency on a variety of graph learning tasks. Code is available at https://github.com/qslim/PDF.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

Music source separation in the time-frequency domain is commonly achieved by applying a soft or binary mask to the magnitude component of (complex) spectrograms. The phase component is usually not estimated, but instead copied from the mixture and applied to the magnitudes of the estimated isolated sources. While this method has several practical advantages, it imposes an upper bound on the performance of the system, where the estimated isolated sources inherently exhibit audible "phase artifacts". In this paper we address these shortcomings by directly estimating masks in the complex domain, extending recent work from the speech enhancement literature. The method is particularly well suited for multi-instrument musical source separation since residual phase artifacts are more pronounced for spectrally overlapping instrument sources, a common scenario in music. We show that complex masks result in better separation than masks that operate solely on the magnitude component.

Time series forecasting is widely used in extensive applications, such as traffic planning and weather forecasting. However, real-world time series usually present intricate temporal variations, making forecasting extremely challenging. Going beyond the mainstream paradigms of plain decomposition and multiperiodicity analysis, we analyze temporal variations in a novel view of multiscale-mixing, which is based on an intuitive but important observation that time series present distinct patterns in different sampling scales. The microscopic and the macroscopic information are reflected in fine and coarse scales respectively, and thereby complex variations can be inherently disentangled. Based on this observation, we propose TimeMixer as a fully MLP-based architecture with Past-Decomposable-Mixing (PDM) and Future-Multipredictor-Mixing (FMM) blocks to take full advantage of disentangled multiscale series in both past extraction and future prediction phases. Concretely, PDM applies the decomposition to multiscale series and further mixes the decomposed seasonal and trend components in fine-to-coarse and coarse-to-fine directions separately, which successively aggregates the microscopic seasonal and macroscopic trend information. FMM further ensembles multiple predictors to utilize complementary forecasting capabilities in multiscale observations. Consequently, TimeMixer is able to achieve consistent state-of-the-art performances in both long-term and short-term forecasting tasks with favorable run-time efficiency.

Factorizing a large matrix into small matrices is a popular strategy for model compression. Singular value decomposition (SVD) plays a vital role in this compression strategy, approximating a learned matrix with fewer parameters. However, SVD minimizes the squared error toward reconstructing the original matrix without gauging the importance of the parameters, potentially giving a larger reconstruction error for those who affect the task accuracy more. In other words, the optimization objective of SVD is not aligned with the trained model's task accuracy. We analyze this previously unexplored problem, make observations, and address it by introducing Fisher information to weigh the importance of parameters affecting the model prediction. This idea leads to our method: Fisher-Weighted SVD (FWSVD). Although the factorized matrices from our approach do not result in smaller reconstruction errors, we find that our resulting task accuracy is much closer to the original model's performance. We perform analysis with the transformer-based language models, showing our weighted SVD largely alleviates the mismatched optimization objectives and can maintain model performance with a higher compression rate. Our method can directly compress a task-specific model while achieving better performance than other compact model strategies requiring expensive model pre-training. Moreover, the evaluation of compressing an already compact model shows our method can further reduce 9% to 30% parameters with an insignificant impact on task accuracy.

This paper proposes a convolutional neural network (CNN)-based detector for faster-than-Nyquist (FTN) signaling that employs structured fixed kernel layers with domain-informed masking to mitigate intersymbol interference (ISI). Unlike standard CNNs with sliding kernels, the proposed method utilizes fixed-position kernels to directly capture ISI effects at varying distances from the central symbol. A hierarchical filter allocation strategy is also introduced, assigning more filters to earlier layers for strong ISI patterns and fewer to later layers for weaker ones. This design improves detection accuracy while reducing redundant operations. Simulation results show that the detector achieves near-optimal bit error rate (BER) performance for tau geq 0.7, closely matching the BCJR algorithm, and offers computational gains of up to 46% and 84% over M-BCJR for BPSK and QPSK, respectively. Comparative analysis with other methods further highlights the efficiency and effectiveness of the proposed approach. To the best of our knowledge, this is the first application of a fixed-kernel CNN architecture tailored for FTN detection in the literature.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

In this paper, we prove representation bottlenecks of a cascaded convolutional decoder network, considering the capacity of representing different frequency components of an input sample. We conduct the discrete Fourier transform on each channel of the feature map in an intermediate layer of the decoder network. Then, we introduce the rule of the forward propagation of such intermediate-layer spectrum maps, which is equivalent to the forward propagation of feature maps through a convolutional layer. Based on this, we find that each frequency component in the spectrum map is forward propagated independently with other frequency components. Furthermore, we prove two bottlenecks in representing feature spectrums. First, we prove that the convolution operation, the zero-padding operation, and a set of other settings all make a convolutional decoder network more likely to weaken high-frequency components. Second, we prove that the upsampling operation generates a feature spectrum, in which strong signals repetitively appears at certain frequencies.

Music demixing is the task of separating different tracks from the given single audio signal into components, such as drums, bass, and vocals from the rest of the accompaniment. Separation of sources is useful for a range of areas, including entertainment and hearing aids. In this paper, we introduce two new benchmarks for the sound source separation tasks and compare popular models for sound demixing, as well as their ensembles, on these benchmarks. For the models' assessments, we provide the leaderboard at https://mvsep.com/quality_checker/, giving a comparison for a range of models. The new benchmark datasets are available for download. We also develop a novel approach for audio separation, based on the ensembling of different models that are suited best for the particular stem. The proposed solution was evaluated in the context of the Music Demixing Challenge 2023 and achieved top results in different tracks of the challenge. The code and the approach are open-sourced on GitHub.

Conditional sound separation in multi-source audio mixtures without having access to single source sound data during training is a long standing challenge. Existing mix-and-separate based methods suffer from significant performance drop with multi-source training mixtures due to the lack of supervision signal for single source separation cases during training. However, in the case of language-conditional audio separation, we do have access to corresponding text descriptions for each audio mixture in our training data, which can be seen as (rough) representations of the audio samples in the language modality. To this end, in this paper, we propose a generic bi-modal separation framework which can enhance the existing unsupervised frameworks to separate single-source signals in a target modality (i.e., audio) using the easily separable corresponding signals in the conditioning modality (i.e., language), without having access to single-source samples in the target modality during training. We empirically show that this is well within reach if we have access to a pretrained joint embedding model between the two modalities (i.e., CLAP). Furthermore, we propose to incorporate our framework into two fundamental scenarios to enhance separation performance. First, we show that our proposed methodology significantly improves the performance of purely unsupervised baselines by reducing the distribution shift between training and test samples. In particular, we show that our framework can achieve 71% boost in terms of Signal-to-Distortion Ratio (SDR) over the baseline, reaching 97.5% of the supervised learning performance. Second, we show that we can further improve the performance of the supervised learning itself by 17% if we augment it by our proposed weakly-supervised framework, that enables a powerful semi-supervised framework for audio separation.

Deep learning-based music source separation has gained a lot of interest in the last decades. Most of the existing methods operate with either spectrograms or waveforms. Spectrogram based models learn suitable masks for separating magnitude spectrogram into different sources, and waveform-based models directly generate waveforms of individual sources. The two types of models have complementary strengths; the former is superior given harmonic sources such as vocals, while the latter demonstrates better results for percussion and bass instruments. In this work, we improved upon the state-of-the-art (SoTA) models and successfully combined the best of both worlds. The backbones of the proposed framework, dubbed Danna-Sep, are two spectrogram-based models including a modified X-UMX and U-Net, and an enhanced Demucs as the waveform-based model. Given an input of mixture, we linearly combined respective outputs from the three models to obtain the final result. We showed in the experiments that, despite its simplicity, Danna-Sep surpassed the SoTA models by a large margin in terms of Source-to-Distortion Ratio.

There have been significant advances in deep learning for music demixing in recent years. However, there has been little attention given to how these neural networks can be adapted for real-time low-latency applications, which could be helpful for hearing aids, remixing audio streams and live shows. In this paper, we investigate the various challenges involved in adapting current demixing models in the literature for this use case. Subsequently, inspired by the Hybrid Demucs architecture, we propose the Hybrid Spectrogram Time-domain Audio Separation Network HS-TasNet, which utilises the advantages of spectral and waveform domains. For a latency of 23 ms, the HS-TasNet obtains an overall signal-to-distortion ratio (SDR) of 4.65 on the MusDB test set, and increases to 5.55 with additional training data. These results demonstrate the potential of efficient demixing for real-time low-latency music applications.

Recently, multi-band spectrogram-based approaches such as Band-Split RNN (BSRNN) have demonstrated promising results for music source separation. In our recent work, we introduce the BS-RoFormer model which inherits the idea of band-split scheme in BSRNN at the front-end, and then uses the hierarchical Transformer with Rotary Position Embedding (RoPE) to model the inner-band and inter-band sequences for multi-band mask estimation. This model has achieved state-of-the-art performance, but the band-split scheme is defined empirically, without analytic supports from the literature. In this paper, we propose Mel-RoFormer, which adopts the Mel-band scheme that maps the frequency bins into overlapped subbands according to the mel scale. In contract, the band-split mapping in BSRNN and BS-RoFormer is non-overlapping and designed based on heuristics. Using the MUSDB18HQ dataset for experiments, we demonstrate that Mel-RoFormer outperforms BS-RoFormer in the separation tasks of vocals, drums, and other stems.

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at https://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

This work investigates the empirical performance of the sparse synthesis versus sparse analysis regularization for the ill-posed inverse problem of audio declipping. We develop a versatile non-convex heuristics which can be readily used with both data models. Based on this algorithm, we report that, in most cases, the two models perform almost similarly in terms of signal enhancement. However, the analysis version is shown to be amenable for real time audio processing, when certain analysis operators are considered. Both versions outperform state-of-the-art methods in the field, especially for the severely saturated signals.

Integrated sensing and communication (ISAC) is envisioned be to one of the paradigms upon which next-generation mobile networks will be built, extending localization and tracking capabilities, as well as giving birth to environment-aware wireless access. A key aspect of sensing integration is parameter estimation, which involves extracting information about the surrounding environment, such as the direction, distance, and velocity of various objects within. This is typically of a high-dimensional nature, which leads to significant computational complexity, if performed jointly across multiple sensing dimensions, such as space, frequency, and time. Additionally, due to the incorporation of sensing on top of the data transmission, the time window available for sensing is likely to be short, resulting in an estimation problem where only a single snapshot is accessible. In this work, we propose PLAIN, a tensor-based estimation architecture that flexibly scales with multiple sensing dimensions and can handle high dimensionality, limited measurement time, and super-resolution requirements. It consists of three stages: a compression stage, where the high dimensional input is converted into lower dimensionality, without sacrificing resolution; a decoupled estimation stage, where the parameters across the different dimensions are estimated in parallel with low complexity; an input-based fusion stage, where the decoupled parameters are fused together to form a paired multidimensional estimate. We investigate the performance of the architecture for different configurations and compare it against practical sequential and joint estimation baselines, as well as theoretical bounds. Our results show that PLAIN, using tools from tensor algebra, subspace-based processing, and compressed sensing, can scale flexibly with dimensionality, while operating with low complexity and maintaining super-resolution.

The performance of music source separation (MSS) models has been greatly improved in recent years thanks to the development of novel neural network architectures and training pipelines. However, recent model designs for MSS were mainly motivated by other audio processing tasks or other research fields, while the intrinsic characteristics and patterns of the music signals were not fully discovered. In this paper, we propose band-split RNN (BSRNN), a frequency-domain model that explictly splits the spectrogram of the mixture into subbands and perform interleaved band-level and sequence-level modeling. The choices of the bandwidths of the subbands can be determined by a priori knowledge or expert knowledge on the characteristics of the target source in order to optimize the performance on a certain type of target musical instrument. To better make use of unlabeled data, we also describe a semi-supervised model finetuning pipeline that can further improve the performance of the model. Experiment results show that BSRNN trained only on MUSDB18-HQ dataset significantly outperforms several top-ranking models in Music Demixing (MDX) Challenge 2021, and the semi-supervised finetuning stage further improves the performance on all four instrument tracks.

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address one limitation of sparse GPs, which is due to the challenge in dealing with a large number of inducing variables without imposing a special structure on the inducing inputs. In particular, we introduce a novel hierarchical prior, which imposes sparsity on the set of inducing variables. We treat our model variationally, and we experimentally show considerable computational gains compared to standard sparse GPs when sparsity on the inducing variables is realized considering the nearest inducing inputs of a random mini-batch of the data. We perform an extensive experimental validation that demonstrates the effectiveness of our approach compared to the state-of-the-art. Our approach enables the possibility to use sparse GPs using a large number of inducing points without incurring a prohibitive computational cost.

In this paper, we study the problem of principal component analysis with generative modeling assumptions, adopting a general model for the observed matrix that encompasses notable special cases, including spiked matrix recovery and phase retrieval. The key assumption is that the underlying signal lies near the range of an L-Lipschitz continuous generative model with bounded k-dimensional inputs. We propose a quadratic estimator, and show that it enjoys a statistical rate of order frac{klog L{m}}, where m is the number of samples. We also provide a near-matching algorithm-independent lower bound. Moreover, we provide a variant of the classic power method, which projects the calculated data onto the range of the generative model during each iteration. We show that under suitable conditions, this method converges exponentially fast to a point achieving the above-mentioned statistical rate. We perform experiments on various image datasets for spiked matrix and phase retrieval models, and illustrate performance gains of our method to the classic power method and the truncated power method devised for sparse principal component analysis.

The landscape of computational building blocks of efficient image restoration architectures is dominated by a combination of convolutional processing and various attention mechanisms. However, convolutional filters, while efficient, are inherently local and therefore struggle with modeling long-range dependencies in images. In contrast, attention excels at capturing global interactions between arbitrary image regions, but suffers from a quadratic cost in image dimension. In this work, we propose Serpent, an efficient architecture for high-resolution image restoration that combines recent advances in state space models (SSMs) with multi-scale signal processing in its core computational block. SSMs, originally introduced for sequence modeling, can maintain a global receptive field with a favorable linear scaling in input size. We propose a novel hierarchical architecture inspired by traditional signal processing principles, that converts the input image into a collection of sequences and processes them in a multi-scale fashion. Our experimental results demonstrate that Serpent can achieve reconstruction quality on par with state-of-the-art techniques, while requiring orders of magnitude less compute (up to 150 fold reduction in FLOPS) and a factor of up to 5times less GPU memory while maintaining a compact model size. The efficiency gains achieved by Serpent are especially notable at high image resolutions.

The reflection superposition phenomenon is complex and widely distributed in the real world, which derives various simplified linear and nonlinear formulations of the problem. In this paper, based on the investigation of the weaknesses of existing models, we propose a more general form of the superposition model by introducing a learnable residue term, which can effectively capture residual information during decomposition, guiding the separated layers to be complete. In order to fully capitalize on its advantages, we further design the network structure elaborately, including a novel dual-stream interaction mechanism and a powerful decomposition network with a semantic pyramid encoder. Extensive experiments and ablation studies are conducted to verify our superiority over state-of-the-art approaches on multiple real-world benchmark datasets. Our code is publicly available at https://github.com/mingcv/DSRNet.

In this work, we define a diffusion-based generative model capable of both music synthesis and source separation by learning the score of the joint probability density of sources sharing a context. Alongside the classic total inference tasks (i.e., generating a mixture, separating the sources), we also introduce and experiment on the partial generation task of source imputation, where we generate a subset of the sources given the others (e.g., play a piano track that goes well with the drums). Additionally, we introduce a novel inference method for the separation task based on Dirac likelihood functions. We train our model on Slakh2100, a standard dataset for musical source separation, provide qualitative results in the generation settings, and showcase competitive quantitative results in the source separation setting. Our method is the first example of a single model that can handle both generation and separation tasks, thus representing a step toward general audio models.

Deep learning-based methods have made significant achievements in music source separation. However, obtaining good results while maintaining a low model complexity remains challenging in super wide-band music source separation. Previous works either overlook the differences in subbands or inadequately address the problem of information loss when generating subband features. In this paper, we propose SCNet, a novel frequency-domain network to explicitly split the spectrogram of the mixture into several subbands and introduce a sparsity-based encoder to model different frequency bands. We use a higher compression ratio on subbands with less information to improve the information density and focus on modeling subbands with more information. In this way, the separation performance can be significantly improved using lower computational consumption. Experiment results show that the proposed model achieves a signal to distortion ratio (SDR) of 9.0 dB on the MUSDB18-HQ dataset without using extra data, which outperforms state-of-the-art methods. Specifically, SCNet's CPU inference time is only 48% of HT Demucs, one of the previous state-of-the-art models.

