README.md

---
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:98112
- loss:MultipleNegativesRankingLoss
base_model: thenlper/gte-small
widget:
- source_sentence: How does a photocell control outdoor lighting?
  sentences:
  - 'To solve this problem, we can use the binomial probability formula:


    P(X = k) = C(n, k) * p^k * (1-p)^(n-k)


    where:

    - P(X = k) is the probability of exactly k successes (faulty keyboards) in n trials
    (laptops produced)

    - C(n, k) is the number of combinations of n items taken k at a time (n! / (k!(n-k)!))

    - p is the probability of success (5% or 0.05)

    - n is the number of trials (400 laptops)

    - k is the number of successes (20 faulty keyboards)


    However, we want to find the probability of at least 20 faulty keyboards, so we
    need to find the sum of probabilities for k = 20, 21, 22, ..., 400.


    P(X >= 20) = 1 - P(X < 20) = 1 - Σ P(X = k) for k = 0 to 19


    Now, we can calculate the probabilities for each value of k and sum them up:


    P(X >= 20) = 1 - Σ C(400, k) * 0.05^k * 0.95^(400-k) for k = 0 to 19


    Using a calculator or software to compute the sum, we get:


    P(X >= 20) ≈ 1 - 0.0184 = 0.9816


    So, the probability that at least 20 laptops will have a faulty keyboard is approximately
    98.16%.'
  - A photocell controls outdoor lighting by detecting the level of ambient light.
    It automatically turns the lights on when it becomes dark and off when it becomes
    light, functioning as a light-dependent switch for energy efficiency and convenience.
  - 'Glycosylation with β-N-acetylglucosamine (O-GlcNAcylation) is one of the most
    complex post-translational modifications. The cycling of O-GlcNAc is controlled
    by two enzymes: UDP-NAc transferase (OGT) and O-GlcNAcase (OGA). We recently reported
    that endothelin-1 (ET-1) augments vascular levels of O-GlcNAcylated proteins.
    Here we tested the hypothesis that O-GlcNAcylation contributes to the vascular
    effects of ET-1 via activation of the RhoA/Rho-kinase pathway. Incubation of vascular
    smooth muscle cells (VSMCs) with ET-1 (0.1 μM) produces a time-dependent increase
    in O-GlcNAc levels. ET-1-induced O-GlcNAcylation is not observed when VSMCs are
    previously transfected with OGT siRNA, treated with ST045849 (OGT inhibitor) or
    atrasentan (ET(A) antagonist). ET-1 as well as PugNAc (OGA inhibitor) augmented
    contractions to phenylephrine in endothelium-denuded rat aortas, an effect that
    was abolished by the Rho kinase inhibitor Y-27632. Incubation of VSMCs with ET-1
    increased expression of the phosphorylated forms of myosin phosphatase target
    subunit 1 (MYPT-1), protein kinase C-potentiated protein phosphatase 1 inhibitor
    protein (protein kinase C-potentiated phosphatase inhibitor-17), and myosin light
    chain (MLC) and RhoA expression and activity, and this effect was abolished by
    both OGT siRNA transfection or OGT inhibition and atrasentan. ET-1 also augmented
    expression of PDZ-Rho GEF (guanine nucleotide exchange factor) and p115-Rho GEF
    in VSMCs and this was prevented by OGT siRNA, ST045849, and atrasentan.'
- source_sentence: A torus has a major radius of 5 cm and a minor radius of 3 cm.
    Find the volume of the torus.
  sentences:
  - 'To find the Hausdorff dimension of the Koch curve, we can use the formula:


    Hausdorff dimension (D) = log(N) / log(1/s)


    where N is the number of self-similar pieces and s is the scaling factor.


    For the Koch curve, each line segment is divided into four segments, each of which
    is 1/3 the length of the original segment. Therefore, N = 4 and s = 1/3.


    Now, we can plug these values into the formula:


    D = log(4) / log(1/3)


    D ≈ 1.2619


    So, the Hausdorff dimension of the Koch curve is approximately 1.2619.'
  - 'To find the volume of a torus, we can use the formula:


    Volume = (π * minor_radius^2) * (2 * π * major_radius)


    where minor_radius is the minor radius of the torus and major_radius is the major
    radius of the torus.


