Note CS inequality for matrix allows penalizing element-wise Frobenius norm to encourage low-rank representations.

Note Some token have more synonyms than others.

Note Customize attention mask with optimized performance comparable with Flashattention

Note Halve KV cache via sharing value embedding across attention blocks

Note PBRS (Potential Based Reward Shaping) can be used for gated regularization

Note Occam razor's principle expressed in mathematical term inspires new ways of training LLM to rely less on quantify of data.

Note The 'learnability' metric require training a small LM beforehand instead of computed online, in that sense, selecting 'easy-to-learn' sample is an old idea.

Note Using a neural network to directly predict outputs makes inference fast but makes search-based reasoning at inference time feel unnatural. In contrast, training a network to predict a loss function naturally supports gradient-based search at inference time—more aligned with tasks like image generation in continuous domains. However, this approach is 3× heavier at both training and inference.

Note Deep learning tends to favor high-entropy representation.

Note Training to stream with monotonously increasing noise level.

Note Current-token prediction with [Mask] token embedding. Iterative inference with re-masking on high-perplexity token.

Note Current-token prediction with interpolated [Mask]--[Predicted Token] embedding

Note Identified the right problem for diffusion language modeling: I can't imagine what I'd say 5 words away without saying the 5 words first.

Note coarse to fine generation with recursive forward propagation

Note Lots of computation process can't be parallelized, speeding up serial computation is also desirable.

Note Recurrent model at multiple levels, aligned in different temporal scales.

Note Down-scale impact of hard examples improve cross entropy loss in post-training stage, a.k.a. "don't break anything yo dog"

Note GRPO training is unstable for MoE model because token_ratio = policy_new(token) / policy_old(token) easily spikes under different routing choices for old and new policies. GSPO instead uses seq_ratio = policy_new(seq) / policy_old(seq) and find this to be more stable.

Note When SFT demo data & RL signal are both available, add two loss together and optimize, when model sucks weight more on SFT and vice versa. Duh..

Note Good.

Note I think the "continuous manifold of semantic space when reasoning token approaches infinity" breaks when they introduce a metric based on "prefix" and then "distance" ...

Note Removing KL regularization loss is not the same as having no KL regularization. PPO style clipping is a powerful implicit KL regularization techniques, we'd be stupid to ignore it and rediscover: hey! this thing reduces KL deviation ...

Note Manual rollout & selection for reasoning process with perplexity target.

Note Creating "path of least resistance" via a prior stage with bottleneck training to encourage latent dependency

Note "Random" mask of frame for reconstruction is important to avoid the "global reconstruction" trap which ignores many important local feature that's obvious for human cognition.

Note Bit of an over-reach: essentially we use teacher model to 'grade' summary of student model, and compute 'group relative advantage', claiming equivalence to mutual information is like claiming GRPO optimizes mutual information, fine but redundant.