An emerging solution for explaining Transformer-based models is to use vector-based analysis on how the representations are formed. However, providing a faithful vector-based explanation for a multi-layer model could be challenging in three aspects: (1) Incorporating all components into the analysis, (2) Aggregating the layer dynamics to determine the information flow and mixture throughout the entire model, and (3) Identifying the connection between the vector-based analysis and the model's predictions. In this paper, we present DecompX to tackle these challenges. DecompX is based on the construction of decomposed token representations and their successive propagation throughout the model without mixing them in between layers. Additionally, our proposal provides multiple advantages over existing solutions for its inclusion of all encoder components (especially nonlinear feed-forward networks) and the classification head. The former allows acquiring precise vectors while the latter transforms the decomposition into meaningful prediction-based values, eliminating the need for norm- or summation-based vector aggregation. According to the standard faithfulness evaluations, DecompX consistently outperforms existing gradient-based and vector-based approaches on various datasets. Our code is available at https://github.com/mohsenfayyaz/DecompX.

As foundational models reshape scientific discovery, a bottleneck persists in dynamical system reconstruction (DSR): the ability to learn across system hierarchies. Many meta-learning approaches have been applied successfully to single systems, but falter when confronted with sparse, loosely related datasets requiring multiple hierarchies to be learned. Mixture of Experts (MoE) offers a natural paradigm to address these challenges. Despite their potential, we demonstrate that naive MoEs are inadequate for the nuanced demands of hierarchical DSR, largely due to their gradient descent-based gating update mechanism which leads to slow updates and conflicted routing during training. To overcome this limitation, we introduce MixER: Mixture of Expert Reconstructors, a novel sparse top-1 MoE layer employing a custom gating update algorithm based on K-means and least squares. Extensive experiments validate MixER's capabilities, demonstrating efficient training and scalability to systems of up to ten parametric ordinary differential equations. However, our layer underperforms state-of-the-art meta-learners in high-data regimes, particularly when each expert is constrained to process only a fraction of a dataset composed of highly related data points. Further analysis with synthetic and neuroscientific time series suggests that the quality of the contextual representations generated by MixER is closely linked to the presence of hierarchical structure in the data.

Adapting large-scale pre-trained generative models in a parameter-efficient manner is gaining traction. Traditional methods like low rank adaptation achieve parameter efficiency by imposing constraints but may not be optimal for tasks requiring high representation capacity. We propose a novel spectrum-aware adaptation framework for generative models. Our method adjusts both singular values and their basis vectors of pretrained weights. Using the Kronecker product and efficient Stiefel optimizers, we achieve parameter-efficient adaptation of orthogonal matrices. We introduce Spectral Orthogonal Decomposition Adaptation (SODA), which balances computational efficiency and representation capacity. Extensive evaluations on text-to-image diffusion models demonstrate SODA's effectiveness, offering a spectrum-aware alternative to existing fine-tuning methods.

Universal source separation (USS) is a fundamental research task for computational auditory scene analysis, which aims to separate mono recordings into individual source tracks. There are three potential challenges awaiting the solution to the audio source separation task. First, previous audio source separation systems mainly focus on separating one or a limited number of specific sources. There is a lack of research on building a unified system that can separate arbitrary sources via a single model. Second, most previous systems require clean source data to train a separator, while clean source data are scarce. Third, there is a lack of USS system that can automatically detect and separate active sound classes in a hierarchical level. To use large-scale weakly labeled/unlabeled audio data for audio source separation, we propose a universal audio source separation framework containing: 1) an audio tagging model trained on weakly labeled data as a query net; and 2) a conditional source separation model that takes query net outputs as conditions to separate arbitrary sound sources. We investigate various query nets, source separation models, and training strategies and propose a hierarchical USS strategy to automatically detect and separate sound classes from the AudioSet ontology. By solely leveraging the weakly labelled AudioSet, our USS system is successful in separating a wide variety of sound classes, including sound event separation, music source separation, and speech enhancement. The USS system achieves an average signal-to-distortion ratio improvement (SDRi) of 5.57 dB over 527 sound classes of AudioSet; 10.57 dB on the DCASE 2018 Task 2 dataset; 8.12 dB on the MUSDB18 dataset; an SDRi of 7.28 dB on the Slakh2100 dataset; and an SSNR of 9.00 dB on the voicebank-demand dataset. We release the source code at https://github.com/bytedance/uss

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced updates becomes increasingly important. Existing methods for updating truncated SVDs employ Rayleigh-Ritz projection procedures, where projection matrices are augmented based on original singular vectors. However, these methods suffer from inefficiency due to the densification of the update matrix and the application of the projection to all singular vectors. To address these limitations, we introduce a novel method for dynamically approximating the truncated SVD of a sparse and temporally evolving matrix. Our approach leverages sparsity in the orthogonalization process of augmented matrices and utilizes an extended decomposition to independently store projections in the column space of singular vectors. Numerical experiments demonstrate a remarkable efficiency improvement of an order of magnitude compared to previous methods. Remarkably, this improvement is achieved while maintaining a comparable precision to existing approaches.

Implicit Neural Representation (INR) has emerged as a powerful tool for encoding discrete signals into continuous, differentiable functions using neural networks. However, these models often have an unfortunate reliance on monolithic architectures to represent high-dimensional data, leading to prohibitive computational costs as dimensionality grows. We propose F-INR, a framework that reformulates INR learning through functional tensor decomposition, breaking down high-dimensional tasks into lightweight, axis-specific sub-networks. Each sub-network learns a low-dimensional data component (e.g., spatial or temporal). Then, we combine these components via tensor operations, reducing forward pass complexity while improving accuracy through specialized learning. F-INR is modular and, therefore, architecture-agnostic, compatible with MLPs, SIREN, WIRE, or other state-of-the-art INR architecture. It is also decomposition-agnostic, supporting CP, TT, and Tucker modes with user-defined rank for speed-accuracy control. In our experiments, F-INR trains 100times faster than existing approaches on video tasks while achieving higher fidelity (+3.4 dB PSNR). Similar gains hold for image compression, physics simulations, and 3D geometry reconstruction. Through this, F-INR offers a new scalable, flexible solution for high-dimensional signal modeling.

Universal source separation targets at separating the audio sources of an arbitrary mix, removing the constraint to operate on a specific domain like speech or music. Yet, the potential of universal source separation is limited because most existing works focus on mixes with predominantly sound events, and small training datasets also limit its potential for supervised learning. Here, we study a single general audio source separation (GASS) model trained to separate speech, music, and sound events in a supervised fashion with a large-scale dataset. We assess GASS models on a diverse set of tasks. Our strong in-distribution results show the feasibility of GASS models, and the competitive out-of-distribution performance in sound event and speech separation shows its generalization abilities. Yet, it is challenging for GASS models to generalize for separating out-of-distribution cinematic and music content. We also fine-tune GASS models on each dataset and consistently outperform the ones without pre-training. All fine-tuned models (except the music separation one) obtain state-of-the-art results in their respective benchmarks.

In a range of recent works, object-centric architectures have been shown to be suitable for unsupervised scene decomposition in the vision domain. Inspired by these methods we present AudioSlots, a slot-centric generative model for blind source separation in the audio domain. AudioSlots is built using permutation-equivariant encoder and decoder networks. The encoder network based on the Transformer architecture learns to map a mixed audio spectrogram to an unordered set of independent source embeddings. The spatial broadcast decoder network learns to generate the source spectrograms from the source embeddings. We train the model in an end-to-end manner using a permutation invariant loss function. Our results on Libri2Mix speech separation constitute a proof of concept that this approach shows promise. We discuss the results and limitations of our approach in detail, and further outline potential ways to overcome the limitations and directions for future work.

Implicitly defined, continuous, differentiable signal representations parameterized by neural networks have emerged as a powerful paradigm, offering many possible benefits over conventional representations. However, current network architectures for such implicit neural representations are incapable of modeling signals with fine detail, and fail to represent a signal's spatial and temporal derivatives, despite the fact that these are essential to many physical signals defined implicitly as the solution to partial differential equations. We propose to leverage periodic activation functions for implicit neural representations and demonstrate that these networks, dubbed sinusoidal representation networks or Sirens, are ideally suited for representing complex natural signals and their derivatives. We analyze Siren activation statistics to propose a principled initialization scheme and demonstrate the representation of images, wavefields, video, sound, and their derivatives. Further, we show how Sirens can be leveraged to solve challenging boundary value problems, such as particular Eikonal equations (yielding signed distance functions), the Poisson equation, and the Helmholtz and wave equations. Lastly, we combine Sirens with hypernetworks to learn priors over the space of Siren functions.

This paper introduces WaveGrad, a conditional model for waveform generation which estimates gradients of the data density. The model is built on prior work on score matching and diffusion probabilistic models. It starts from a Gaussian white noise signal and iteratively refines the signal via a gradient-based sampler conditioned on the mel-spectrogram. WaveGrad offers a natural way to trade inference speed for sample quality by adjusting the number of refinement steps, and bridges the gap between non-autoregressive and autoregressive models in terms of audio quality. We find that it can generate high fidelity audio samples using as few as six iterations. Experiments reveal WaveGrad to generate high fidelity audio, outperforming adversarial non-autoregressive baselines and matching a strong likelihood-based autoregressive baseline using fewer sequential operations. Audio samples are available at https://wavegrad.github.io/.

Pre-trained foundation models have demonstrated remarkable success in vision and language, yet their potential for general machine signal modeling-covering acoustic, vibration, and other industrial sensor data-remains under-explored. Existing approach using sub-band-based encoders has achieved competitive results but are limited by fixed input lengths, and the absence of explicit frequency positional encoding. In this work, we propose a novel foundation model that integrates an advanced band-split architecture with relative frequency positional embeddings, enabling precise spectral localization across arbitrary sampling configurations. The model supports inputs of arbitrary length without padding or segmentation, producing a concise embedding that retains both temporal and spectral fidelity. We evaluate our method on SIREN (https://github.com/yucongzh/SIREN), a newly introduced large-scale benchmark for machine signal encoding that unifies multiple datasets, including all DCASE task 2 challenges (2020-2025) and widely-used industrial signal corpora. Experimental results demonstrate consistent state-of-the-art performance in anomaly detection and fault identification, confirming the effectiveness and generalization capability of the proposed model. We open-sourced ECHO on https://github.com/yucongzh/ECHO.

We study the computational limits of Low-Rank Adaptation (LoRA) update for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient computation of LoRA adaptation leads to possible algorithmic speedup. This allows us to (i) identify a phase transition behavior and (ii) prove the existence of nearly linear algorithms by controlling the LoRA update computation term by term, assuming the Strong Exponential Time Hypothesis (SETH). For the former, we identify a sharp transition in the efficiency of all possible rank-r LoRA update algorithms for transformers, based on specific norms resulting from the multiplications of the input sequence X, pretrained weights W^star, and adapter matrices alpha B A / r. Specifically, we derive a shared upper bound threshold for such norms and show that efficient (sub-quadratic) approximation algorithms of LoRA exist only below this threshold. For the latter, we prove the existence of nearly linear approximation algorithms for LoRA adaptation by utilizing the hierarchical low-rank structures of LoRA gradients and approximating the gradients with a series of chained low-rank approximations. To showcase our theory, we consider two practical scenarios: partial (e.g., only W_V and W_Q) and full adaptations (e.g., W_Q, W_V, and W_K) of weights in attention heads.

Iterative algorithms based on thresholding, feedback and null space tuning (NST+HT+FB) for sparse signal recovery are exceedingly effective and fast, particularly for large scale problems. The core algorithm is shown to converge in finitely many steps under a (preconditioned) restricted isometry condition. In this paper, we present a new perspective to analyze the algorithm, which turns out that the efficiency of the algorithm can be further elaborated by an estimate of the number of iterations for the guaranteed convergence. The convergence condition of NST+HT+FB is also improved. Moreover, an adaptive scheme (AdptNST+HT+FB) without the knowledge of the sparsity level is proposed with its convergence guarantee. The number of iterations for the finite step of convergence of the AdptNST+HT+FB scheme is also derived. It is further shown that the number of iterations can be significantly reduced by exploiting the structure of the specific sparse signal or the random measurement matrix.

We provide a new LLM-compression solution via SVD, unlocking new possibilities for LLM compression beyond quantization and pruning. We point out that the optimal use of SVD lies in truncating activations, rather than merely using activations as an optimization distance. Building on this principle, we address three critical challenges in SVD-based LLM compression: including (1) How can we determine the optimal activation truncation position for each weight matrix in LLMs? (2) How can we efficiently reconstruct the weight matrices based on truncated activations? (3) How can we address the inherent "injection" nature that results in the information loss of the SVD? We propose Dobi-SVD, which establishes a new, principled approach to SVD-based LLM compression.

We quantify the upper bound on the size of the implicit neural representation (INR) model from a digital perspective. The upper bound of the model size increases exponentially as the required bit-precision increases. To this end, we present a bit-plane decomposition method that makes INR predict bit-planes, producing the same effect as reducing the upper bound of the model size. We validate our hypothesis that reducing the upper bound leads to faster convergence with constant model size. Our method achieves lossless representation in 2D image and audio fitting, even for high bit-depth signals, such as 16-bit, which was previously unachievable. We pioneered the presence of bit bias, which INR prioritizes as the most significant bit (MSB). We expand the application of the INR task to bit depth expansion, lossless image compression, and extreme network quantization. Our source code is available at https://github.com/WooKyoungHan/LosslessINR

Universal sound separation aims to extract clean audio tracks corresponding to distinct events from mixed audio, which is critical for artificial auditory perception. However, current methods heavily rely on artificially mixed audio for training, which limits their ability to generalize to naturally mixed audio collected in real-world environments. To overcome this limitation, we propose ClearSep, an innovative framework that employs a data engine to decompose complex naturally mixed audio into multiple independent tracks, thereby allowing effective sound separation in real-world scenarios. We introduce two remix-based evaluation metrics to quantitatively assess separation quality and use these metrics as thresholds to iteratively apply the data engine alongside model training, progressively optimizing separation performance. In addition, we propose a series of training strategies tailored to these separated independent tracks to make the best use of them. Extensive experiments demonstrate that ClearSep achieves state-of-the-art performance across multiple sound separation tasks, highlighting its potential for advancing sound separation in natural audio scenarios. For more examples and detailed results, please visit our demo page at https://clearsep.github.io.

Deep neural network based methods have been successfully applied to music source separation. They typically learn a mapping from a mixture spectrogram to a set of source spectrograms, all with magnitudes only. This approach has several limitations: 1) its incorrect phase reconstruction degrades the performance, 2) it limits the magnitude of masks between 0 and 1 while we observe that 22% of time-frequency bins have ideal ratio mask values of over~1 in a popular dataset, MUSDB18, 3) its potential on very deep architectures is under-explored. Our proposed system is designed to overcome these. First, we propose to estimate phases by estimating complex ideal ratio masks (cIRMs) where we decouple the estimation of cIRMs into magnitude and phase estimations. Second, we extend the separation method to effectively allow the magnitude of the mask to be larger than 1. Finally, we propose a residual UNet architecture with up to 143 layers. Our proposed system achieves a state-of-the-art MSS result on the MUSDB18 dataset, especially, a SDR of 8.98~dB on vocals, outperforming the previous best performance of 7.24~dB. The source code is available at: https://github.com/bytedance/music_source_separation

Sparse Autoencoders (SAEs) have proven to be powerful tools for interpreting neural networks by decomposing hidden representations into disentangled, interpretable features via sparsity constraints. However, conventional SAEs are constrained by the fixed sparsity level chosen during training; meeting different sparsity requirements therefore demands separate models and increases the computational footprint during both training and evaluation. We introduce a novel training objective, HierarchicalTopK, which trains a single SAE to optimise reconstructions across multiple sparsity levels simultaneously. Experiments with Gemma-2 2B demonstrate that our approach achieves Pareto-optimal trade-offs between sparsity and explained variance, outperforming traditional SAEs trained at individual sparsity levels. Further analysis shows that HierarchicalTopK preserves high interpretability scores even at higher sparsity. The proposed objective thus closes an important gap between flexibility and interpretability in SAE design.

We demonstrate the efficacy of using intermediate representations from a single foundation model to enhance various music downstream tasks. We introduce SoniDo , a music foundation model (MFM) designed to extract hierarchical features from target music samples. By leveraging hierarchical intermediate features, SoniDo constrains the information granularity, leading to improved performance across various downstream tasks including both understanding and generative tasks. We specifically evaluated this approach on representative tasks such as music tagging, music transcription, music source separation, and music mixing. Our results reveal that the features extracted from foundation models provide valuable enhancements in training downstream task models. This highlights the capability of using features extracted from music foundation models as a booster for downstream tasks. Our approach not only benefits existing task-specific models but also supports music downstream tasks constrained by data scarcity. This paves the way for more effective and accessible music processing solutions.

