sentence-transformers tensorboard safetensors bert sentence-similarity feature-extraction generated_from_trainer dataset_size:21701 loss:CosineSimilarityLoss arxiv:1908.10084 base_model:sentence-transformers/all-MiniLM-L6-v2 base_model:finetune:sentence-transformers/all-MiniLM-L6-v2 autotrain_compatible text-embeddings-inference endpoints_compatible region:us
---
base_model: sentence-transformers/all-MiniLM-L6-v2
library_name: sentence-transformers
pipeline_tag: sentence-similarity
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:21701
- loss:CosineSimilarityLoss
widget:
- source_sentence: 'Let $p$ be a [[Definition:Prime Number|prime number]].Let $\struct
    {\Q_p, \norm {\,\cdot\,}_p}$ be the [[Definition:P-adic Number|$p$-adic numbers]].Let
    $a \in \Q_p$.For all $\epsilon \in \R_{>0}$, let $\map {B_\epsilon} a$ denote
    the [[Definition:Open Ball in P-adic Numbers|open $\epsilon$-ball]] of $a$. Then::$\forall
    n \in Z : \set{\map {B^-_{p^{-m} } } {a + i p^n} : i = 0, \dotsc, p^\paren {m
    - n} - 1}$ is a [[Definition:Set|set]] of [[Definition:Pairwise Disjoint|pairwise
    disjoint]] [[Definition:Open Ball of Normed Division Ring|open balls]].'
  sentences:
  - Let $n \in \Z_{> 0}$ be a [[Definition:Positive Integer|positive integer]].Let
    $I_n$ be defined as::$\displaystyle I_n = \int_0^{\frac \pi 2} \sin^n x \rd x$Then
    $\left\langle{I_n}\right\rangle$ is a [[Definition:Decreasing Real Sequence|decreasing
    sequence of real numbers]] which satisfies::$n I_n = \left({n - 1}\right) I_{n
    - 2}$Thus::$I_n = \dfrac {n - 1} n  I_{n - 2}$is a [[Definition:Reduction Formula|reduction
    formula]] for $I_n$.
  - 'Let $\struct {S, \preceq_1}$ be a [[Definition:Totally Ordered Set|totally ordered
    set]].Let $\struct {T, \preceq_2}$ be an [[Definition:Ordered Set|ordered set]].Let
    $\phi: S \to T$ be a [[Definition:Mapping|mapping]].Then $\phi$ is an [[Definition:Order
    Embedding|order embedding]] {{iff}} $\phi$ is [[Definition:Strictly Increasing
    Mapping|strictly increasing]].That is::$\forall x, y \in S: x \preceq_1 y \iff
    \map \phi x \preceq_2 \map \phi y${{iff}}::$\forall x, y \in S: x \prec_1 y \implies
    \map \phi x \prec_2 \map \phi y$'
  - The [[Definition:Quaternion Group|Quaternion Group]] can be [[Definition:Generator
    of Group|generated]] by the [[Definition:Square Matrix|matrices]]::$\mathbf a
    = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}\qquad\mathbf b = \begin{bmatrix}
    0 & i \\ i & 0 \end{bmatrix}$where $i$ is the [[Definition:Imaginary Unit|imaginary
    unit]]::$i^2 = -1$
- source_sentence: 'Let $\psi: S_1 \to S_2$ be defined by::$\forall x \in S_1: \map
    \psi x = \displaystyle \lim_{n \mathop \to \infty} \map {\psi''} {x_n}$where $x
    = \displaystyle \lim_{n \mathop \to \infty} x_n$ for some [[Definition:Sequence|sequence]]
    $\sequence {x_n} \subseteq R_1$Then $\psi$ is a [[Definition:Well-Defined Mapping|well-defined
    mapping]].'
  sentences:
  - Let $X$ be a [[Definition:Trivial Topological Space|trivial topological space]].Then
    $X$ is [[Definition:Indiscrete Space|indiscrete]].
  - Let $\omega \in A \setminus B$, where $A \setminus B$ denotes the [[Definition:Set
    Difference|difference]] of $A$ and $B$.Then '''$A$ [[Definition:Occurrence of
    Event|occurs]] but $B$ does not [[Definition:Occurrence of Event|occur]]'''.
  - === [[Definition:Cosine/Definition from Triangle|Definition from Triangle]] ==={{:Definition:Cosine/Definition
    from Triangle}}=== [[Definition:Cosine/Definition from Circle|Definition from
    Circle]] ==={{:Definition:Cosine/Definition from Circle}}=== [[Definition:Cosine/Real
    Function|Real Numbers]] ==={{:Definition:Cosine/Real Function}}=== [[Definition:Cosine/Complex
    Function|Complex Numbers]] ==={{:Definition:Cosine/Complex Function}}
- source_sentence: Let $S$ be a [[Definition:Finite Set|finite set]].Let $\mathscr
    B$ be a [[Definition:Non-Empty Set|non-empty]] [[Definition:Set|set]] of [[Definition:Subset|subsets]]
    of $S$ satisfying the [[Leigh.Samphier/Sandbox/Definition:Base Axiom (Matroid)/Definition
    1|base axiom]]:{{:Leigh.Samphier/Sandbox/Definition:Base Axiom (Matroid)/Definition
    1}}Then $\mathscr B$ is the set of [[Definition:Base of Matroid|bases]] of a [[Definition:Matroid|matroid]]
    on $S$.
  sentences:
  - Let $M = \struct{S,\mathscr I}$ be an [[Definition:Independence System|independence
    system]].