    Given that the major radius is 5 cm and the minor radius is 3 cm, we can plug
    these values into the formula:


    Volume = (π * 3^2) * (2 * π * 5)


    Volume = (π * 9) * (10 * π)


    Volume = 90 * π^2


    The volume of the torus is approximately 282.74 cubic centimeters.'
  - The purpose of the present study was to elucidate the mechanisms of action mediating
    enhancement of basal glucose uptake in skeletal muscle cells by seven medicinal
    plant products recently identified from the pharmacopeia of native Canadian populations
    (Spoor et al., 2006). Activity of the major signaling pathways that regulate glucose
    uptake was assessed by western immunoblot in C2C12 muscle cells treated with extracts
    from these plant species. Effects of extracts on mitochondrial function were assessed
    by respirometry in isolated rat liver mitochondria. Metabolic stress induced by
    extracts was assessed by measuring ATP concentration and rate of cell medium acidification
    in C2C12 myotubes and H4IIE hepatocytes. Extracts were applied at a dose of 15-100
    microg/ml. The effect of all seven products was achieved through a common mechanism
    mediated not by the insulin signaling pathway but rather by the AMP-activated
    protein kinase (AMPK) pathway in response to the disruption of mitochondrial function
    and ensuing metabolic stress. Disruption of mitochondrial function occurred in
    the form of uncoupling of oxidative phosphorylation and/or inhibition of ATPsynthase.
    Activity of the AMPK pathway, in some instances comparable to that stimulated
    by 4mM of the AMP-mimetic AICAR, was in several cases sustained for at least 18h
    post-treatment. Duration of metabolic stress, however, was in most cases in the
    order of 1h.
- source_sentence: Consider the elliptic curve given by the equation $y^2=x^3-2x+5$
    over the field of rational numbers $\mathbb{Q}$. Let $P=(1,2)$ and $Q=(-1,2)$
    be two points on the curve. Find the equation of the line passing through $P$
    and $Q$ and show that it intersects the curve at another point $R$. Then, find
    the coordinates of the point $R$.
  sentences:
  - Fifteen novel derivatives of D-DIBOA, including aromatic ring modifications and
    the addition of side chains in positions C-2 and N-4, had previously been synthesised
    and their phytotoxicity on standard target species (STS) evaluated. This strategy
    combined steric, electronic, solubility and lipophilicity requirements to achieve
    the maximum phytotoxic activity. An evaluation of the bioactivity of these compounds
    on the systems Oryza sativa-Echinochloa crus-galli and Triticum aestivum-Avena
    fatua is reported here. All compounds showed inhibition profiles on the two species
    Echinochloa crus-galli (L.) Beauv. and Avena fatua L. The most marked effects
    were caused by 6F-4Pr-D-DIBOA, 6F-4Val-D-DIBOA, 6Cl-4Pr-D-DIBOA and 6Cl-4Val-D-DIBOA.
    The IC(50) values for the systems Echinochloa crus-galli-Oryza sativa and Avena
    fatua-Triticum aestivum for all compounds were compared. The compound that showed
    the greatest selectivity for the system Echinochloa crus-galli-Oryza sativa was
    8Cl-4Pr-D-DIBOA, which was 15 times more selective than the commercial herbicide
    propanil (Cotanil-35). With regard to the system Avena fatua-Triticum aestivum,
    the compounds that showed the highest selectivities were 8Cl-4Val-D-DIBOA and
    6F-4Pr-D-DIBOA. The results obtained for 6F-4Pr-D-DIBOA are of great interest
    because of the high phytotoxicity to Avena fatua (IC(50) = 6 µM, r(2) = 0.9616).
  - 'To find the equation of the line passing through points $P=(1,2)$ and $Q=(-1,2)$,
    we first find the slope of the line. Since the y-coordinates of both points are
    the same, the slope is 0. Therefore, the line is horizontal and its equation is
    given by:


    $y = 2$


    Now, we want to find the point $R$ where this line intersects the elliptic curve
    $y^2 = x^3 - 2x + 5$. Since we know that $y=2$, we can substitute this value into
    the equation of the curve:


    $(2)^2 = x^3 - 2x + 5$


    Simplifying, we get:


    $4 = x^3 - 2x + 5$


    Rearranging the terms, we have:


    $x^3 - 2x + 1 = 0$


    We know that $x=1$ and $x=-1$ are solutions to this equation since they correspond
    to the points $P$ and $Q$. To find the third solution, we can use synthetic division
    or factor the polynomial. Factoring, we get:


    $(x-1)(x+1)(x-1) = 0$


    So, the third solution is $x=1$. Substituting this value back into the equation
    of the line, we find the corresponding y-coordinate:


    $y = 2$


    Thus, the third point of intersection is $R=(1,2)$. However, in the context of
    elliptic curves, we should take the "sum" of the points $P$ and $Q$ as the negative
    of the third intersection point. Since $R=(1,2)$, the negative of this point is
    given by $-R=(1,-2)$. Therefore, the "sum" of the points $P$ and $Q$ on the elliptic
    curve is:


    $P + Q = -R = (1,-2)$.'
  - The use of geospatial analysis may be subject to regulatory compliance depending
    on the specific application and the jurisdiction in which it is used. For example,
    the use of geospatial data for marketing purposes may be subject to privacy regulations,
    and the use of geospatial data for land use planning may be subject to environmental
    regulations. It is important to consult with legal counsel to ensure compliance
    with all applicable laws and regulations.
- source_sentence: Does sLEDAI-2K Conceal Worsening in a Particular System When There
    Is Overall Improvement?
  sentences:
  - To determine whether the Systemic Lupus Erythematosus Disease Activity Index 2000
    (SLEDAI-2K) is valid in identifying patients who had a clinically important overall
    improvement with no worsening in other descriptors/systems. Consecutive patients
    with systemic lupus erythematosus with active disease who attended the Lupus Clinic
    between 2000 and 2012 were studied. Based on the change in the total SLEDAI-2K
    scores on last visit, patients were grouped as improved, flared/worsened, and
    unchanged. Patients showing improvement were evaluated for the presence of new
    active descriptors at last visit compared with baseline visit. Of the 158 patients
    studied, 109 patients had improved, 38 remained unchanged, and 11 flared/worsened
    at last visit. In the improved group, 11 patients had a new laboratory descriptor
    that was not present at baseline visit. In those 11 patients, this new laboratory
    descriptor was not clinically significant and did not require a change in disease
    management.
  - 'To find the dot product of two vectors using their magnitudes, angle between
    them, and trigonometry, we can use the formula:


    Dot product = |A| * |B| * cos(θ)


    where |A| and |B| are the magnitudes of the vectors, and θ is the angle between
    them.


    In this case, |A| = 5 units, |B| = 8 units, and θ = 60 degrees.


    First, we need to convert the angle from degrees to radians:


    θ = 60 * (π / 180) = π / 3 radians


    Now, we can find the dot product:


    Dot product = 5 * 8 * cos(π / 3)

    Dot product = 40 * (1/2)