Autoregressive models have achieved impressive results over a wide range of domains in terms of generation quality and downstream task performance. In the continuous domain, a key factor behind this success is the usage of quantized latent spaces (e.g., obtained via VQ-VAE autoencoders), which allow for dimensionality reduction and faster inference times. However, using existing pre-trained models to perform new non-trivial tasks is difficult since it requires additional fine-tuning or extensive training to elicit prompting. This paper introduces LASS as a way to perform vector-quantized Latent Autoregressive Source Separation (i.e., de-mixing an input signal into its constituent sources) without requiring additional gradient-based optimization or modifications of existing models. Our separation method relies on the Bayesian formulation in which the autoregressive models are the priors, and a discrete (non-parametric) likelihood function is constructed by performing frequency counts over latent sums of addend tokens. We test our method on images and audio with several sampling strategies (e.g., ancestral, beam search) showing competitive results with existing approaches in terms of separation quality while offering at the same time significant speedups in terms of inference time and scalability to higher dimensional data.

Recently, using diffusion models for zero-shot image restoration (IR) has become a new hot paradigm. This type of method only needs to use the pre-trained off-the-shelf diffusion models, without any finetuning, and can directly handle various IR tasks. The upper limit of the restoration performance depends on the pre-trained diffusion models, which are in rapid evolution. However, current methods only discuss how to deal with fixed-size images, but dealing with images of arbitrary sizes is very important for practical applications. This paper focuses on how to use those diffusion-based zero-shot IR methods to deal with any size while maintaining the excellent characteristics of zero-shot. A simple way to solve arbitrary size is to divide it into fixed-size patches and solve each patch independently. But this may yield significant artifacts since it neither considers the global semantics of all patches nor the local information of adjacent patches. Inspired by the Range-Null space Decomposition, we propose the Mask-Shift Restoration to address local incoherence and propose the Hierarchical Restoration to alleviate out-of-domain issues. Our simple, parameter-free approaches can be used not only for image restoration but also for image generation of unlimited sizes, with the potential to be a general tool for diffusion models. Code: https://github.com/wyhuai/DDNM/tree/main/hq_demo

Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way that couples spatial and spectral features of the signal that is not obvious in the usual discrete representation, paving the way for continuous signal processing and machine learning approaches that were not previously possible. Although INRs using sinusoidal activation functions have been studied in terms of Fourier theory, recent works have shown the advantage of using wavelets instead of sinusoids as activation functions, due to their ability to simultaneously localize in both frequency and space. In this work, we approach such INRs and demonstrate how they resolve high-frequency features of signals from coarse approximations done in the first layer of the MLP. This leads to multiple prescriptions for the design of INR architectures, including the use of complex wavelets, decoupling of low and band-pass approximations, and initialization schemes based on the singularities of the desired signal.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide better global temporal encodings using hyperdimensional computing (HDC) mechanisms. HDC (also known as Vector Symbolic Architectures, VSA) is a general method to explicitly represent and process information in high-dimensional vectors. It has previously been used successfully in combination with deep neural networks and other signal processing algorithms. We argue that the internal high-dimensional representation of MiniROCKET is well suited to be complemented by the algebra of HDC. This leads to a more general formulation, HDC-MiniROCKET, where the original algorithm is only a special case. We will discuss and demonstrate that HDC-MiniROCKET can systematically overcome catastrophic failures of MiniROCKET on simple synthetic datasets. These results are confirmed by experiments on the 128 datasets from the UCR time series classification benchmark. The extension with HDC can achieve considerably better results on datasets with high temporal dependence without increasing the computational effort for inference.

We study the sparse recovery problem with an underdetermined linear system characterized by a Kronecker-structured dictionary and a Kronecker-supported sparse vector. We cast this problem into the sparse Bayesian learning (SBL) framework and rely on the expectation-maximization method for a solution. To this end, we model the Kronecker-structured support with a hierarchical Gaussian prior distribution parameterized by a Kronecker-structured hyperparameter, leading to a non-convex optimization problem. The optimization problem is solved using the alternating minimization (AM) method and a singular value decomposition (SVD)-based method, resulting in two algorithms. Further, we analytically guarantee that the AM-based method converges to the stationary point of the SBL cost function. The SVD-based method, though it adopts approximations, is empirically shown to be more efficient and accurate. We then apply our algorithm to estimate the uplink wireless channel in an intelligent reflecting surface-aided MIMO system and extend the AM-based algorithm to address block sparsity in the channel. We also study the SBL cost to show that the minima of the cost function are achieved at sparse solutions and that incorporating the Kronecker structure reduces the number of local minima of the SBL cost function. Our numerical results demonstrate the effectiveness of our algorithms compared to the state-of-the-art.

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

In this report, we present our award-winning solutions for the Music Demixing Track of Sound Demixing Challenge 2023. First, we propose TFC-TDF-UNet v3, a time-efficient music source separation model that achieves state-of-the-art results on the MUSDB benchmark. We then give full details regarding our solutions for each Leaderboard, including a loss masking approach for noise-robust training. Code for reproducing model training and final submissions is available at github.com/kuielab/sdx23.

With the growth of neural network size, model compression has attracted increasing interest in recent research. As one of the most common techniques, pruning has been studied for a long time. By exploiting the structured sparsity of the neural network, existing methods can prune neurons instead of individual weights. However, in most existing pruning methods, surviving neurons are randomly connected in the neural network without any structure, and the non-zero weights within each neuron are also randomly distributed. Such irregular sparse structure can cause very high control overhead and irregular memory access for the hardware and even increase the neural network computational complexity. In this paper, we propose a three-layer hierarchical prior to promote a more regular sparse structure during pruning. The proposed three-layer hierarchical prior can achieve per-neuron weight-level structured sparsity and neuron-level structured sparsity. We derive an efficient Turbo-variational Bayesian inferencing (Turbo-VBI) algorithm to solve the resulting model compression problem with the proposed prior. The proposed Turbo-VBI algorithm has low complexity and can support more general priors than existing model compression algorithms. Simulation results show that our proposed algorithm can promote a more regular structure in the pruned neural networks while achieving even better performance in terms of compression rate and inferencing accuracy compared with the baselines.

Diffusion models have demonstrated remarkable success in generative tasks, yet their iterative denoising process results in slow inference, limiting their practicality. While existing acceleration methods exploit the well-known U-shaped similarity pattern between adjacent steps through caching mechanisms, they lack theoretical foundation and rely on simplistic computation reuse, often leading to performance degradation. In this work, we provide a theoretical understanding by analyzing the denoising process through the second-order Adams-Bashforth method, revealing a linear relationship between the outputs of consecutive steps. This analysis explains why the outputs of adjacent steps exhibit a U-shaped pattern. Furthermore, extending Adams-Bashforth method to higher order, we propose a novel caching-based acceleration approach for diffusion models, instead of directly reusing cached results, with a truncation error bound of only \(O(h^k)\) where h is the step size. Extensive validation across diverse image and video diffusion models (including HunyuanVideo and FLUX.1-dev) with various schedulers demonstrates our method's effectiveness in achieving nearly 3times speedup while maintaining original performance levels, offering a practical real-time solution without compromising generation quality.

Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive (top-down) algorithms recursively partition the nodes into two communities, until a stopping rule indicates that no further split is needed. In contrast, agglomerative (bottom-up) algorithms first identify the smallest community structure and then repeatedly merge the communities using a linkage method. In this article, we establish theoretical guarantees for the recovery of the hierarchical tree and community structure of a Hierarchical Stochastic Block Model by a bottom-up algorithm. We also establish that this bottom-up algorithm attains the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy. Notably, these recovery conditions are less restrictive compared to those existing for top-down algorithms. This shows that bottom-up algorithms extend the feasible region for achieving exact recovery at intermediate levels. Numerical experiments on both synthetic and real data sets confirm the superiority of bottom-up algorithms over top-down algorithms. We also observe that top-down algorithms can produce dendrograms with inversions. These findings contribute to a better understanding of hierarchical clustering techniques and their applications in network analysis.

In spite of their huge success, transformer models remain difficult to scale in depth. In this work, we develop a unified signal propagation theory and provide formulae that govern the moments of the forward and backward signal through the transformer model. Our framework can be used to understand and mitigate vanishing/exploding gradients, rank collapse, and instability associated with high attention scores. We also propose DeepScaleLM, an initialization and scaling scheme that conserves unit output/gradient moments throughout the model, enabling the training of very deep models with 100s of layers. We find that transformer models could be much deeper - our deep models with fewer parameters outperform shallow models in Language Modeling, Speech Translation, and Image Classification, across Encoder-only, Decoder-only and Encoder-Decoder variants, for both Pre-LN and Post-LN transformers, for multiple datasets and model sizes. These improvements also translate into improved performance on downstream Question Answering tasks and improved robustness for image classification.

Source separation models either work on the spectrogram or waveform domain. In this work, we show how to perform end-to-end hybrid source separation, letting the model decide which domain is best suited for each source, and even combining both. The proposed hybrid version of the Demucs architecture won the Music Demixing Challenge 2021 organized by Sony. This architecture also comes with additional improvements, such as compressed residual branches, local attention or singular value regularization. Overall, a 1.4 dB improvement of the Signal-To-Distortion (SDR) was observed across all sources as measured on the MusDB HQ dataset, an improvement confirmed by human subjective evaluation, with an overall quality rated at 2.83 out of 5 (2.36 for the non hybrid Demucs), and absence of contamination at 3.04 (against 2.37 for the non hybrid Demucs and 2.44 for the second ranking model submitted at the competition).

We introduce a hierarchical filtering procedure for generative models of sequences on trees, enabling control over the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformer architectures can implement the optimal Belief Propagation algorithm on both root classification and masked language modeling tasks. Correlations at larger distances corresponding to increasing layers of the hierarchy are sequentially included as the network is trained. We analyze how the transformer layers succeed by focusing on attention maps from models trained with varying degrees of filtering. These attention maps show clear evidence for iterative hierarchical reconstruction of correlations, and we can relate these observations to a plausible implementation of the exact inference algorithm for the network sizes considered.

We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving graph spectra, which are also computationally expensive due to the temporal aspect along with the graph vertex domain. We view the problem as an optimization over the Laplacian of the continuous time dynamic graph. Additionally, we propose pseudo-spectrum relaxations that decompose the transformation process, making it highly computationally efficient. The EFT method adeptly captures the evolving graph's structural and positional properties, making it effective for downstream tasks on evolving graphs. Hence, as a reference implementation, we develop a simple neural model induced with EFT for capturing evolving graph spectra. We empirically validate our theoretical findings on a number of large-scale and standard temporal graph benchmarks and demonstrate that our model achieves state-of-the-art performance.

As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit intrinsic correlations over time. Capitalizing on this, we introduce Correlation Mode Decomposition (CMD). This algorithm clusters the parameter space into groups, termed modes, that display synchronized behavior across epochs. This enables CMD to efficiently represent the training dynamics of complex networks, like ResNets and Transformers, using only a few modes. Moreover, test set generalization is enhanced. We introduce an efficient CMD variant, designed to run concurrently with training. Our experiments indicate that CMD surpasses the state-of-the-art method for compactly modeled dynamics on image classification. Our modeling can improve training efficiency and lower communication overhead, as shown by our preliminary experiments in the context of federated learning.

Denoising diffusion models enable conditional generation and density modeling of complex relationships like images and text. However, the nature of the learned relationships is opaque making it difficult to understand precisely what relationships between words and parts of an image are captured, or to predict the effect of an intervention. We illuminate the fine-grained relationships learned by diffusion models by noticing a precise relationship between diffusion and information decomposition. Exact expressions for mutual information and conditional mutual information can be written in terms of the denoising model. Furthermore, pointwise estimates can be easily estimated as well, allowing us to ask questions about the relationships between specific images and captions. Decomposing information even further to understand which variables in a high-dimensional space carry information is a long-standing problem. For diffusion models, we show that a natural non-negative decomposition of mutual information emerges, allowing us to quantify informative relationships between words and pixels in an image. We exploit these new relations to measure the compositional understanding of diffusion models, to do unsupervised localization of objects in images, and to measure effects when selectively editing images through prompt interventions.

Diffusion models are rising as a powerful solution for high-fidelity image generation, which exceeds GANs in quality in many circumstances. However, their slow training and inference speed is a huge bottleneck, blocking them from being used in real-time applications. A recent DiffusionGAN method significantly decreases the models' running time by reducing the number of sampling steps from thousands to several, but their speeds still largely lag behind the GAN counterparts. This paper aims to reduce the speed gap by proposing a novel wavelet-based diffusion scheme. We extract low-and-high frequency components from both image and feature levels via wavelet decomposition and adaptively handle these components for faster processing while maintaining good generation quality. Furthermore, we propose to use a reconstruction term, which effectively boosts the model training convergence. Experimental results on CelebA-HQ, CIFAR-10, LSUN-Church, and STL-10 datasets prove our solution is a stepping-stone to offering real-time and high-fidelity diffusion models. Our code and pre-trained checkpoints are available at https://github.com/VinAIResearch/WaveDiff.git.

Given the recent advances in music source separation and automatic mixing, removing audio effects in music tracks is a meaningful step toward developing an automated remixing system. This paper focuses on removing distortion audio effects applied to guitar tracks in music production. We explore whether effect removal can be solved by neural networks designed for source separation and audio effect modeling. Our approach proves particularly effective for effects that mix the processed and clean signals. The models achieve better quality and significantly faster inference compared to state-of-the-art solutions based on sparse optimization. We demonstrate that the models are suitable not only for declipping but also for other types of distortion effects. By discussing the results, we stress the usefulness of multiple evaluation metrics to assess different aspects of reconstruction in distortion effect removal.

Mixture of Experts (MoE) LLMs face significant obstacles due to their massive parameter scale, which imposes memory, storage, and deployment challenges. Although recent expert merging methods promise greater efficiency by consolidating multiple experts, they are fundamentally hindered by parameter conflicts arising from expert specialization. In this paper, we present Sub-MoE, a novel MoE compression framework via Subspace Expert Merging. Our key insight is to perform joint Singular Value Decomposition (SVD) on concatenated expert weights, reducing conflicting parameters by extracting shared U-matrices while enabling effective merging of the expert-specific V components. Specifically, Sub-MoE consists of two innovative phases: (1) Adaptive Expert Clustering, which groups functionally coherent experts via K-means clustering based on cosine similarity of expert outputs; and (2) Subspace Expert Merging, which first enforces Experts Union Decomposition to derive the shared U-matrix across experts in the same group, then pursues frequency-based merging for individual V-matrices, and finalizes expert reconstruction using the merged V-matrix. In this way, we align and fuse experts in a shared subspace, and can be extended with intra-expert compression for further inference optimization. Extensive experiments on Mixtral, DeepSeek, and Qwen-1.5|3 MoE LLMs demonstrate that our Sub-MoE significantly outperforms existing expert pruning and merging methods. Notably, our Sub-MoE maintains 96\%|86\% of original performance with 25\%|50\% expert reduction on Mixtral-8x7B in zero-shot benchmarks. Code will be released at https://github.com/lliai/MoERazor.

Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the derivation of the reduced problem, but are limited to linear data compression for which the reduced solution is sought as a linear combination of spatial modes. Nonlinear data compression must be used when the solution manifold is not embedded in a low-dimensional subspace. Early methods involve piecewise linear data compression, by constructing a dictionary of reduced-order models tailored to a partition of the solution manifold. In this work, we introduce the concept of optimal partition of the solution manifold in terms of normalized Kolmogorov widths, and prove that the optimal partitions can be found by means of a representative-based clustering algorithm using the sine dissimilarity measure on the solution manifold.

Radio frequency (RF) signal mapping, which is the process of analyzing and predicting the RF signal strength and distribution across specific areas, is crucial for cellular network planning and deployment. Traditional approaches to RF signal mapping rely on statistical models constructed based on measurement data, which offer low complexity but often lack accuracy, or ray tracing tools, which provide enhanced precision for the target area but suffer from increased computational complexity. Recently, machine learning (ML) has emerged as a data-driven method for modeling RF signal propagation, which leverages models trained on synthetic datasets to perform RF signal mapping in "unseen" areas. In this paper, we present Geo2SigMap, an ML-based framework for efficient and high-fidelity RF signal mapping using geographic databases. First, we develop an automated framework that seamlessly integrates three open-source tools: OpenStreetMap (geographic databases), Blender (computer graphics), and Sionna (ray tracing), enabling the efficient generation of large-scale 3D building maps and ray tracing models. Second, we propose a cascaded U-Net model, which is pre-trained on synthetic datasets and employed to generate detailed RF signal maps, leveraging environmental information and sparse measurement data. Finally, we evaluate the performance of Geo2SigMap via a real-world measurement campaign, where three types of user equipment (UE) collect over 45,000 data points related to cellular information from six LTE cells operating in the citizens broadband radio service (CBRS) band. Our results show that Geo2SigMap achieves an average root-mean-square-error (RMSE) of 6.04 dB for predicting the reference signal received power (RSRP) at the UE, representing an average RMSE improvement of 3.59 dB compared to existing methods.

Cinematic audio source separation is a relatively new subtask of audio source separation, with the aim of extracting the dialogue, music, and effects stems from their mixture. In this work, we developed a model generalizing the Bandsplit RNN for any complete or overcomplete partitions of the frequency axis. Psychoacoustically motivated frequency scales were used to inform the band definitions which are now defined with redundancy for more reliable feature extraction. A loss function motivated by the signal-to-noise ratio and the sparsity-promoting property of the 1-norm was proposed. We additionally exploit the information-sharing property of a common-encoder setup to reduce computational complexity during both training and inference, improve separation performance for hard-to-generalize classes of sounds, and allow flexibility during inference time with detachable decoders. Our best model sets the state of the art on the Divide and Remaster dataset with performance above the ideal ratio mask for the dialogue stem.

We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior knowledge of the unknown signal is helpful for accurate recovery. Motivated by the power of score-based generative models (SGM, also known as diffusion models) in capturing the rich structure of natural signals beyond simple sparsity, we propose an unsupervised data-driven approach called quantized compressed sensing with SGM (QCS-SGM), where the prior distribution is modeled by a pre-trained SGM. To perform posterior sampling, an annealed pseudo-likelihood score called noise perturbed pseudo-likelihood score is introduced and combined with the prior score of SGM. The proposed QCS-SGM applies to an arbitrary number of quantization bits. Experiments on a variety of baseline datasets demonstrate that the proposed QCS-SGM significantly outperforms existing state-of-the-art algorithms by a large margin for both in-distribution and out-of-distribution samples. Moreover, as a posterior sampling method, QCS-SGM can be easily used to obtain confidence intervals or uncertainty estimates of the reconstructed results. The code is available at https://github.com/mengxiangming/QCS-SGM.

Developing architectures suitable for modeling raw audio is a challenging problem due to the high sampling rates of audio waveforms. Standard sequence modeling approaches like RNNs and CNNs have previously been tailored to fit the demands of audio, but the resultant architectures make undesirable computational tradeoffs and struggle to model waveforms effectively. We propose SaShiMi, a new multi-scale architecture for waveform modeling built around the recently introduced S4 model for long sequence modeling. We identify that S4 can be unstable during autoregressive generation, and provide a simple improvement to its parameterization by drawing connections to Hurwitz matrices. SaShiMi yields state-of-the-art performance for unconditional waveform generation in the autoregressive setting. Additionally, SaShiMi improves non-autoregressive generation performance when used as the backbone architecture for a diffusion model. Compared to prior architectures in the autoregressive generation setting, SaShiMi generates piano and speech waveforms which humans find more musical and coherent respectively, e.g. 2x better mean opinion scores than WaveNet on an unconditional speech generation task. On a music generation task, SaShiMi outperforms WaveNet on density estimation and speed at both training and inference even when using 3x fewer parameters. Code can be found at https://github.com/HazyResearch/state-spaces and samples at https://hazyresearch.stanford.edu/sashimi-examples.

Efficiently compressing high-dimensional audio signals into a compact and informative latent space is crucial for various tasks, including generative modeling and music information retrieval (MIR). Existing audio autoencoders, however, often struggle to achieve high compression ratios while preserving audio fidelity and facilitating efficient downstream applications. We introduce Music2Latent2, a novel audio autoencoder that addresses these limitations by leveraging consistency models and a novel approach to representation learning based on unordered latent embeddings, which we call summary embeddings. Unlike conventional methods that encode local audio features into ordered sequences, Music2Latent2 compresses audio signals into sets of summary embeddings, where each embedding can capture distinct global features of the input sample. This enables to achieve higher reconstruction quality at the same compression ratio. To handle arbitrary audio lengths, Music2Latent2 employs an autoregressive consistency model trained on two consecutive audio chunks with causal masking, ensuring coherent reconstruction across segment boundaries. Additionally, we propose a novel two-step decoding procedure that leverages the denoising capabilities of consistency models to further refine the generated audio at no additional cost. Our experiments demonstrate that Music2Latent2 outperforms existing continuous audio autoencoders regarding audio quality and performance on downstream tasks. Music2Latent2 paves the way for new possibilities in audio compression.

This paper introduces SINGA:PURA, a strongly labelled polyphonic urban sound dataset with spatiotemporal context. The data were collected via several recording units deployed across Singapore as a part of a wireless acoustic sensor network. These recordings were made as part of a project to identify and mitigate noise sources in Singapore, but also possess a wider applicability to sound event detection, classification, and localization. This paper introduces an accompanying hierarchical label taxonomy, which has been designed to be compatible with other existing datasets for urban sound tagging while also able to capture sound events unique to the Singaporean context. This paper details the data collection, annotation, and processing methodologies for the creation of the dataset. We further perform exploratory data analysis and include the performance of a baseline model on the dataset as a benchmark.

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

Recently, the end-to-end approach that learns hierarchical representations from raw data using deep convolutional neural networks has been successfully explored in the image, text and speech domains. This approach was applied to musical signals as well but has been not fully explored yet. To this end, we propose sample-level deep convolutional neural networks which learn representations from very small grains of waveforms (e.g. 2 or 3 samples) beyond typical frame-level input representations. Our experiments show how deep architectures with sample-level filters improve the accuracy in music auto-tagging and they provide results comparable to previous state-of-the-art performances for the Magnatagatune dataset and Million Song Dataset. In addition, we visualize filters learned in a sample-level DCNN in each layer to identify hierarchically learned features and show that they are sensitive to log-scaled frequency along layer, such as mel-frequency spectrogram that is widely used in music classification systems.

We introduce PixelPlayer, a system that, by leveraging large amounts of unlabeled videos, learns to locate image regions which produce sounds and separate the input sounds into a set of components that represents the sound from each pixel. Our approach capitalizes on the natural synchronization of the visual and audio modalities to learn models that jointly parse sounds and images, without requiring additional manual supervision. Experimental results on a newly collected MUSIC dataset show that our proposed Mix-and-Separate framework outperforms several baselines on source separation. Qualitative results suggest our model learns to ground sounds in vision, enabling applications such as independently adjusting the volume of sound sources.

We present a novel global compression framework for deep neural networks that automatically analyzes each layer to identify the optimal per-layer compression ratio, while simultaneously achieving the desired overall compression. Our algorithm hinges on the idea of compressing each convolutional (or fully-connected) layer by slicing its channels into multiple groups and decomposing each group via low-rank decomposition. At the core of our algorithm is the derivation of layer-wise error bounds from the Eckart Young Mirsky theorem. We then leverage these bounds to frame the compression problem as an optimization problem where we wish to minimize the maximum compression error across layers and propose an efficient algorithm towards a solution. Our experiments indicate that our method outperforms existing low-rank compression approaches across a wide range of networks and data sets. We believe that our results open up new avenues for future research into the global performance-size trade-offs of modern neural networks. Our code is available at https://github.com/lucaslie/torchprune.

Recently, universal waveform generation tasks have been investigated conditioned on various out-of-distribution scenarios. Although GAN-based methods have shown their strength in fast waveform generation, they are vulnerable to train-inference mismatch scenarios such as two-stage text-to-speech. Meanwhile, diffusion-based models have shown their powerful generative performance in other domains; however, they stay out of the limelight due to slow inference speed in waveform generation tasks. Above all, there is no generator architecture that can explicitly disentangle the natural periodic features of high-resolution waveform signals. In this paper, we propose PeriodWave, a novel universal waveform generation model. First, we introduce a period-aware flow matching estimator that can capture the periodic features of the waveform signal when estimating the vector fields. Additionally, we utilize a multi-period estimator that avoids overlaps to capture different periodic features of waveform signals. Although increasing the number of periods can improve the performance significantly, this requires more computational costs. To reduce this issue, we also propose a single period-conditional universal estimator that can feed-forward parallel by period-wise batch inference. Additionally, we utilize discrete wavelet transform to losslessly disentangle the frequency information of waveform signals for high-frequency modeling, and introduce FreeU to reduce the high-frequency noise for waveform generation. The experimental results demonstrated that our model outperforms the previous models both in Mel-spectrogram reconstruction and text-to-speech tasks. All source code will be available at https://github.com/sh-lee-prml/PeriodWave.

We present AERO, a audio super-resolution model that processes speech and music signals in the spectral domain. AERO is based on an encoder-decoder architecture with U-Net like skip connections. We optimize the model using both time and frequency domain loss functions. Specifically, we consider a set of reconstruction losses together with perceptual ones in the form of adversarial and feature discriminator loss functions. To better handle phase information the proposed method operates over the complex-valued spectrogram using two separate channels. Unlike prior work which mainly considers low and high frequency concatenation for audio super-resolution, the proposed method directly predicts the full frequency range. We demonstrate high performance across a wide range of sample rates considering both speech and music. AERO outperforms the evaluated baselines considering Log-Spectral Distance, ViSQOL, and the subjective MUSHRA test. Audio samples and code are available at https://pages.cs.huji.ac.il/adiyoss-lab/aero

Perceiving a scene most fully requires all the senses. Yet modeling how objects look and sound is challenging: most natural scenes and events contain multiple objects, and the audio track mixes all the sound sources together. We propose to learn audio-visual object models from unlabeled video, then exploit the visual context to perform audio source separation in novel videos. Our approach relies on a deep multi-instance multi-label learning framework to disentangle the audio frequency bases that map to individual visual objects, even without observing/hearing those objects in isolation. We show how the recovered disentangled bases can be used to guide audio source separation to obtain better-separated, object-level sounds. Our work is the first to learn audio source separation from large-scale "in the wild" videos containing multiple audio sources per video. We obtain state-of-the-art results on visually-aided audio source separation and audio denoising. Our video results: http://vision.cs.utexas.edu/projects/separating_object_sounds/

In this study, we examine the representation learning abilities of Denoising Diffusion Models (DDM) that were originally purposed for image generation. Our philosophy is to deconstruct a DDM, gradually transforming it into a classical Denoising Autoencoder (DAE). This deconstructive procedure allows us to explore how various components of modern DDMs influence self-supervised representation learning. We observe that only a very few modern components are critical for learning good representations, while many others are nonessential. Our study ultimately arrives at an approach that is highly simplified and to a large extent resembles a classical DAE. We hope our study will rekindle interest in a family of classical methods within the realm of modern self-supervised learning.

Low Rank Decomposition of matrix - splitting a large matrix into a product of two smaller matrix offers a means for compression that reduces the parameters of a model without sparsification, and hence delivering more speedup on modern hardware. Moreover, unlike quantization, the compressed linear layers remain fully differentiable and all the parameters trainable, while being able to leverage the existing highly efficient kernels over floating point matrices. We study the potential to compress Large Language Models (LLMs) for monolingual Code generation via Low Rank Decomposition (LoRD) and observe that ranks for the linear layers in these models can be reduced by upto 39.58% with less than 1% increase in perplexity. We then use Low Rank Decomposition (LoRD) to compress StarCoder 16B to 13.2B parameter with no drop and to 12.3B with minimal drop in HumanEval Pass@1 score, in less than 10 minutes on a single A100. The compressed models speeds up inference by up to 22.35% with just a single line of change in code over huggingface's implementation with pytorch backend. Low Rank Decomposition (LoRD) models remain compatible with state of the art near-lossless quantization method such as SpQR, which allows leveraging further compression gains of quantization. Lastly, QLoRA over Low Rank Decomposition (LoRD) model further reduces memory requirements by as much as 21.2% over vanilla QLoRA while offering similar gains from parameter efficient fine tuning. Our work shows Low Rank Decomposition (LoRD) as a promising new paradigm for LLM compression.

Music is characterized by complex hierarchical structures. Developing a comprehensive model to capture these structures has been a significant challenge in the field of Music Information Retrieval (MIR). Prior research has mainly focused on addressing individual tasks for specific hierarchical levels, rather than providing a unified approach. In this paper, we introduce a versatile, all-in-one model that jointly performs beat and downbeat tracking as well as functional structure segmentation and labeling. The model leverages source-separated spectrograms as inputs and employs dilated neighborhood attentions to capture temporal long-term dependencies, along with non-dilated attentions for local instrumental dependencies. Consequently, the proposed model achieves state-of-the-art performance in all four tasks on the Harmonix Set while maintaining a relatively lower number of parameters compared to recent state-of-the-art models. Furthermore, our ablation study demonstrates that the concurrent learning of beats, downbeats, and segments can lead to enhanced performance, with each task mutually benefiting from the others.

We propose DeepASA, a one-for-all model for auditory scene analysis that performs multi-input multi-output (MIMO) source separation, dereverberation, sound event detection (SED), audio classification, and direction-of-arrival estimation (DoAE) within a unified framework. DeepASA is designed for complex auditory scenes where multiple, often similar, sound sources overlap in time and move dynamically in space. To achieve robust and consistent inference across tasks, we introduce an object-oriented processing (OOP) strategy. This approach encapsulates diverse auditory features into object-centric representations and refines them through a chain-of-inference (CoI) mechanism. The pipeline comprises a dynamic temporal kernel-based feature extractor, a transformer-based aggregator, and an object separator that yields per-object features. These features feed into multiple task-specific decoders. Our object-centric representations naturally resolve the parameter association ambiguity inherent in traditional track-wise processing. However, early-stage object separation can lead to failure in downstream ASA tasks. To address this, we implement temporal coherence matching (TCM) within the chain-of-inference, enabling multi-task fusion and iterative refinement of object features using estimated auditory parameters. We evaluate DeepASA on representative spatial audio benchmark datasets, including ASA2, MC-FUSS, and STARSS23. Experimental results show that our model achieves state-of-the-art performance across all evaluated tasks, demonstrating its effectiveness in both source separation and auditory parameter estimation under diverse spatial auditory scenes.

Low-light photography produces images with low signal-to-noise ratios due to limited photons. In such conditions, common approximations like the Gaussian noise model fall short, and many denoising techniques fail to remove noise effectively. Although deep-learning methods perform well, they require large datasets of paired images that are impractical to acquire. As a remedy, synthesizing realistic low-light noise has gained significant attention. In this paper, we investigate the ability of diffusion models to capture the complex distribution of low-light noise. We show that a naive application of conventional diffusion models is inadequate for this task and propose three key adaptations that enable high-precision noise generation without calibration or post-processing: a two-branch architecture to better model signal-dependent and signal-independent noise, the incorporation of positional information to capture fixed-pattern noise, and a tailored diffusion noise schedule. Consequently, our model enables the generation of large datasets for training low-light denoising networks, leading to state-of-the-art performance. Through comprehensive analysis, including statistical evaluation and noise decomposition, we provide deeper insights into the characteristics of the generated data.

Neural vocoders often struggle with aliasing in latent feature spaces, caused by time-domain nonlinear operations and resampling layers. Aliasing folds high-frequency components into the low-frequency range, making aliased and original frequency components indistinguishable and introducing two practical issues. First, aliasing complicates the waveform generation process, as the subsequent layers must address these aliasing effects, increasing the computational complexity. Second, it limits extrapolation performance, particularly in handling high fundamental frequencies, which degrades the perceptual quality of generated speech waveforms. This paper demonstrates that 1) time-domain nonlinear operations inevitably introduce aliasing but provide a strong inductive bias for harmonic generation, and 2) time-frequency-domain processing can achieve aliasing-free waveform synthesis but lacks the inductive bias for effective harmonic generation. Building on this insight, we propose Wavehax, an aliasing-free neural WAVEform generator that integrates 2D convolution and a HArmonic prior for reliable Complex Spectrogram estimation. Experimental results show that Wavehax achieves speech quality comparable to existing high-fidelity neural vocoders and exhibits exceptional robustness in scenarios requiring high fundamental frequency extrapolation, where aliasing effects become typically severe. Moreover, Wavehax requires less than 5% of the multiply-accumulate operations and model parameters compared to HiFi-GAN V1, while achieving over four times faster CPU inference speed.

We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of 1-bit quantization -- allow a high accuracy approximation of the underlying kernels, and the approximation error decays at least polynomially fast as the dimension of the RFFs increases. We also show that the quantized RFFs can be further compressed, yielding an excellent trade-off between memory use and accuracy. Namely, the approximation error now decays exponentially as a function of the bits used. Moreover, we empirically show by testing the performance of our methods on several machine learning tasks that our method compares favorably to other state of the art quantization methods in this context.

Most modern approaches for audio processing are opaque, in the sense that they do not provide an explanation for their decisions. For this reason, various methods have been proposed to explain the outputs generated by these models. Good explanations can result in interesting insights about the data or the model, as well as increase trust in the system. Unfortunately, evaluating the quality of explanations is far from trivial since, for most tasks, there is no clear ground truth explanation to use as reference. In this work, we propose a benchmark for time-localized explanations for audio classification models that uses time annotations of target events as a proxy for ground truth explanations. We use this benchmark to systematically optimize and compare various approaches for model-agnostic post-hoc explanation, obtaining, in some cases, close to perfect explanations. Finally, we illustrate the utility of the explanations for uncovering spurious correlations.