    Dot product = 20


    So, the dot product of the two vectors is 20.'
  - To determine if hospitals that routinely discharge patients early after lobectomy
    have increased readmissions. Hospitals are increasingly motivated to reduce length
    of stay (LOS) after lung cancer surgery, yet it is unclear if a routine of early
    discharge is associated with increased readmissions. The relationship between
    hospital discharge practices and readmission rates is therefore of tremendous
    clinical and financial importance. The National Cancer Database was queried for
    patients undergoing lobectomy for lung cancer from 2004 to 2013 at Commission
    on Cancer-accredited hospitals, which performed at least 25 lobectomies in a 2-year
    period. Facility discharge practices were characterized by a facility's median
    LOS relative to the median LOS for all patients in that same time period. In all,
    59,734 patients met inclusion criteria; 2687 (4.5%) experienced an unplanned readmission.
    In a hierarchical logistic regression model, a routine of early discharge (defined
    as a facility's tendency to discharge patients faster than the population median
    in the same time period) was not associated with increased risk of readmission
    (odds ratio 1.12, 95% confidence interval 0.97-1.28, P = 0.12). In a risk-adjusted
    hospital readmission rate analysis, hospitals that discharged patients early did
    not experience more readmissions (P = 0.39). The lack of effect of early discharge
    practices on readmission rates was observed for both minimally invasive and thoracotomy
    approaches.
- source_sentence: Does systemic administration of urocortin after intracerebral hemorrhage
    reduce neurological deficits and neuroinflammation in rats?
  sentences:
  - Intracerebral hemorrhage (ICH) remains a serious clinical problem lacking effective
    treatment. Urocortin (UCN), a novel anti-inflammatory neuropeptide, protects injured
    cardiomyocytes and dopaminergic neurons. Our preliminary studies indicate UCN
    alleviates ICH-induced brain injury when administered intracerebroventricularly
    (ICV). The present study examines the therapeutic effect of UCN on ICH-induced
    neurological deficits and neuroinflammation when administered by the more convenient
    intraperitoneal (i.p.) route. ICH was induced in male Sprague-Dawley rats by intrastriatal
    infusion of bacterial collagenase VII-S or autologous blood. UCN (2.5 or 25 μg/kg)
    was administered i.p. at 60 minutes post-ICH. Penetration of i.p. administered
    fluorescently labeled UCN into the striatum was examined by fluorescence microscopy.
    Neurological deficits were evaluated by modified neurological severity score (mNSS).
    Brain edema was assessed using the dry/wet method. Blood-brain barrier (BBB) disruption
    was assessed using the Evans blue assay. Hemorrhagic volume and lesion volume
    were assessed by Drabkin's method and morphometric assay, respectively. Pro-inflammatory
    cytokine (TNF-α, IL-1β, and IL-6) expression was evaluated by enzyme-linked immunosorbent
    assay (ELISA). Microglial activation and neuronal loss were evaluated by immunohistochemistry.
    Administration of UCN reduced neurological deficits from 1 to 7 days post-ICH.
    Surprisingly, although a higher dose (25 μg/kg, i.p.) also reduced the functional
    deficits associated with ICH, it is significantly less effective than the lower
    dose (2.5 μg/kg, i.p.). Beneficial results with the low dose of UCN included a
    reduction in neurological deficits from 1 to 7 days post-ICH, as well as a reduction
    in brain edema, BBB disruption, lesion volume, microglial activation and neuronal
    loss 3 days post-ICH, and suppression of TNF-α, IL-1β, and IL-6 production 1,
    3 and 7 days post-ICH.
  - 'A perfect number is a positive integer that is equal to the sum of its proper
    divisors (excluding itself). The first perfect numbers are 6, 28, 496, and 8128.
    Perfect numbers can be generated using the formula 2^(p-1) * (2^p - 1), where
    p and 2^p - 1 are both prime numbers.


    The first five (p, 2^p - 1) pairs are:

    (2, 3) - 6

    (3, 7) - 28

    (5, 31) - 496

    (7, 127) - 8128

    (13, 8191) - 33,550,336


    To find the 6th perfect number, we need to find the next prime number p such that
    2^p - 1 is also prime. The next such pair is (17, 131071). Using the formula:


    2^(17-1) * (2^17 - 1) = 2^16 * 131071 = 65,536 * 131071 = 8,589,869,056


    So, the 6th perfect number is 8,589,869,056.'
  - 'In type theory, the successor function $S$ is used to represent the next number
    in the sequence. When you apply the successor function $S$ three times to the
    number 0, you get:


    1. $S(0)$, which represents 1.

    2. $S(S(0))$, which represents 2.

    3. $S(S(S(0)))$, which represents 3.


    So, the result of applying the successor function $S$ three times to the number
    0 in type theory is 3.'
pipeline_tag: sentence-similarity
library_name: sentence-transformers
metrics:
- cosine_accuracy@1
- cosine_accuracy@3
- cosine_accuracy@5
- cosine_accuracy@10
- cosine_precision@1
- cosine_precision@3
- cosine_precision@5
- cosine_recall@1
- cosine_recall@3
- cosine_recall@5
- cosine_ndcg@10
- cosine_mrr@10
- cosine_map@100
model-index:
- name: SentenceTransformer based on thenlper/gte-small
  results:
  - task:
      type: logging
      name: Logging
    dataset:
      name: ir eval
      type: ir-eval
    metrics:
    - type: cosine_accuracy@1
      value: 0.9291020819957809
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.9819315784646427
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.9933963129413923
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.9984407961111621
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.9291020819957809
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.32731052615488093
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.19867926258827848
      name: Cosine Precision@5
    - type: cosine_recall@1
      value: 0.9291020819957809
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.9819315784646427
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.9933963129413923
      name: Cosine Recall@5
    - type: cosine_ndcg@10
      value: 0.9670096227619588
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.9565327512887825
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.9565967419425125
      name: Cosine Map@100
---

# SentenceTransformer based on thenlper/gte-small

This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [thenlper/gte-small](https://huggingface.co/thenlper/gte-small). It maps sentences & paragraphs to a 384-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more.