Video diffusion models (DMs) have enabled high-quality video synthesis. Yet, their substantial computational and memory demands pose serious challenges to real-world deployment, even on high-end GPUs. As a commonly adopted solution, quantization has proven notable success in reducing cost for image DMs, while its direct application to video DMs remains ineffective. In this paper, we present QVGen, a novel quantization-aware training (QAT) framework tailored for high-performance and inference-efficient video DMs under extremely low-bit quantization (e.g., 4-bit or below). We begin with a theoretical analysis demonstrating that reducing the gradient norm is essential to facilitate convergence for QAT. To this end, we introduce auxiliary modules (Phi) to mitigate large quantization errors, leading to significantly enhanced convergence. To eliminate the inference overhead of Phi, we propose a rank-decay strategy that progressively eliminates Phi. Specifically, we repeatedly employ singular value decomposition (SVD) and a proposed rank-based regularization gamma to identify and decay low-contributing components. This strategy retains performance while zeroing out inference overhead. Extensive experiments across 4 state-of-the-art (SOTA) video DMs, with parameter sizes ranging from 1.3B sim14B, show that QVGen is the first to reach full-precision comparable quality under 4-bit settings. Moreover, it significantly outperforms existing methods. For instance, our 3-bit CogVideoX-2B achieves improvements of +25.28 in Dynamic Degree and +8.43 in Scene Consistency on VBench.

We introduce the Subspace Power Method (SPM) for calculating the CP decomposition of low-rank real symmetric tensors. This algorithm calculates one new CP component at a time, alternating between applying the shifted symmetric higher-order power method (SS-HOPM) to a certain modified tensor, constructed from a matrix flattening of the original tensor; and using appropriate deflation steps. We obtain rigorous guarantees for SPM regarding convergence and global optima for input tensors of dimension d and order m of CP rank up to O(d^{lfloor m/2rfloor}), via results in classical algebraic geometry and optimization theory. As a by-product of our analysis we prove that SS-HOPM converges unconditionally, settling a conjecture in [Kolda, T.G., Mayo, J.R.: Shifted power method for computing tensor eigenpairs. SIAM Journal on Matrix Analysis and Applications 32(4), 1095-1124 (2011)]. We present numerical experiments which demonstrate that SPM is efficient and robust to noise, being up to one order of magnitude faster than state-of-the-art CP decomposition algorithms in certain experiments. Furthermore, prior knowledge of the CP rank is not required by SPM.

Recent successful applications of convolutional neural networks (CNNs) to audio classification and speech recognition have motivated the search for better input representations for more efficient training. Visual displays of an audio signal, through various time-frequency representations such as spectrograms offer a rich representation of the temporal and spectral structure of the original signal. In this letter, we compare various popular signal processing methods to obtain this representation, such as short-time Fourier transform (STFT) with linear and Mel scales, constant-Q transform (CQT) and continuous Wavelet transform (CWT), and assess their impact on the classification performance of two environmental sound datasets using CNNs. This study supports the hypothesis that time-frequency representations are valuable in learning useful features for sound classification. Moreover, the actual transformation used is shown to impact the classification accuracy, with Mel-scaled STFT outperforming the other discussed methods slightly and baseline MFCC features to a large degree. Additionally, we observe that the optimal window size during transformation is dependent on the characteristics of the audio signal and architecturally, 2D convolution yielded better results in most cases compared to 1D.

Recent progress in separating the speech signals from multiple overlapping speakers using a single audio channel has brought us closer to solving the cocktail party problem. However, most studies in this area use a constrained problem setup, comparing performance when speakers overlap almost completely, at artificially low sampling rates, and with no external background noise. In this paper, we strive to move the field towards more realistic and challenging scenarios. To that end, we created the WSJ0 Hipster Ambient Mixtures (WHAM!) dataset, consisting of two speaker mixtures from the wsj0-2mix dataset combined with real ambient noise samples. The samples were collected in coffee shops, restaurants, and bars in the San Francisco Bay Area, and are made publicly available. We benchmark various speech separation architectures and objective functions to evaluate their robustness to noise. While separation performance decreases as a result of noise, we still observe substantial gains relative to the noisy signals for most approaches.

Real-world multichannel time series prediction faces growing demands for efficiency across edge and cloud environments, making channel compression a timely and essential problem. Motivated by success of Multiple-Input Multiple-Output (MIMO) methods, we propose a predictability-aware compression-decompression framework to reduce runtime, lower communication cost, and maintain prediction accuracy across diverse predictors. The core idea involves using a circular periodicity key matrix with orthogonality to capture underlying time series predictability during compression and to mitigate reconstruction errors during decompression by relaxing oversimplified data assumptions. Theoretical and empirical analyses show that the proposed framework is both time-efficient and scalable under a large number of channels. Extensive experiments on six datasets across various predictors demonstrate that the proposed method achieves superior overall performance by jointly considering prediction accuracy and runtime, while maintaining strong compatibility with diverse predictors.

Spectral analysis provides one of the most effective paradigms for information-preserving dimensionality reduction, as simple descriptions of naturally occurring signals are often obtained via few terms of periodic basis functions. In this work, we study deep neural networks designed to harness the structure in frequency domain for efficient learning of long-range correlations in space or time: frequency-domain models (FDMs). Existing FDMs are based on complex-valued transforms i.e. Fourier Transforms (FT), and layers that perform computation on the spectrum and input data separately. This design introduces considerable computational overhead: for each layer, a forward and inverse FT. Instead, this work introduces a blueprint for frequency domain learning through a single transform: transform once (T1). To enable efficient, direct learning in the frequency domain we derive a variance-preserving weight initialization scheme and investigate methods for frequency selection in reduced-order FDMs. Our results noticeably streamline the design process of FDMs, pruning redundant transforms, and leading to speedups of 3x to 10x that increase with data resolution and model size. We perform extensive experiments on learning the solution operator of spatio-temporal dynamics, including incompressible Navier-Stokes, turbulent flows around airfoils and high-resolution video of smoke. T1 models improve on the test performance of FDMs while requiring significantly less computation (5 hours instead of 32 for our large-scale experiment), with over 20% reduction in average predictive error across tasks.

Recent years have seen progress beyond domain-specific sound separation for speech or music towards universal sound separation for arbitrary sounds. Prior work on universal sound separation has investigated separating a target sound out of an audio mixture given a text query. Such text-queried sound separation systems provide a natural and scalable interface for specifying arbitrary target sounds. However, supervised text-queried sound separation systems require costly labeled audio-text pairs for training. Moreover, the audio provided in existing datasets is often recorded in a controlled environment, causing a considerable generalization gap to noisy audio in the wild. In this work, we aim to approach text-queried universal sound separation by using only unlabeled data. We propose to leverage the visual modality as a bridge to learn the desired audio-textual correspondence. The proposed CLIPSep model first encodes the input query into a query vector using the contrastive language-image pretraining (CLIP) model, and the query vector is then used to condition an audio separation model to separate out the target sound. While the model is trained on image-audio pairs extracted from unlabeled videos, at test time we can instead query the model with text inputs in a zero-shot setting, thanks to the joint language-image embedding learned by the CLIP model. Further, videos in the wild often contain off-screen sounds and background noise that may hinder the model from learning the desired audio-textual correspondence. To address this problem, we further propose an approach called noise invariant training for training a query-based sound separation model on noisy data. Experimental results show that the proposed models successfully learn text-queried universal sound separation using only noisy unlabeled videos, even achieving competitive performance against a supervised model in some settings.

Harmonic retrieval techniques are the foundation of radio channel sounding, estimation and modeling. This paper introduces a Deep Learning approach for two-dimensional spectral estimation from frequency and time samples of a radio channel transfer function. Our work can estimate two-dimensional parameters from a signal containing an unknown number of paths. In contrast to existing deep learning-based methods, the signal parameters are not estimated via classification but instead in a quasi-grid-free manner. This alleviates the bias, spectral leakage, and ghost targets that grid-based approaches inherently produce. The proposed architecture also reliably estimates the number of spectral components in the measurement. Hence, the architecture jointly solves the model order selection problem and the parameter estimation task. Additionally, we propose a multi-channel windowing of the data during preprocessing, increasing the resulting estimator's robustness. We verify the performance compared to existing harmonic retrieval methods and also show how it can be integrated into an existing maximum likelihood estimator for efficient initialization of a gradient-based iteration.

Vision tasks are characterized by the properties of locality and translation invariance. The superior performance of convolutional neural networks (CNNs) on these tasks is widely attributed to the inductive bias of locality and weight sharing baked into their architecture. Existing attempts to quantify the statistical benefits of these biases in CNNs over locally connected convolutional neural networks (LCNs) and fully connected neural networks (FCNs) fall into one of the following categories: either they disregard the optimizer and only provide uniform convergence upper bounds with no separating lower bounds, or they consider simplistic tasks that do not truly mirror the locality and translation invariance as found in real-world vision tasks. To address these deficiencies, we introduce the Dynamic Signal Distribution (DSD) classification task that models an image as consisting of k patches, each of dimension d, and the label is determined by a d-sparse signal vector that can freely appear in any one of the k patches. On this task, for any orthogonally equivariant algorithm like gradient descent, we prove that CNNs require O(k+d) samples, whereas LCNs require Omega(kd) samples, establishing the statistical advantages of weight sharing in translation invariant tasks. Furthermore, LCNs need O(k(k+d)) samples, compared to Omega(k^2d) samples for FCNs, showcasing the benefits of locality in local tasks. Additionally, we develop information theoretic tools for analyzing randomized algorithms, which may be of interest for statistical research.

The separation power of a machine learning model refers to its ability to distinguish between different inputs and is often used as a proxy for its expressivity. Indeed, knowing the separation power of a family of models is a necessary condition to obtain fine-grained universality results. In this paper, we analyze the separation power of equivariant neural networks, such as convolutional and permutation-invariant networks. We first present a complete characterization of inputs indistinguishable by models derived by a given architecture. From this results, we derive how separability is influenced by hyperparameters and architectural choices-such as activation functions, depth, hidden layer width, and representation types. Notably, all non-polynomial activations, including ReLU and sigmoid, are equivalent in expressivity and reach maximum separation power. Depth improves separation power up to a threshold, after which further increases have no effect. Adding invariant features to hidden representations does not impact separation power. Finally, block decomposition of hidden representations affects separability, with minimal components forming a hierarchy in separation power that provides a straightforward method for comparing the separation power of models.

Deep generative modeling has the potential to cause significant harm to society. Recognizing this threat, a magnitude of research into detecting so-called "Deepfakes" has emerged. This research most often focuses on the image domain, while studies exploring generated audio signals have, so-far, been neglected. In this paper we make three key contributions to narrow this gap. First, we provide researchers with an introduction to common signal processing techniques used for analyzing audio signals. Second, we present a novel data set, for which we collected nine sample sets from five different network architectures, spanning two languages. Finally, we supply practitioners with two baseline models, adopted from the signal processing community, to facilitate further research in this area.

Modeling and synthesizing low-light raw noise is a fundamental problem for computational photography and image processing applications. Although most recent works have adopted physics-based models to synthesize noise, the signal-independent noise in low-light conditions is far more complicated and varies dramatically across camera sensors, which is beyond the description of these models. To address this issue, we introduce a new perspective to synthesize the signal-independent noise by a generative model. Specifically, we synthesize the signal-dependent and signal-independent noise in a physics- and learning-based manner, respectively. In this way, our method can be considered as a general model, that is, it can simultaneously learn different noise characteristics for different ISO levels and generalize to various sensors. Subsequently, we present an effective multi-scale discriminator termed Fourier transformer discriminator (FTD) to distinguish the noise distribution accurately. Additionally, we collect a new low-light raw denoising (LRD) dataset for training and benchmarking. Qualitative validation shows that the noise generated by our proposed noise model can be highly similar to the real noise in terms of distribution. Furthermore, extensive denoising experiments demonstrate that our method performs favorably against state-of-the-art methods on different sensors.

The use of deep unfolding networks in compressive sensing (CS) has seen wide success as they provide both simplicity and interpretability. However, since most deep unfolding networks are iterative, this incurs significant redundancies in the network. In this work, we propose a novel recursion-based framework to enhance the efficiency of deep unfolding models. First, recursions are used to effectively eliminate the redundancies in deep unfolding networks. Secondly, we randomize the number of recursions during training to decrease the overall training time. Finally, to effectively utilize the power of recursions, we introduce a learnable unit to modulate the features of the model based on both the total number of iterations and the current iteration index. To evaluate the proposed framework, we apply it to both ISTA-Net+ and COAST. Extensive testing shows that our proposed framework allows the network to cut down as much as 75% of its learnable parameters while mostly maintaining its performance, and at the same time, it cuts around 21% and 42% from the training time for ISTA-Net+ and COAST respectively. Moreover, when presented with a limited training dataset, the recursive models match or even outperform their respective non-recursive baseline. Codes and pretrained models are available at https://github.com/Rawwad-Alhejaili/Recursions-Are-All-You-Need .

Singular Value Decomposition (SVD) has recently seen a surge of interest as a simple yet powerful tool for large language models (LLMs) compression, with a growing number of works demonstrating 20-80% parameter reductions at minimal accuracy loss. Previous SVD-based approaches have focused primarily on reducing the memory footprint of model weights, largely overlooking the additional activation memory overhead incurred during inference when applying truncated factors via standard dense CUDA kernels. Our experiments demonstrate that this activation overhead, scaling with sequence length and hidden dimension, prevents current SVD compression techniques from achieving any reduction in peak inference memory, thereby limiting their viability for real-world, on-device deployments. We introduce FlashSVD, a novel, end-to-end rank-aware streaming inference framework specifically designed for SVD-compressed large language models. FlashSVD can be seamlessly integrated with any model that employs SVD-based methods for parameter reduction. By fusing low-rank projection kernels directly into both the self-attention and feed-forward network (FFN) pipelines, FlashSVD avoid materializing full-size activation buffers. Instead, small tiles of the truncated factors are loaded into on-chip SRAM, multiplied and reduced on the fly, and immediately evicted, preserving high GPU occupancy and adding no extra latency. On standard encoder benchmarks (e.g., BERT-Base), FlashSVD cuts peak activation memory by up to 70.2% and intermediate transient memory by 75%, all while incur no accuracy loss with upstreaming compression methods, offering a practical path toward memory-constrained deployment of low-rank LLMs.

The scaling up has brought tremendous success in the fields of vision and language in recent years. When it comes to audio, however, researchers encounter a major challenge in scaling up the training data, as most natural audio contains diverse interfering signals. To address this limitation, we introduce Omni-modal Sound Separation (OmniSep), a novel framework capable of isolating clean soundtracks based on omni-modal queries, encompassing both single-modal and multi-modal composed queries. Specifically, we introduce the Query-Mixup strategy, which blends query features from different modalities during training. This enables OmniSep to optimize multiple modalities concurrently, effectively bringing all modalities under a unified framework for sound separation. We further enhance this flexibility by allowing queries to influence sound separation positively or negatively, facilitating the retention or removal of specific sounds as desired. Finally, OmniSep employs a retrieval-augmented approach known as Query-Aug, which enables open-vocabulary sound separation. Experimental evaluations on MUSIC, VGGSOUND-CLEAN+, and MUSIC-CLEAN+ datasets demonstrate effectiveness of OmniSep, achieving state-of-the-art performance in text-, image-, and audio-queried sound separation tasks. For samples and further information, please visit the demo page at https://omnisep.github.io/.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

The online estimation of rhythmic information, such as beat positions, downbeat positions, and meter, is critical for many real-time music applications. Musical rhythm comprises complex hierarchical relationships across time, rendering its analysis intrinsically challenging and at times subjective. Furthermore, systems which attempt to estimate rhythmic information in real-time must be causal and must produce estimates quickly and efficiently. In this work, we introduce an online system for joint beat, downbeat, and meter tracking, which utilizes causal convolutional and recurrent layers, followed by a pair of sequential Monte Carlo particle filters applied during inference. The proposed system does not need to be primed with a time signature in order to perform downbeat tracking, and is instead able to estimate meter and adjust the predictions over time. Additionally, we propose an information gate strategy to significantly decrease the computational cost of particle filtering during the inference step, making the system much faster than previous sampling-based methods. Experiments on the GTZAN dataset, which is unseen during training, show that the system outperforms various online beat and downbeat tracking systems and achieves comparable performance to a baseline offline joint method.

Denoising and filtering are widely used in routine seismic-data-processing to improve the signal-to-noise ratio (SNR) of recorded signals and by doing so to improve subsequent analyses. In this paper we develop a new denoising/decomposition method, DeepDenoiser, based on a deep neural network. This network is able to learn simultaneously a sparse representation of data in the time-frequency domain and a non-linear function that maps this representation into masks that decompose input data into a signal of interest and noise (defined as any non-seismic signal). We show that DeepDenoiser achieves impressive denoising of seismic signals even when the signal and noise share a common frequency band. Our method properly handles a variety of colored noise and non-earthquake signals. DeepDenoiser can significantly improve the SNR with minimal changes in the waveform shape of interest, even in presence of high noise levels. We demonstrate the effect of our method on improving earthquake detection. There are clear applications of DeepDenoiser to seismic imaging, micro-seismic monitoring, and preprocessing of ambient noise data. We also note that potential applications of our approach are not limited to these applications or even to earthquake data, and that our approach can be adapted to diverse signals and applications in other settings.

We consider the problem of computing the Walsh-Hadamard Transform (WHT) of some N-length input vector in the presence of noise, where the N-point Walsh spectrum is K-sparse with K = {O}(N^{delta}) scaling sub-linearly in the input dimension N for some 0<delta<1. Over the past decade, there has been a resurgence in research related to the computation of Discrete Fourier Transform (DFT) for some length-N input signal that has a K-sparse Fourier spectrum. In particular, through a sparse-graph code design, our earlier work on the Fast Fourier Aliasing-based Sparse Transform (FFAST) algorithm computes the K-sparse DFT in time {O}(Klog K) by taking {O}(K) noiseless samples. Inspired by the coding-theoretic design framework, Scheibler et al. proposed the Sparse Fast Hadamard Transform (SparseFHT) algorithm that elegantly computes the K-sparse WHT in the absence of noise using {O}(Klog N) samples in time {O}(Klog^2 N). However, the SparseFHT algorithm explicitly exploits the noiseless nature of the problem, and is not equipped to deal with scenarios where the observations are corrupted by noise. Therefore, a question of critical interest is whether this coding-theoretic framework can be made robust to noise. Further, if the answer is yes, what is the extra price that needs to be paid for being robust to noise? In this paper, we show, quite interestingly, that there is {\it no extra price} that needs to be paid for being robust to noise other than a constant factor. In other words, we can maintain the same sample complexity {O}(Klog N) and the computational complexity {O}(Klog^2 N) as those of the noiseless case, using our SParse Robust Iterative Graph-based Hadamard Transform (SPRIGHT) algorithm.

Neural audio autoencoders create compact latent representations that preserve perceptually important information, serving as the foundation for both modern audio compression systems and generation approaches like next-token prediction and latent diffusion. Despite their prevalence, most audio processing operations, such as spatial and spectral up-sampling, still inefficiently operate on raw waveforms or spectral representations rather than directly on these compressed representations. We propose a framework that performs audio processing operations entirely within an autoencoder's latent space, eliminating the need to decode to raw audio formats. Our approach dramatically simplifies training by operating solely in the latent domain, with a latent L1 reconstruction term, augmented by a single latent adversarial discriminator. This contrasts sharply with raw-audio methods that typically require complex combinations of multi-scale losses and discriminators. Through experiments in bandwidth extension and mono-to-stereo up-mixing, we demonstrate computational efficiency gains of up to 100x while maintaining quality comparable to post-processing on raw audio. This work establishes a more efficient paradigm for audio processing pipelines that already incorporate autoencoders, enabling significantly faster and more resource-efficient workflows across various audio tasks.

In this work, we present DeFTAN-II, an efficient multichannel speech enhancement model based on transformer architecture and subgroup processing. Despite the success of transformers in speech enhancement, they face challenges in capturing local relations, reducing the high computational complexity, and lowering memory usage. To address these limitations, we introduce subgroup processing in our model, combining subgroups of locally emphasized features with other subgroups containing original features. The subgroup processing is implemented in several blocks of the proposed network. In the proposed split dense blocks extracting spatial features, a pair of subgroups is sequentially concatenated and processed by convolution layers to effectively reduce the computational complexity and memory usage. For the F- and T-transformers extracting temporal and spectral relations, we introduce cross-attention between subgroups to identify relationships between locally emphasized and non-emphasized features. The dual-path feedforward network then aggregates attended features in terms of the gating of local features processed by dilated convolutions. Through extensive comparisons with state-of-the-art multichannel speech enhancement models, we demonstrate that DeFTAN-II with subgroup processing outperforms existing methods at significantly lower computational complexity. Moreover, we evaluate the model's generalization capability on real-world data without fine-tuning, which further demonstrates its effectiveness in practical scenarios.

Recent progress in image generation has sparked research into controlling these models through condition signals, with various methods addressing specific challenges in conditional generation. Instead of proposing another specialized technique, we introduce a simple, unified framework to handle diverse conditional generation tasks involving a specific image-condition correlation. By learning a joint distribution over a correlated image pair (e.g. image and depth) with a diffusion model, our approach enables versatile capabilities via different inference-time sampling schemes, including controllable image generation (e.g. depth to image), estimation (e.g. image to depth), signal guidance, joint generation (image & depth), and coarse control. Previous attempts at unification often introduce significant complexity through multi-stage training, architectural modification, or increased parameter counts. In contrast, our simple formulation requires a single, computationally efficient training stage, maintains the standard model input, and adds minimal learned parameters (15% of the base model). Moreover, our model supports additional capabilities like non-spatially aligned and coarse conditioning. Extensive results show that our single model can produce comparable results with specialized methods and better results than prior unified methods. We also demonstrate that multiple models can be effectively combined for multi-signal conditional generation.

Recent research in medical image analysis with deep learning almost exclusively focuses on grid- or voxel-based data representations. We challenge this common choice by introducing MedFuncta, a modality-agnostic continuous data representation based on neural fields. We demonstrate how to scale neural fields from single instances to large datasets by exploiting redundancy in medical signals and by applying an efficient meta-learning approach with a context reduction scheme. We further address the spectral bias in commonly used SIREN activations, by introducing an omega_0-schedule, improving reconstruction quality and convergence speed. We validate our proposed approach on a large variety of medical signals of different dimensions and modalities (1D: ECG; 2D: Chest X-ray, Retinal OCT, Fundus Camera, Dermatoscope, Colon Histopathology, Cell Microscopy; 3D: Brain MRI, Lung CT) and successfully demonstrate that we can solve relevant downstream tasks on these representations. We additionally release a large-scale dataset of > 550k annotated neural fields to promote research in this direction.

Speech processing algorithms often rely on statistical knowledge of the underlying process. Despite many years of research, however, the debate on the most appropriate statistical model for speech still continues. Speech is commonly modeled as a wide-sense stationary (WSS) process. However, the use of the WSS model for spectrally correlated processes is fundamentally wrong, as WSS implies spectral uncorrelation. In this paper, we demonstrate that voiced speech can be more accurately represented as a cyclostationary (CS) process. By employing the CS rather than the WSS model for processes that are inherently correlated across frequency, it is possible to improve the estimation of cross-power spectral densities (PSDs), source separation, and beamforming. We illustrate how the correlation between harmonic frequencies of CS processes can enhance system identification, and validate our findings using both simulated and real speech data.

In this paper we propose a novel model for unconditional audio generation based on generating one audio sample at a time. We show that our model, which profits from combining memory-less modules, namely autoregressive multilayer perceptrons, and stateful recurrent neural networks in a hierarchical structure is able to capture underlying sources of variations in the temporal sequences over very long time spans, on three datasets of different nature. Human evaluation on the generated samples indicate that our model is preferred over competing models. We also show how each component of the model contributes to the exhibited performance.

We introduce meta-factorization, a theory that describes matrix decompositions as solutions of linear matrix equations: the projector and the reconstruction equation. Meta-factorization reconstructs known factorizations, reveals their internal structures, and allows for introducing modifications, as illustrated with SVD, QR, and UTV factorizations. The prospect of meta-factorization also provides insights into computational aspects of generalized matrix inverses and randomized linear algebra algorithms. The relations between the Moore-Penrose pseudoinverse, generalized Nystr\"{o}m method, and the CUR decomposition are revealed here as an illustration. Finally, meta-factorization offers hints on the structure of new factorizations and provides the potential of creating them.

This paper studies the role of over-parametrization in solving non-convex optimization problems. The focus is on the important class of low-rank matrix sensing, where we propose an infinite hierarchy of non-convex problems via the lifting technique and the Burer-Monteiro factorization. This contrasts with the existing over-parametrization technique where the search rank is limited by the dimension of the matrix and it does not allow a rich over-parametrization of an arbitrary degree. We show that although the spurious solutions of the problem remain stationary points through the hierarchy, they will be transformed into strict saddle points (under some technical conditions) and can be escaped via local search methods. This is the first result in the literature showing that over-parametrization creates a negative curvature for escaping spurious solutions. We also derive a bound on how much over-parametrization is requited to enable the elimination of spurious solutions.

Brain-computer interfaces (BCIs) offer transformative potential, but decoding neural signals presents significant challenges. The core premise of this paper is built around demonstrating methods to elucidate the underlying low-dimensional geometric structure present in high-dimensional brainwave data in order to assist in downstream BCI-related neural classification tasks. We demonstrate two pipelines related to electroencephalography (EEG) signal processing: (1) a preliminary pipeline removing noise from individual EEG channels, and (2) a downstream manifold learning pipeline uncovering geometric structure across networks of EEG channels. We conduct preliminary validation using two EEG datasets and situate our demonstration in the context of the BCI-relevant imagined digit decoding problem. Our preliminary pipeline uses an attention-based EEG filtration network to extract clean signal from individual EEG channels. Our primary pipeline uses a fast Fourier transform, a Laplacian eigenmap, a discrete analog of Ricci flow via Ollivier's notion of Ricci curvature, and a graph convolutional network to perform dimensionality reduction on high-dimensional multi-channel EEG data in order to enable regularizable downstream classification. Our system achieves competitive performance with existing signal processing and classification benchmarks; we demonstrate a mean test correlation coefficient of >0.95 at 2 dB on semi-synthetic neural denoising and a downstream EEG-based classification accuracy of 0.97 on distinguishing digit- versus non-digit- thoughts. Results are preliminary and our geometric machine learning pipeline should be validated by more extensive follow-up studies; generalizing these results to larger inter-subject sample sizes, different hardware systems, and broader use cases will be crucial.

Recently, diffusion-based methods for monocular 3D human pose estimation have achieved state-of-the-art (SOTA) performance by directly regressing the 3D joint coordinates from the 2D pose sequence. Although some methods decompose the task into bone length and bone direction prediction based on the human anatomical skeleton to explicitly incorporate more human body prior constraints, the performance of these methods is significantly lower than that of the SOTA diffusion-based methods. This can be attributed to the tree structure of the human skeleton. Direct application of the disentangled method could amplify the accumulation of hierarchical errors, propagating through each hierarchy. Meanwhile, the hierarchical information has not been fully explored by the previous methods. To address these problems, a Disentangled Diffusion-based 3D Human Pose Estimation method with Hierarchical Spatial and Temporal Denoiser is proposed, termed DDHPose. In our approach: (1) We disentangle the 3D pose and diffuse the bone length and bone direction during the forward process of the diffusion model to effectively model the human pose prior. A disentanglement loss is proposed to supervise diffusion model learning. (2) For the reverse process, we propose Hierarchical Spatial and Temporal Denoiser (HSTDenoiser) to improve the hierarchical modeling of each joint. Our HSTDenoiser comprises two components: the Hierarchical-Related Spatial Transformer (HRST) and the Hierarchical-Related Temporal Transformer (HRTT). HRST exploits joint spatial information and the influence of the parent joint on each joint for spatial modeling, while HRTT utilizes information from both the joint and its hierarchical adjacent joints to explore the hierarchical temporal correlations among joints. Code and models are available at https://github.com/Andyen512/DDHPose

In this paper, we introduce Jointist, an instrument-aware multi-instrument framework that is capable of transcribing, recognizing, and separating multiple musical instruments from an audio clip. Jointist consists of the instrument recognition module that conditions the other modules: the transcription module that outputs instrument-specific piano rolls, and the source separation module that utilizes instrument information and transcription results. The instrument conditioning is designed for an explicit multi-instrument functionality while the connection between the transcription and source separation modules is for better transcription performance. Our challenging problem formulation makes the model highly useful in the real world given that modern popular music typically consists of multiple instruments. However, its novelty necessitates a new perspective on how to evaluate such a model. During the experiment, we assess the model from various aspects, providing a new evaluation perspective for multi-instrument transcription. We also argue that transcription models can be utilized as a preprocessing module for other music analysis tasks. In the experiment on several downstream tasks, the symbolic representation provided by our transcription model turned out to be helpful to spectrograms in solving downbeat detection, chord recognition, and key estimation.

Low-rank adaptation (LoRA) has become a prevalent method for adapting pre-trained large language models to downstream tasks. However, the simple low-rank decomposition form may constrain the hypothesis space. To address this limitation, we introduce Location-aware Cosine Adaptation (LoCA), a novel frequency-domain parameter-efficient fine-tuning method based on inverse Discrete Cosine Transform (iDCT) with selective locations of learnable components. We begin with a comprehensive theoretical comparison between frequency-domain and low-rank decompositions for fine-tuning pre-trained large models. Our analysis reveals that frequency-domain decomposition with carefully selected frequency components can surpass the expressivity of traditional low-rank-based methods. Furthermore, we demonstrate that iDCT offers a more efficient implementation compared to inverse Discrete Fourier Transform (iDFT), allowing for better selection and tuning of frequency components while maintaining equivalent expressivity to the optimal iDFT-based adaptation. By employing finite-difference approximation to estimate gradients for discrete locations of learnable coefficients on the DCT spectrum, LoCA dynamically selects the most informative frequency components during training. Experiments on diverse language and vision fine-tuning tasks demonstrate that LoCA offers enhanced parameter efficiency while maintains computational feasibility comparable to low-rank-based methods.

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from complex analysis and spectral theory -- extend spectral convolutions to directed graphs. We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed theory, we conduct experiments in real world settings, showcasing that directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many datasets and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.

Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrical signals, contain significant information in the phase of the signal. We explore complex-valued deep convolutional networks to leverage non-linear feature maps. Seismic data commonly has a lowcut filter applied, to attenuate noise from ocean waves and similar long wavelength contributions. Discarding the phase information leads to low-frequency aliasing analogous to the Nyquist-Shannon theorem for high frequencies. In non-stationary data, the phase content can stabilize training and improve the generalizability of neural networks. While it has been shown that phase content can be restored in deep neural networks, we show how including phase information in feature maps improves both training and inference from deterministic physical data. Furthermore, we show that the reduction of parameters in a complex network outperforms larger real-valued networks.

Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: (i) Estimate latent variables associated to rows and columns; (ii) Partition the table in blocks according to the row/column latents; (iii) Apply a sequential (e.g. Lempel-Ziv) coder to each of the blocks; (iv) Append a compressed encoding of the latents. We evaluate it on several benchmark datasets, and study optimal compression in a probabilistic model for that tabular data, whereby latent values are independent and table entries are conditionally independent given the latent values. We prove that the model has a well defined entropy rate and satisfies an asymptotic equipartition property. We also prove that classical compression schemes such as Lempel-Ziv and finite-state encoders do not achieve this rate. On the other hand, the latent estimation strategy outlined above achieves the optimal rate.

Diffusion models (DMs) have recently been introduced in image deblurring and exhibited promising performance, particularly in terms of details reconstruction. However, the diffusion model requires a large number of inference iterations to recover the clean image from pure Gaussian noise, which consumes massive computational resources. Moreover, the distribution synthesized by the diffusion model is often misaligned with the target results, leading to restrictions in distortion-based metrics. To address the above issues, we propose the Hierarchical Integration Diffusion Model (HI-Diff), for realistic image deblurring. Specifically, we perform the DM in a highly compacted latent space to generate the prior feature for the deblurring process. The deblurring process is implemented by a regression-based method to obtain better distortion accuracy. Meanwhile, the highly compact latent space ensures the efficiency of the DM. Furthermore, we design the hierarchical integration module to fuse the prior into the regression-based model from multiple scales, enabling better generalization in complex blurry scenarios. Comprehensive experiments on synthetic and real-world blur datasets demonstrate that our HI-Diff outperforms state-of-the-art methods. Code and trained models are available at https://github.com/zhengchen1999/HI-Diff.