## Model Details

### Model Description
- **Model Type:** Sentence Transformer
- **Base model:** [thenlper/gte-small](https://huggingface.co/thenlper/gte-small) <!-- at revision 17e1f347d17fe144873b1201da91788898c639cd -->
- **Maximum Sequence Length:** 512 tokens
- **Output Dimensionality:** 384 dimensions
- **Similarity Function:** Cosine Similarity
<!-- - **Training Dataset:** Unknown -->
<!-- - **Language:** Unknown -->
<!-- - **License:** Unknown -->

### Model Sources

- **Documentation:** [Sentence Transformers Documentation](https://sbert.net)
- **Repository:** [Sentence Transformers on GitHub](https://github.com/UKPLab/sentence-transformers)
- **Hugging Face:** [Sentence Transformers on Hugging Face](https://huggingface.co/models?library=sentence-transformers)

### Full Model Architecture

```
SentenceTransformer(
  (0): Transformer({'max_seq_length': 512, 'do_lower_case': False}) with Transformer model: BertModel 
  (1): Pooling({'word_embedding_dimension': 384, 'pooling_mode_cls_token': False, 'pooling_mode_mean_tokens': True, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True})
  (2): Normalize()
)
```

## Usage

### Direct Usage (Sentence Transformers)

First install the Sentence Transformers library:

```bash
pip install -U sentence-transformers
```

Then you can load this model and run inference.
```python
from sentence_transformers import SentenceTransformer

# Download from the 🤗 Hub
model = SentenceTransformer("sucharush/gte_MNR")
# Run inference
sentences = [
    'Does systemic administration of urocortin after intracerebral hemorrhage reduce neurological deficits and neuroinflammation in rats?',
    "Intracerebral hemorrhage (ICH) remains a serious clinical problem lacking effective treatment. Urocortin (UCN), a novel anti-inflammatory neuropeptide, protects injured cardiomyocytes and dopaminergic neurons. Our preliminary studies indicate UCN alleviates ICH-induced brain injury when administered intracerebroventricularly (ICV). The present study examines the therapeutic effect of UCN on ICH-induced neurological deficits and neuroinflammation when administered by the more convenient intraperitoneal (i.p.) route. ICH was induced in male Sprague-Dawley rats by intrastriatal infusion of bacterial collagenase VII-S or autologous blood. UCN (2.5 or 25 μg/kg) was administered i.p. at 60 minutes post-ICH. Penetration of i.p. administered fluorescently labeled UCN into the striatum was examined by fluorescence microscopy. Neurological deficits were evaluated by modified neurological severity score (mNSS). Brain edema was assessed using the dry/wet method. Blood-brain barrier (BBB) disruption was assessed using the Evans blue assay. Hemorrhagic volume and lesion volume were assessed by Drabkin's method and morphometric assay, respectively. Pro-inflammatory cytokine (TNF-α, IL-1β, and IL-6) expression was evaluated by enzyme-linked immunosorbent assay (ELISA). Microglial activation and neuronal loss were evaluated by immunohistochemistry. Administration of UCN reduced neurological deficits from 1 to 7 days post-ICH. Surprisingly, although a higher dose (25 μg/kg, i.p.) also reduced the functional deficits associated with ICH, it is significantly less effective than the lower dose (2.5 μg/kg, i.p.). Beneficial results with the low dose of UCN included a reduction in neurological deficits from 1 to 7 days post-ICH, as well as a reduction in brain edema, BBB disruption, lesion volume, microglial activation and neuronal loss 3 days post-ICH, and suppression of TNF-α, IL-1β, and IL-6 production 1, 3 and 7 days post-ICH.",
    'In type theory, the successor function $S$ is used to represent the next number in the sequence. When you apply the successor function $S$ three times to the number 0, you get:\n\n1. $S(0)$, which represents 1.\n2. $S(S(0))$, which represents 2.\n3. $S(S(S(0)))$, which represents 3.\n\nSo, the result of applying the successor function $S$ three times to the number 0 in type theory is 3.',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 384]

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]
```

<!--
### Direct Usage (Transformers)

<details><summary>Click to see the direct usage in Transformers</summary>

</details>
-->

<!--
### Downstream Usage (Sentence Transformers)

You can finetune this model on your own dataset.