In this paper, we propose an algorithm that allows joint refinement of camera pose and scene geometry represented by decomposed low-rank tensor, using only 2D images as supervision. First, we conduct a pilot study based on a 1D signal and relate our findings to 3D scenarios, where the naive joint pose optimization on voxel-based NeRFs can easily lead to sub-optimal solutions. Moreover, based on the analysis of the frequency spectrum, we propose to apply convolutional Gaussian filters on 2D and 3D radiance fields for a coarse-to-fine training schedule that enables joint camera pose optimization. Leveraging the decomposition property in decomposed low-rank tensor, our method achieves an equivalent effect to brute-force 3D convolution with only incurring little computational overhead. To further improve the robustness and stability of joint optimization, we also propose techniques of smoothed 2D supervision, randomly scaled kernel parameters, and edge-guided loss mask. Extensive quantitative and qualitative evaluations demonstrate that our proposed framework achieves superior performance in novel view synthesis as well as rapid convergence for optimization.

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability to large numbers of variables. Moreover, these methods frequently assume linearity or invertibility, restricting their applicability to real-world scenarios. We present new theoretical results on the identifiability of nonlinear latent hierarchical causal models, relaxing previous assumptions in literature about the deterministic nature of latent variables and exogenous noise. Building on these insights, we develop a novel differentiable causal discovery algorithm that efficiently estimates the structure of such models. To the best of our knowledge, this is the first work to propose a differentiable causal discovery method for nonlinear latent hierarchical models. Our approach outperforms existing methods in both accuracy and scalability. We demonstrate its practical utility by learning interpretable hierarchical latent structures from high-dimensional image data and demonstrate its effectiveness on downstream tasks.

Source separation is a fundamental task in speech, music, and audio processing, and it also provides cleaner and larger data for training generative models. However, improving separation performance in practice often depends on increasingly large networks, inflating training and deployment costs. Motivated by recent advances in inference-time scaling for generative modeling, we propose Training-Time and Inference-Time Scalable Discriminative Source Separation (TISDiSS), a unified framework that integrates early-split multi-loss supervision, shared-parameter design, and dynamic inference repetitions. TISDiSS enables flexible speed-performance trade-offs by adjusting inference depth without retraining additional models. We further provide systematic analyses of architectural and training choices and show that training with more inference repetitions improves shallow-inference performance, benefiting low-latency applications. Experiments on standard speech separation benchmarks demonstrate state-of-the-art performance with a reduced parameter count, establishing TISDiSS as a scalable and practical framework for adaptive source separation. Code is available at https://github.com/WingSingFung/TISDiSS.

Hindustani music is a performance-driven oral tradition that exhibits the rendition of rich melodic patterns. In this paper, we focus on generative modeling of singers' vocal melodies extracted from audio recordings, as the voice is musically prominent within the tradition. Prior generative work in Hindustani music models melodies as coarse discrete symbols which fails to capture the rich expressive melodic intricacies of singing. Thus, we propose to use a finely quantized pitch contour, as an intermediate representation for hierarchical audio modeling. We propose GaMaDHaNi, a modular two-level hierarchy, consisting of a generative model on pitch contours, and a pitch contour to audio synthesis model. We compare our approach to non-hierarchical audio models and hierarchical models that use a self-supervised intermediate representation, through a listening test and qualitative analysis. We also evaluate audio model's ability to faithfully represent the pitch contour input using Pearson correlation coefficient. By using pitch contours as an intermediate representation, we show that our model may be better equipped to listen and respond to musicians in a human-AI collaborative setting by highlighting two potential interaction use cases (1) primed generation, and (2) coarse pitch conditioning.

Finding the mode of a high dimensional probability distribution D is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when D is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy (1-epsilon) for any epsilon > 0. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless P = NP. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

The Fisher information is a fundamental concept for characterizing the sensitivity of parameters in neural networks. However, leveraging the full observed Fisher information is too expensive for large models, so most methods rely on simple diagonal approximations. While efficient, this approach ignores parameter correlations, often resulting in reduced performance on downstream tasks. In this work, we mitigate these limitations and propose Generalized Fisher-Weighted SVD (GFWSVD), a post-training LLM compression technique that accounts for both diagonal and off-diagonal elements of the Fisher information matrix, providing a more accurate reflection of parameter importance. To make the method tractable, we introduce a scalable adaptation of the Kronecker-factored approximation algorithm for the observed Fisher information. We demonstrate the effectiveness of our method on LLM compression, showing improvements over existing compression baselines. For example, at a 20 compression rate on the MMLU benchmark, our method outperforms FWSVD, which is based on a diagonal approximation of the Fisher information, by 5 percent, SVD-LLM by 3 percent, and ASVD by 6 percent compression rate.

Within the ambit of VoIP (Voice over Internet Protocol) telecommunications, the complexities introduced by acoustic transformations merit rigorous analysis. This research, rooted in the exploration of proprietary sender-side denoising effects, meticulously evaluates platforms such as Google Meets and Zoom. The study draws upon the Deep Noise Suppression (DNS) 2020 dataset, ensuring a structured examination tailored to various denoising settings and receiver interfaces. A methodological novelty is introduced via Blinder-Oaxaca decomposition, traditionally an econometric tool, repurposed herein to analyze acoustic-phonetic perturbations within VoIP systems. To further ground the implications of these transformations, psychoacoustic metrics, specifically PESQ and STOI, were used to explain of perceptual quality and intelligibility. Cumulatively, the insights garnered underscore the intricate landscape of VoIP-influenced acoustic dynamics. In addition to the primary findings, a multitude of metrics are reported, extending the research purview. Moreover, out-of-domain benchmarking for both time and time-frequency domain speech enhancement models is included, thereby enhancing the depth and applicability of this inquiry.

We consider the image transmission problem over a noisy wireless channel via deep learning-based joint source-channel coding (DeepJSCC) along with a denoising diffusion probabilistic model (DDPM) at the receiver. Specifically, we are interested in the perception-distortion trade-off in the practical finite block length regime, in which separate source and channel coding can be highly suboptimal. We introduce a novel scheme that utilizes the range-null space decomposition of the target image. We transmit the range-space of the image after encoding and employ DDPM to progressively refine its null space contents. Through extensive experiments, we demonstrate significant improvements in distortion and perceptual quality of reconstructed images compared to standard DeepJSCC and the state-of-the-art generative learning-based method. We will publicly share our source code to facilitate further research and reproducibility.

Multimodal large language models (MLLMs) have made remarkable strides, largely driven by their ability to process increasingly long and complex contexts, such as high-resolution images, extended video sequences, and lengthy audio input. While this ability significantly enhances MLLM capabilities, it introduces substantial computational challenges, primarily due to the quadratic complexity of self-attention mechanisms with numerous input tokens. To mitigate these bottlenecks, token compression has emerged as an auspicious and critical approach, efficiently reducing the number of tokens during both training and inference. In this paper, we present the first systematic survey and synthesis of the burgeoning field of multimodal long context token compression. Recognizing that effective compression strategies are deeply tied to the unique characteristics and redundancies of each modality, we categorize existing approaches by their primary data focus, enabling researchers to quickly access and learn methods tailored to their specific area of interest: (1) image-centric compression, which addresses spatial redundancy in visual data; (2) video-centric compression, which tackles spatio-temporal redundancy in dynamic sequences; and (3) audio-centric compression, which handles temporal and spectral redundancy in acoustic signals. Beyond this modality-driven categorization, we further dissect methods based on their underlying mechanisms, including transformation-based, similarity-based, attention-based, and query-based approaches. By providing a comprehensive and structured overview, this survey aims to consolidate current progress, identify key challenges, and inspire future research directions in this rapidly evolving domain. We also maintain a public repository to continuously track and update the latest advances in this promising area.

High spatial frequency information, including fine details like textures, significantly contributes to the accuracy of semantic segmentation. However, according to the Nyquist-Shannon Sampling Theorem, high-frequency components are vulnerable to aliasing or distortion when propagating through downsampling layers such as strided-convolution. Here, we propose a novel Spatial Frequency Modulation (SFM) that modulates high-frequency features to a lower frequency before downsampling and then demodulates them back during upsampling. Specifically, we implement modulation through adaptive resampling (ARS) and design a lightweight add-on that can densely sample the high-frequency areas to scale up the signal, thereby lowering its frequency in accordance with the Frequency Scaling Property. We also propose Multi-Scale Adaptive Upsampling (MSAU) to demodulate the modulated feature and recover high-frequency information through non-uniform upsampling This module further improves segmentation by explicitly exploiting information interaction between densely and sparsely resampled areas at multiple scales. Both modules can seamlessly integrate with various architectures, extending from convolutional neural networks to transformers. Feature visualization and analysis confirm that our method effectively alleviates aliasing while successfully retaining details after demodulation. Finally, we validate the broad applicability and effectiveness of SFM by extending it to image classification, adversarial robustness, instance segmentation, and panoptic segmentation tasks. The code is available at https://github.com/Linwei-Chen/SFM.

Music source separation (MSS) aims to separate a music recording into multiple musically distinct stems, such as vocals, bass, drums, and more. Recently, deep learning approaches such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs) have been used, but the improvement is still limited. In this paper, we propose a novel frequency-domain approach based on a Band-Split RoPE Transformer (called BS-RoFormer). BS-RoFormer relies on a band-split module to project the input complex spectrogram into subband-level representations, and then arranges a stack of hierarchical Transformers to model the inner-band as well as inter-band sequences for multi-band mask estimation. To facilitate training the model for MSS, we propose to use the Rotary Position Embedding (RoPE). The BS-RoFormer system trained on MUSDB18HQ and 500 extra songs ranked the first place in the MSS track of Sound Demixing Challenge (SDX23). Benchmarking a smaller version of BS-RoFormer on MUSDB18HQ, we achieve state-of-the-art result without extra training data, with 9.80 dB of average SDR.

We demonstrate how conditional generation from diffusion models can be used to tackle a variety of realistic tasks in the production of music in 44.1kHz stereo audio with sampling-time guidance. The scenarios we consider include continuation, inpainting and regeneration of musical audio, the creation of smooth transitions between two different music tracks, and the transfer of desired stylistic characteristics to existing audio clips. We achieve this by applying guidance at sampling time in a simple framework that supports both reconstruction and classification losses, or any combination of the two. This approach ensures that generated audio can match its surrounding context, or conform to a class distribution or latent representation specified relative to any suitable pre-trained classifier or embedding model.

Score-based generative models (SGMs) have recently shown impressive results for difficult generative tasks such as the unconditional and conditional generation of natural images and audio signals. In this work, we extend these models to the complex short-time Fourier transform (STFT) domain, proposing a novel training task for speech enhancement using a complex-valued deep neural network. We derive this training task within the formalism of stochastic differential equations (SDEs), thereby enabling the use of predictor-corrector samplers. We provide alternative formulations inspired by previous publications on using generative diffusion models for speech enhancement, avoiding the need for any prior assumptions on the noise distribution and making the training task purely generative which, as we show, results in improved enhancement performance.

We introduce Audio-SDS, a generalization of Score Distillation Sampling (SDS) to text-conditioned audio diffusion models. While SDS was initially designed for text-to-3D generation using image diffusion, its core idea of distilling a powerful generative prior into a separate parametric representation extends to the audio domain. Leveraging a single pretrained model, Audio-SDS enables a broad range of tasks without requiring specialized datasets. In particular, we demonstrate how Audio-SDS can guide physically informed impact sound simulations, calibrate FM-synthesis parameters, and perform prompt-specified source separation. Our findings illustrate the versatility of distillation-based methods across modalities and establish a robust foundation for future work using generative priors in audio tasks.

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to implement. We study a challenging problem called self-calibration, i.e., the task of designing an algorithm for devices so that the algorithm is able to perform calibration automatically. More precisely, we consider the setup y = A(d) x + epsilon where only partial information about the sensing matrix A(d) is known and where A(d) linearly depends on d. The goal is to estimate the calibration parameter d (resolve the uncertainty in the sensing process) and the signal/object of interests x simultaneously. For three different models of practical relevance, we show how such a bilinear inverse problem, including blind deconvolution as an important example, can be solved via a simple linear least squares approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus potentially allowing for real-time deployment. We also present a variation of the least squares approach, which leads to a~spectral method, where the solution to the bilinear inverse problem can be found by computing the singular vector associated with the smallest singular value of a certain matrix derived from the bilinear system. Explicit theoretical guarantees and stability theory are derived for both techniques; and the number of sampling complexity is nearly optimal (up to a poly-log factor). Applications in imaging sciences and signal processing are discussed and numerical simulations are presented to demonstrate the effectiveness and efficiency of our approach.

Recent developments in Parameter-Efficient Fine-Tuning (PEFT) methods for pretrained deep neural networks have captured widespread interest. In this work, we study the enhancement of current PEFT methods by incorporating the spectral information of pretrained weight matrices into the fine-tuning procedure. We investigate two spectral adaptation mechanisms, namely additive tuning and orthogonal rotation of the top singular vectors, both are done via first carrying out Singular Value Decomposition (SVD) of pretrained weights and then fine-tuning the top spectral space. We provide a theoretical analysis of spectral fine-tuning and show that our approach improves the rank capacity of low-rank adapters given a fixed trainable parameter budget. We show through extensive experiments that the proposed fine-tuning model enables better parameter efficiency and tuning performance as well as benefits multi-adapter fusion. The code will be open-sourced for reproducibility.

Existing neural audio codecs usually sacrifice computational complexity for audio quality. They build the feature transformation layers mainly on convolutional blocks, which are not inherently appropriate for capturing local redundancies of audio signals. As compensation, either adversarial losses from a discriminator or a large number of model parameters are required to improve the codec. To that end, we propose Efficient Speech Codec (ESC), a lightweight parameter-efficient codec laid on cross-scale residual vector quantization and transformers. Our model leverages mirrored hierarchical window-attention transformer blocks and performs step-wise decoding from coarse-to-fine feature representations. To enhance codebook utilization, we design a learning paradigm that involves a pre-training stage to assist with codec training. Extensive results show that ESC can achieve high audio quality with much lower complexity, which is a prospective alternative in place of existing codecs.

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .

Neural audio codecs have recently gained popularity because they can represent audio signals with high fidelity at very low bitrates, making it feasible to use language modeling approaches for audio generation and understanding. Residual Vector Quantization (RVQ) has become the standard technique for neural audio compression using a cascade of VQ codebooks. This paper proposes the Multi-Scale Neural Audio Codec, a simple extension of RVQ where the quantizers can operate at different temporal resolutions. By applying a hierarchy of quantizers at variable frame rates, the codec adapts to the audio structure across multiple timescales. This leads to more efficient compression, as demonstrated by extensive objective and subjective evaluations. The code and model weights are open-sourced at https://github.com/hubertsiuzdak/snac.

Deep Click-Through Rate (CTR) prediction models play an important role in modern industrial recommendation scenarios. However, high memory overhead and computational costs limit their deployment in resource-constrained environments. Low-rank approximation is an effective method for computer vision and natural language processing models, but its application in compressing CTR prediction models has been less explored. Due to the limited memory and computing resources, compression of CTR prediction models often confronts three fundamental challenges, i.e., (1). How to reduce the model sizes to adapt to edge devices? (2). How to speed up CTR prediction model inference? (3). How to retain the capabilities of original models after compression? Previous low-rank compression research mostly uses tensor decomposition, which can achieve a high parameter compression ratio, but brings in AUC degradation and additional computing overhead. To address these challenges, we propose a unified low-rank decomposition framework for compressing CTR prediction models. We find that even with the most classic matrix decomposition SVD method, our framework can achieve better performance than the original model. To further improve the effectiveness of our framework, we locally compress the output features instead of compressing the model weights. Our unified low-rank compression framework can be applied to embedding tables and MLP layers in various CTR prediction models. Extensive experiments on two academic datasets and one real industrial benchmark demonstrate that, with 3-5x model size reduction, our compressed models can achieve both faster inference and higher AUC than the uncompressed original models. Our code is at https://github.com/yuhao318/Atomic_Feature_Mimicking.

Pixel-wise predictions are required in a wide variety of tasks such as image restoration, image segmentation, or disparity estimation. Common models involve several stages of data resampling, in which the resolution of feature maps is first reduced to aggregate information and then increased to generate a high-resolution output. Previous works have shown that resampling operations are subject to artifacts such as aliasing. During downsampling, aliases have been shown to compromise the prediction stability of image classifiers. During upsampling, they have been leveraged to detect generated content. Yet, the effect of aliases during upsampling has not yet been discussed w.r.t. the stability and robustness of pixel-wise predictions. While falling under the same term (aliasing), the challenges for correct upsampling in neural networks differ significantly from those during downsampling: when downsampling, some high frequencies can not be correctly represented and have to be removed to avoid aliases. However, when upsampling for pixel-wise predictions, we actually require the model to restore such high frequencies that can not be encoded in lower resolutions. The application of findings from signal processing is therefore a necessary but not a sufficient condition to achieve the desirable output. In contrast, we find that the availability of large spatial context during upsampling allows to provide stable, high-quality pixel-wise predictions, even when fully learning all filter weights.

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.

This article focuses on estimating relative transfer functions (RTFs) for beamforming applications. Traditional methods often assume that spectra are uncorrelated, an assumption that is often violated in practical scenarios due to factors such as time-domain windowing or the non-stationary nature of signals, as observed in speech. To overcome these limitations, we propose an RTF estimation technique that leverages spectral and spatial correlations through subspace analysis. Additionally, we derive Cram\'er--Rao bounds (CRBs) for the RTF estimation task, providing theoretical insights into the achievable estimation accuracy. These bounds reveal that channel estimation can be performed more accurately if the noise or the target signal exhibits spectral correlations. Experiments with both real and synthetic data show that our technique outperforms the narrowband maximum-likelihood estimator, known as covariance whitening (CW), when the target exhibits spectral correlations. Although the proposed algorithm generally achieves accuracy close to the theoretical bound, there is potential for further improvement, especially in scenarios with highly spectrally correlated noise. While channel estimation has various applications, we demonstrate the method using a minimum variance distortionless (MVDR) beamformer for multichannel speech enhancement. A free Python implementation is also provided.

We present a joint audio-visual model for isolating a single speech signal from a mixture of sounds such as other speakers and background noise. Solving this task using only audio as input is extremely challenging and does not provide an association of the separated speech signals with speakers in the video. In this paper, we present a deep network-based model that incorporates both visual and auditory signals to solve this task. The visual features are used to "focus" the audio on desired speakers in a scene and to improve the speech separation quality. To train our joint audio-visual model, we introduce AVSpeech, a new dataset comprised of thousands of hours of video segments from the Web. We demonstrate the applicability of our method to classic speech separation tasks, as well as real-world scenarios involving heated interviews, noisy bars, and screaming children, only requiring the user to specify the face of the person in the video whose speech they want to isolate. Our method shows clear advantage over state-of-the-art audio-only speech separation in cases of mixed speech. In addition, our model, which is speaker-independent (trained once, applicable to any speaker), produces better results than recent audio-visual speech separation methods that are speaker-dependent (require training a separate model for each speaker of interest).

Hyperspectral unmixing is one of the crucial steps for many hyperspectral applications. The problem of hyperspectral unmixing has proven to be a difficult task in unsupervised work settings where the endmembers and abundances are both unknown. What is more, this task becomes more challenging in the case that the spectral bands are degraded with noise. This paper presents a robust model for unsupervised hyperspectral unmixing. Specifically, our model is developed with the correntropy based metric where the non-negative constraints on both endmembers and abundances are imposed to keep physical significance. In addition, a sparsity prior is explicitly formulated to constrain the distribution of the abundances of each endmember. To solve our model, a half-quadratic optimization technique is developed to convert the original complex optimization problem into an iteratively re-weighted NMF with sparsity constraints. As a result, the optimization of our model can adaptively assign small weights to noisy bands and give more emphasis on noise-free bands. In addition, with sparsity constraints, our model can naturally generate sparse abundances. Experiments on synthetic and real data demonstrate the effectiveness of our model in comparison to the related state-of-the-art unmixing models.

Source separation for music is the task of isolating contributions, or stems, from different instruments recorded individually and arranged together to form a song. Such components include voice, bass, drums and any other accompaniments.Contrarily to many audio synthesis tasks where the best performances are achieved by models that directly generate the waveform, the state-of-the-art in source separation for music is to compute masks on the magnitude spectrum. In this paper, we compare two waveform domain architectures. We first adapt Conv-Tasnet, initially developed for speech source separation,to the task of music source separation. While Conv-Tasnet beats many existing spectrogram-domain methods, it suffersfrom significant artifacts, as shown by human evaluations. We propose instead Demucs, a novel waveform-to-waveform model,with a U-Net structure and bidirectional LSTM.Experiments on the MusDB dataset show that, with proper data augmentation, Demucs beats allexisting state-of-the-art architectures, including Conv-Tasnet, with 6.3 SDR on average, (and up to 6.8 with 150 extra training songs, even surpassing the IRM oracle for the bass source).Using recent development in model quantization, Demucs can be compressed down to 120MBwithout any loss of accuracy.We also provide human evaluations, showing that Demucs benefit from a large advantagein terms of the naturalness of the audio. However, it suffers from some bleeding,especially between the vocals and other source.

We observe that despite their hierarchical convolutional nature, the synthesis process of typical generative adversarial networks depends on absolute pixel coordinates in an unhealthy manner. This manifests itself as, e.g., detail appearing to be glued to image coordinates instead of the surfaces of depicted objects. We trace the root cause to careless signal processing that causes aliasing in the generator network. Interpreting all signals in the network as continuous, we derive generally applicable, small architectural changes that guarantee that unwanted information cannot leak into the hierarchical synthesis process. The resulting networks match the FID of StyleGAN2 but differ dramatically in their internal representations, and they are fully equivariant to translation and rotation even at subpixel scales. Our results pave the way for generative models better suited for video and animation.

Despite significant recent progress across multiple subtasks of audio source separation, few music source separation systems support separation beyond the four-stem vocals, drums, bass, and other (VDBO) setup. Of the very few current systems that support source separation beyond this setup, most continue to rely on an inflexible decoder setup that can only support a fixed pre-defined set of stems. Increasing stem support in these inflexible systems correspondingly requires increasing computational complexity, rendering extensions of these systems computationally infeasible for long-tail instruments. In this work, we propose Banquet, a system that allows source separation of multiple stems using just one decoder. A bandsplit source separation model is extended to work in a query-based setup in tandem with a music instrument recognition PaSST model. On the MoisesDB dataset, Banquet, at only 24.9 M trainable parameters, approached the performance level of the significantly more complex 6-stem Hybrid Transformer Demucs on VDBO stems and outperformed it on guitar and piano. The query-based setup allows for the separation of narrow instrument classes such as clean acoustic guitars, and can be successfully applied to the extraction of less common stems such as reeds and organs. Implementation is available at https://github.com/kwatcharasupat/query-bandit.

The sound codec's dual roles in minimizing data transmission latency and serving as tokenizers underscore its critical importance. Recent years have witnessed significant developments in codec models. The ideal sound codec should preserve content, paralinguistics, speakers, and audio information. However, the question of which codec achieves optimal sound information preservation remains unanswered, as in different papers, models are evaluated on their selected experimental settings. This study introduces Codec-SUPERB, an acronym for Codec sound processing Universal PERformance Benchmark. It is an ecosystem designed to assess codec models across representative sound applications and signal-level metrics rooted in sound domain knowledge.Codec-SUPERB simplifies result sharing through an online leaderboard, promoting collaboration within a community-driven benchmark database, thereby stimulating new development cycles for codecs. Furthermore, we undertake an in-depth analysis to offer insights into codec models from both application and signal perspectives, diverging from previous codec papers mainly concentrating on signal-level comparisons. Finally, we will release codes, the leaderboard, and data to accelerate progress within the community.

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where (a) the number of unknowns may potentially be larger than the number of observations and (b) f* admits a sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

In speech enhancement and source separation, signal-to-noise ratio is a ubiquitous objective measure of denoising/separation quality. A decade ago, the BSS_eval toolkit was developed to give researchers worldwide a way to evaluate the quality of their algorithms in a simple, fair, and hopefully insightful way: it attempted to account for channel variations, and to not only evaluate the total distortion in the estimated signal but also split it in terms of various factors such as remaining interference, newly added artifacts, and channel errors. In recent years, hundreds of papers have been relying on this toolkit to evaluate their proposed methods and compare them to previous works, often arguing that differences on the order of 0.1 dB proved the effectiveness of a method over others. We argue here that the signal-to-distortion ratio (SDR) implemented in the BSS_eval toolkit has generally been improperly used and abused, especially in the case of single-channel separation, resulting in misleading results. We propose to use a slightly modified definition, resulting in a simpler, more robust measure, called scale-invariant SDR (SI-SDR). We present various examples of critical failure of the original SDR that SI-SDR overcomes.

Deep generative models applied to audio have improved by a large margin the state-of-the-art in many speech and music related tasks. However, as raw waveform modelling remains an inherently difficult task, audio generative models are either computationally intensive, rely on low sampling rates, are complicated to control or restrict the nature of possible signals. Among those models, Variational AutoEncoders (VAE) give control over the generation by exposing latent variables, although they usually suffer from low synthesis quality. In this paper, we introduce a Realtime Audio Variational autoEncoder (RAVE) allowing both fast and high-quality audio waveform synthesis. We introduce a novel two-stage training procedure, namely representation learning and adversarial fine-tuning. We show that using a post-training analysis of the latent space allows a direct control between the reconstruction fidelity and the representation compactness. By leveraging a multi-band decomposition of the raw waveform, we show that our model is the first able to generate 48kHz audio signals, while simultaneously running 20 times faster than real-time on a standard laptop CPU. We evaluate synthesis quality using both quantitative and qualitative subjective experiments and show the superiority of our approach compared to existing models. Finally, we present applications of our model for timbre transfer and signal compression. All of our source code and audio examples are publicly available.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Previous research has shown that the principal singular vectors of a pre-trained model's weight matrices capture critical knowledge. In contrast, those associated with small singular values may contain noise or less reliable information. As a result, the LoRA-based parameter-efficient fine-tuning (PEFT) approach, which does not constrain the use of the spectral space, may not be effective for tasks that demand high representation capacity. In this study, we enhance existing PEFT techniques by incorporating the spectral information of pre-trained weight matrices into the fine-tuning process. We investigate spectral adaptation strategies with a particular focus on the additive adjustment of top singular vectors. This is accomplished by applying singular value decomposition (SVD) to the pre-trained weight matrices and restricting the fine-tuning within the top spectral space. Extensive speaker verification experiments on VoxCeleb1 and CN-Celeb1 demonstrate enhanced tuning performance with the proposed approach. Code is released at https://github.com/lizhepolyu/SpectralFT.

Hyperspectral image (HSI) restoration aims at recovering clean images from degraded observations and plays a vital role in downstream tasks. Existing model-based methods have limitations in accurately modeling the complex image characteristics with handcraft priors, and deep learning-based methods suffer from poor generalization ability. To alleviate these issues, this paper proposes an unsupervised HSI restoration framework with pre-trained diffusion model (HIR-Diff), which restores the clean HSIs from the product of two low-rank components, i.e., the reduced image and the coefficient matrix. Specifically, the reduced image, which has a low spectral dimension, lies in the image field and can be inferred from our improved diffusion model where a new guidance function with total variation (TV) prior is designed to ensure that the reduced image can be well sampled. The coefficient matrix can be effectively pre-estimated based on singular value decomposition (SVD) and rank-revealing QR (RRQR) factorization. Furthermore, a novel exponential noise schedule is proposed to accelerate the restoration process (about 5times acceleration for denoising) with little performance decrease. Extensive experimental results validate the superiority of our method in both performance and speed on a variety of HSI restoration tasks, including HSI denoising, noisy HSI super-resolution, and noisy HSI inpainting. The code is available at https://github.com/LiPang/HIRDiff.

Audio codec models are widely used in audio communication as a crucial technique for compressing audio into discrete representations. Nowadays, audio codec models are increasingly utilized in generation fields as intermediate representations. For instance, AudioLM is an audio generation model that uses the discrete representation of SoundStream as a training target, while VALL-E employs the Encodec model as an intermediate feature to aid TTS tasks. Despite their usefulness, two challenges persist: (1) training these audio codec models can be difficult due to the lack of publicly available training processes and the need for large-scale data and GPUs; (2) achieving good reconstruction performance requires many codebooks, which increases the burden on generation models. In this study, we propose a group-residual vector quantization (GRVQ) technique and use it to develop a novel High Fidelity Audio Codec model, HiFi-Codec, which only requires 4 codebooks. We train all the models using publicly available TTS data such as LibriTTS, VCTK, AISHELL, and more, with a total duration of over 1000 hours, using 8 GPUs. Our experimental results show that HiFi-Codec outperforms Encodec in terms of reconstruction performance despite requiring only 4 codebooks. To facilitate research in audio codec and generation, we introduce AcademiCodec, the first open-source audio codec toolkit that offers training codes and pre-trained models for Encodec, SoundStream, and HiFi-Codec. Code and pre-trained model can be found on: https://github.com/yangdongchao/AcademiCodec{https://github.com/yangdongchao/AcademiCodec}

Circuit analysis of any certain model behavior is a central task in mechanistic interpretability. We introduce our circuit discovery pipeline with Sparse Autoencoders (SAEs) and a variant called Transcoders. With these two modules inserted into the model, the model's computation graph with respect to OV and MLP circuits becomes strictly linear. Our methods do not require linear approximation to compute the causal effect of each node. This fine-grained graph identifies both end-to-end and local circuits accounting for either logits or intermediate features. We can scalably apply this pipeline with a technique called Hierarchical Attribution. We analyze three kinds of circuits in GPT-2 Small: bracket, induction, and Indirect Object Identification circuits. Our results reveal new findings underlying existing discoveries.

We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we propose an innovative second-order algorithm that employs a Newton-type method with hard thresholding. This algorithm overcomes the linear convergence limitations of first-order methods while preserving their hallmark per-iteration computational efficiency. We provide theoretical guarantees that our algorithm converges to the s-sparse ground truth signal x^{natural} in R^n (up to a global sign) at a quadratic convergence rate after at most O(log (Vertx^{natural} Vert /x_{min}^{natural})) iterations, using Omega(s^2log n) Gaussian random samples. Numerical experiments show that our algorithm achieves a significantly faster convergence rate than state-of-the-art methods.

This paper deals with the problem of audio source separation. To handle the complex and ill-posed nature of the problems of audio source separation, the current state-of-the-art approaches employ deep neural networks to obtain instrumental spectra from a mixture. In this study, we propose a novel network architecture that extends the recently developed densely connected convolutional network (DenseNet), which has shown excellent results on image classification tasks. To deal with the specific problem of audio source separation, an up-sampling layer, block skip connection and band-dedicated dense blocks are incorporated on top of DenseNet. The proposed approach takes advantage of long contextual information and outperforms state-of-the-art results on SiSEC 2016 competition by a large margin in terms of signal-to-distortion ratio. Moreover, the proposed architecture requires significantly fewer parameters and considerably less training time compared with other methods.

This paper presents a novel radar signal detection pipeline focused on detecting large targets such as cars and SUVs. Traditional methods, such as Ordered-Statistic Constant False Alarm Rate (OS-CFAR), commonly used in automotive radar, are designed for point or isotropic target models. These may not adequately capture the Range-Doppler (RD) scattering patterns of larger targets, especially in high-resolution radar systems. Additional modules such as association and tracking are necessary to refine and consolidate the detections over multiple dwells. To address these limitations, we propose a detection technique based on the probability density function (pdf) of RD segments, leveraging the Kolmogorov-Arnold neural network (KAN) to learn the data and generate interpretable symbolic expressions for binary hypotheses. Beside the Monte-Carlo study showing better performance for the proposed KAN expression over OS-CFAR, it is shown to exhibit a probability of detection (PD) of 96% when transfer learned with field data. The false alarm rate (PFA) is comparable with OS-CFAR designed with PFA = 10^{-6}. Additionally, the study also examines impact of the number of pdf bins representing RD segment on performance of the KAN-based detection.

Component-level audio Spoofing (Comp-Spoof) targets a new form of audio manipulation where only specific components of a signal, such as speech or environmental sound, are forged or substituted while other components remain genuine. Existing anti-spoofing datasets and methods treat an utterance or a segment as entirely bona fide or entirely spoofed, and thus cannot accurately detect component-level spoofing. To address this, we construct a new dataset, CompSpoof, covering multiple combinations of bona fide and spoofed speech and environmental sound. We further propose a separation-enhanced joint learning framework that separates audio components apart and applies anti-spoofing models to each one. Joint learning is employed, preserving information relevant for detection. Extensive experiments demonstrate that our method outperforms the baseline, highlighting the necessity of separate components and the importance of detecting spoofing for each component separately. Datasets and code are available at: https://github.com/XuepingZhang/CompSpoof.

To achieve promising results on removing noise from real-world images, most of existing denoising networks are formulated with complex network structure, making them impractical for deployment. Some attempts focused on reducing the number of filters and feature channels but suffered from large performance loss, and a more practical and lightweight denoising network with fast inference speed is of high demand. To this end, a Thumbnail based Denoising Network dubbed Thunder, is proposed and implemented as a lightweight structure for fast restoration without comprising the denoising capabilities. Specifically, the Thunder model contains two newly-established modules: (1) a wavelet-based Thumbnail Subspace Encoder (TSE) which can leverage sub-bands correlation to provide an approximate thumbnail based on the low-frequent feature; (2) a Subspace Projection based Refine Module (SPR) which can restore the details for thumbnail progressively based on the subspace projection approach. Extensive experiments have been carried out on two real-world denoising benchmarks, demonstrating that the proposed Thunder outperforms the existing lightweight models and achieves competitive performance on PSNR and SSIM when compared with the complex designs.