<details><summary>Click to expand</summary>

</details>
-->

<!--
### Out-of-Scope Use

*List how the model may foreseeably be misused and address what users ought not to do with the model.*
-->

## Evaluation

### Metrics

#### Logging

* Dataset: `ir-eval`
* Evaluated with <code>__main__.LoggingEvaluator</code>

| Metric             | Value     |
|:-------------------|:----------|
| cosine_accuracy@1  | 0.9291    |
| cosine_accuracy@3  | 0.9819    |
| cosine_accuracy@5  | 0.9934    |
| cosine_accuracy@10 | 0.9984    |
| cosine_precision@1 | 0.9291    |
| cosine_precision@3 | 0.3273    |
| cosine_precision@5 | 0.1987    |
| cosine_recall@1    | 0.9291    |
| cosine_recall@3    | 0.9819    |
| cosine_recall@5    | 0.9934    |
| **cosine_ndcg@10** | **0.967** |
| cosine_mrr@10      | 0.9565    |
| cosine_map@100     | 0.9566    |

<!--
## Bias, Risks and Limitations

*What are the known or foreseeable issues stemming from this model? You could also flag here known failure cases or weaknesses of the model.*
-->

<!--
### Recommendations

*What are recommendations with respect to the foreseeable issues? For example, filtering explicit content.*
-->

## Training Details

### Training Dataset

#### Unnamed Dataset

* Size: 98,112 training samples
* Columns: <code>sentence_0</code> and <code>sentence_1</code>
* Approximate statistics based on the first 1000 samples:
  |         | sentence_0                                                                         | sentence_1                                                                          |
  |:--------|:-----------------------------------------------------------------------------------|:------------------------------------------------------------------------------------|
  | type    | string                                                                             | string                                                                              |
  | details | <ul><li>min: 6 tokens</li><li>mean: 44.14 tokens</li><li>max: 512 tokens</li></ul> | <ul><li>min: 12 tokens</li><li>mean: 321.5 tokens</li><li>max: 512 tokens</li></ul> |
* Samples:
  | sentence_0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | sentence_1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           |
  |:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  | <code>Are transcobalamin II receptor polymorphisms associated with increased risk for neural tube defects?</code>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          | <code>Women who have low cobalamin (vitamin B(12)) levels are at increased risk for having children with neural tube defects (NTDs). The transcobalamin II receptor (TCblR) mediates uptake of cobalamin into cells. Inherited variants in the TCblR gene as NTD risk factors were evaluated. Case-control and family-based tests of association were used to screen common variation in TCblR as genetic risk factors for NTDs in a large Irish group. A confirmatory group of NTD triads was used to test positive findings. 2 tightly linked variants associated with NTDs in a recessive model were found: TCblR rs2336573 (G220R; p(corr)=0.0080, corrected for multiple hypothesis testing) and TCblR rs9426 (p(corr)=0.0279). These variants were also associated with NTDs in a family-based test before multiple test correction (log-linear analysis of a recessive model: rs2336573 (G220R; RR=6.59, p=0.0037) and rs9426 (RR=6.71, p=0.0035)). A copy number variant distal to TCblR and two previously unreported exonic insertio...</code>                                                             |
  | <code>A company produces three products: Product A, B, and C. The monthly sales figures and marketing expenses (in thousands of dollars) for each product for the last six months are given below:<br><br>| Product | Sales1 | Sales2 | Sales3 | Sales4 | Sales5 | Sales6 | Marketing Expense1 | Marketing Expense2 | Marketing Expense3 | Marketing Expense4 | Marketing Expense5 | Marketing Expense6 |<br>|---------|--------|--------|--------|--------|--------|--------|--------------------|--------------------|--------------------|--------------------|--------------------|--------------------|<br>| A       | 50     | 45     | 55     | 52     | 48     | 56     | 20                  | 18                  | 25                  | 22                  | 19                  | 30                  |<br>| B       | 40     | 48     | 35     | 37     | 45     | 38     | 12                  | 15                  | 10                  | 14                  | 17                  | 11                  |<br>| C       | 60     | 65     | ...</code> | <code>To calculate the covariance between the sales of Product A and Product B, we first need to find the mean sales for both products. Then, we will calculate the deviations from the mean for each month's sales and multiply these deviations for both products. Finally, we will sum these products and divide by the number of months minus 1.<br><br>Mean sales for Product A:<br>(50 + 45 + 55 + 52 + 48 + 56) / 6 = 306 / 6 = 51<br><br>Mean sales for Product B:<br>(40 + 48 + 35 + 37 + 45 + 38) / 6 = 243 / 6 = 40.5<br><br>Deviations from the mean for Product A:<br>(50 - 51, 45 - 51, 55 - 51, 52 - 51, 48 - 51, 56 - 51) = (-1, -6, 4, 1, -3, 5)<br><br>Deviations from the mean for Product B:<br>(40 - 40.5, 48 - 40.5, 35 - 40.5, 37 - 40.5, 45 - 40.5, 38 - 40.5) = (-0.5, 7.5, -5.5, -3.5, 4.5, -2.5)<br><br>Multiply the deviations for both products:<br>(-1 * -0.5, -6 * 7.5, 4 * -5.5, 1 * -3.5, -3 * 4.5, 5 * -2.5) = (0.5, 45, -22, -3.5, -13.5, -12.5)<br><br>Sum of the products of deviations:<br>0.5 + 45 - 22 - 3.5 - 13.5 - 12.5 = -6<br><br>Covariance between the sale...</code> |
  | <code>Consider a basketball player who has a free-throw shooting percentage of 80%. The player attempts 10 free throws in a game. <br><br>If the player makes a free throw, there is an 80% chance that they will make their next free throw attempt. If they miss a free throw, there's a 60% chance that they will make their next free throw attempt.<br><br>What is the probability that the player makes exactly 7 out of their 10 free throw attempts?</code>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | <code>To solve this problem, we can use the concept of conditional probability and the binomial theorem. Let's denote the probability of making a free throw after a successful attempt as P(S) = 0.8 and the probability of making a free throw after a missed attempt as P(M) = 0.6.<br><br>We need to find the probability of making exactly 7 out of 10 free throw attempts. There are multiple ways this can happen, and we need to consider all possible sequences of 7 successes (S) and 3 misses (M). We can represent these sequences as a string of S and M, for example, SSSSSSSMMM.<br><br>There are C(10, 7) = 10! / (7! * 3!) = 120 ways to arrange 7 successes and 3 misses in a sequence of 10 attempts. For each of these sequences, we can calculate the probability of that specific sequence occurring and then sum up the probabilities of all sequences.<br><br>Let's calculate the probability of a specific sequence. For example, consider the sequence SSSSSSSMMM. The probability of this sequence occurring is:<br><br>P(SSSSSSSMMM) = P(S...</code>                                     |
* Loss: [<code>MultipleNegativesRankingLoss</code>](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#multiplenegativesrankingloss) with these parameters:
  ```json
  {
      "scale": 20.0,
      "similarity_fct": "cos_sim"
  }
  ```

### Training Hyperparameters
#### Non-Default Hyperparameters

- `eval_strategy`: steps
- `per_device_train_batch_size`: 32
- `per_device_eval_batch_size`: 32
- `num_train_epochs`: 1
- `batch_sampler`: no_duplicates
- `multi_dataset_batch_sampler`: round_robin

#### All Hyperparameters
<details><summary>Click to expand</summary>

- `overwrite_output_dir`: False
- `do_predict`: False
- `eval_strategy`: steps
- `prediction_loss_only`: True
- `per_device_train_batch_size`: 32
- `per_device_eval_batch_size`: 32
- `per_gpu_train_batch_size`: None
- `per_gpu_eval_batch_size`: None
- `gradient_accumulation_steps`: 1
- `eval_accumulation_steps`: None
- `torch_empty_cache_steps`: None
- `learning_rate`: 5e-05
- `weight_decay`: 0.0
- `adam_beta1`: 0.9
- `adam_beta2`: 0.999
- `adam_epsilon`: 1e-08
- `max_grad_norm`: 1
- `num_train_epochs`: 1
- `max_steps`: -1
- `lr_scheduler_type`: linear
- `lr_scheduler_kwargs`: {}
- `warmup_ratio`: 0.0
- `warmup_steps`: 0
- `log_level`: passive
- `log_level_replica`: warning
- `log_on_each_node`: True
- `logging_nan_inf_filter`: True
- `save_safetensors`: True
- `save_on_each_node`: False
- `save_only_model`: False
- `restore_callback_states_from_checkpoint`: False
- `no_cuda`: False
- `use_cpu`: False
- `use_mps_device`: False
- `seed`: 42
- `data_seed`: None
- `jit_mode_eval`: False
- `use_ipex`: False
- `bf16`: False
- `fp16`: False
- `fp16_opt_level`: O1
- `half_precision_backend`: auto
- `bf16_full_eval`: False
- `fp16_full_eval`: False
- `tf32`: None
- `local_rank`: 0
- `ddp_backend`: None
- `tpu_num_cores`: None
- `tpu_metrics_debug`: False
- `debug`: []
- `dataloader_drop_last`: False
- `dataloader_num_workers`: 0
- `dataloader_prefetch_factor`: None
- `past_index`: -1
- `disable_tqdm`: False
- `remove_unused_columns`: True
- `label_names`: None
- `load_best_model_at_end`: False
- `ignore_data_skip`: False
- `fsdp`: []
- `fsdp_min_num_params`: 0
- `fsdp_config`: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}
- `tp_size`: 0
- `fsdp_transformer_layer_cls_to_wrap`: None
- `accelerator_config`: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
- `deepspeed`: None
- `label_smoothing_factor`: 0.0
- `optim`: adamw_torch
- `optim_args`: None
- `adafactor`: False
- `group_by_length`: False
- `length_column_name`: length
- `ddp_find_unused_parameters`: None
- `ddp_bucket_cap_mb`: None
- `ddp_broadcast_buffers`: False
- `dataloader_pin_memory`: True
- `dataloader_persistent_workers`: False
- `skip_memory_metrics`: True
- `use_legacy_prediction_loop`: False
- `push_to_hub`: False
- `resume_from_checkpoint`: None
- `hub_model_id`: None
- `hub_strategy`: every_save
- `hub_private_repo`: None
- `hub_always_push`: False
- `gradient_checkpointing`: False
- `gradient_checkpointing_kwargs`: None
- `include_inputs_for_metrics`: False
- `include_for_metrics`: []
- `eval_do_concat_batches`: True
- `fp16_backend`: auto
- `push_to_hub_model_id`: None
- `push_to_hub_organization`: None
- `mp_parameters`: 
- `auto_find_batch_size`: False
- `full_determinism`: False
- `torchdynamo`: None
- `ray_scope`: last
- `ddp_timeout`: 1800
- `torch_compile`: False
- `torch_compile_backend`: None
- `torch_compile_mode`: None
- `include_tokens_per_second`: False
- `include_num_input_tokens_seen`: False
- `neftune_noise_alpha`: None
- `optim_target_modules`: None
- `batch_eval_metrics`: False
- `eval_on_start`: False
- `use_liger_kernel`: False
- `eval_use_gather_object`: False
- `average_tokens_across_devices`: False
- `prompts`: None
- `batch_sampler`: no_duplicates
- `multi_dataset_batch_sampler`: round_robin

</details>

### Training Logs
| Epoch  | Step | Training Loss | ir-eval_cosine_ndcg@10 |
|:------:|:----:|:-------------:|:----------------------:|
| 0.1631 | 500  | 0.0634        | 0.9563                 |
| 0.3262 | 1000 | 0.005         | 0.9627                 |
| 0.4892 | 1500 | 0.0037        | 0.9631                 |
| 0.6523 | 2000 | 0.0029        | 0.9660                 |
| 0.8154 | 2500 | 0.0033        | 0.9663                 |
| 0.9785 | 3000 | 0.0027        | 0.9670                 |
| 1.0    | 3066 | -             | 0.9670                 |


### Framework Versions
- Python: 3.12.8
- Sentence Transformers: 3.4.1
- Transformers: 4.51.3
- PyTorch: 2.5.1+cu124
- Accelerate: 1.3.0
- Datasets: 3.2.0
- Tokenizers: 0.21.0

## Citation

### BibTeX

#### Sentence Transformers
```bibtex
@inproceedings{reimers-2019-sentence-bert,
    title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
    author = "Reimers, Nils and Gurevych, Iryna",
    booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
    month = "11",
    year = "2019",
    publisher = "Association for Computational Linguistics",
    url = "https://arxiv.org/abs/1908.10084",
}
```

#### MultipleNegativesRankingLoss
```bibtex
@misc{henderson2017efficient,
    title={Efficient Natural Language Response Suggestion for Smart Reply},
    author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil},
    year={2017},
    eprint={1705.00652},
    archivePrefix={arXiv},
    primaryClass={cs.CL}
}
```

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