  - 'Let $F$ be a [[Definition:Subset|subset]] of $S_1$.$f$ ''''''preserves supremum
    of'''''' $F$ {{iff}}:$F$ admits a [[Definition:Supremum of Set|supremum]] in $\left({S_1,
    \preceq_1}\right)$ implies:: $f^\to \left({F}\right)$ admits a [[Definition:Supremum
    of Set|supremum]] in $\left({S_2, \preceq_2}\right)$ and $\sup \left({f^\to\left({F}\right)}\right)
    = f \left({\sup F}\right)$'
  - Let $\sequence {a_n}$ be a [[Definition:Sequence|sequence in $\R$]].If $\displaystyle
    \lim_{k \mathop \to \infty} a_k \ne 0$, then $\displaystyle \sum_{i \mathop =
    1}^\infty a_n$ [[Definition:Divergent Series|diverges]].
- source_sentence: Let $\alpha$, $\beta$ and $\gamma$ be [[Definition:Cut (Analysis)|cuts]].Let
    $\alpha \beta$ denote the [[Definition:Multiplication of Cuts|product]] of $\alpha$
    and $\beta$.Then::$\paren {\alpha \beta} \gamma = \alpha \paren {\beta \gamma}$
  sentences:
  - Let $m \in \Z$ such that $m > 1$.The '''additive group of integers modulo $m$'''
    $\struct {\Z_m, +_m}$ is the [[Definition:Set|set]] of [[Definition:Integers Modulo
    m|integers modulo $m$]] under the [[Definition:Binary Operation|operation]] of
    [[Definition:Modulo Addition|addition modulo $m$]].
  - 'Let $\left({S, \mathcal R}\right)$ be a [[Definition:Relational Structure|relational
    structure]], that is, a [[Definition:Set|set]] $S$ endowed with a [[Definition:Endorelation|binary
    relation]] $\mathcal R$.Let $T \subseteq S$ be a [[Definition:Subset|subset]]
    of $S$.Then $T$ is a ''''''cofinal subset of $S$ with respect to $\mathcal R$''''''
    {{iff}}::$\forall x \in S: \exists t \in T: x \mathop {\mathcal R} t$'
  - A '''Diophantine equation''' is an [[Definition:Indeterminate Equation|indeterminate]]
    [[Definition:Polynomial Equation|polynomial equation]] that allows the variables
    to take [[Definition:Integer|integer]] values only.
- source_sentence: Let $m$ be a [[Definition:Number|numbers]] which is presented to
    $d$ [[Definition:Significant Figures|significant figures]].Then the most [[Definition:Significant
    Figures|significant figures]] that $\sqrt m$ can have is also $d$.
  sentences:
  - :$\displaystyle \int x \csc a x \rd x = \frac 1 {a^2} \paren {a x + \frac {\paren
    {a x}^3} {18} + \frac {7 \paren {a x}^5} {1800} + \cdots + \frac {\paren {-1}^{n
    - 1} 2 \paren {2^{2 n - 1} - 1} B_n \paren {a x}^{2 n + 1} } {\paren {2 n + 1}!}
    + \cdots} + C$where $B_{2 n}$ is the $2 n$th [[Definition:Bernoulli Numbers|Bernoulli
    number]].
  - === [[Definition:Golden Mean/Definition 1|Definition 1]] ==={{:Definition:Golden
    Mean/Definition 1}}=== [[Definition:Golden Mean/Definition 2|Definition 2]] ==={{:Definition:Golden
    Mean/Definition 2}}
  - Let $G$ be a [[Definition:Group|group]].Let $N$ be a [[Definition:Subgroup|subgroup]]
    of $G$.$N$ is a '''normal subgroup of $G$''' {{iff}}:=== [[Definition:Normal Subgroup/Definition
    1|Definition 1]] ==={{:Definition:Normal Subgroup/Definition 1}}=== [[Definition:Normal
    Subgroup/Definition 2|Definition 2]] ==={{:Definition:Normal Subgroup/Definition
    2}}=== [[Definition:Normal Subgroup/Definition 3|Definition 3]] ==={{:Definition:Normal
    Subgroup/Definition 3}}=== [[Definition:Normal Subgroup/Definition 4|Definition
    4]] ==={{:Definition:Normal Subgroup/Definition 4}}=== [[Definition:Normal Subgroup/Definition
    5|Definition 5]] ==={{:Definition:Normal Subgroup/Definition 5}}=== [[Definition:Normal
    Subgroup/Definition 6|Definition 6]] ==={{:Definition:Normal Subgroup/Definition
    6}}=== [[Definition:Normal Subgroup/Definition 7|Definition 7]] ==={{:Definition:Normal
    Subgroup/Definition 7}}
---

# SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2

This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [sentence-transformers/all-MiniLM-L6-v2](https://huggingface.co/sentence-transformers/all-MiniLM-L6-v2) on the train dataset. 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:** [sentence-transformers/all-MiniLM-L6-v2](https://huggingface.co/sentence-transformers/all-MiniLM-L6-v2) <!-- at revision fa97f6e7cb1a59073dff9e6b13e2715cf7475ac9 -->
- **Maximum Sequence Length:** 256 tokens
- **Output Dimensionality:** 384 dimensions
- **Similarity Function:** Cosine Similarity
- **Training Dataset:**
    - train
<!-- - **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': 256, '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("TONKKrongyuth/finetune-all-minilm-I6-v2-proofwiki_w-theorem")
# Run inference
sentences = [
    'Let $m$ be a [[Definition:Number|numbers]] which is presented to $d$ [[Definition:Significant Figures|significant figures]].Then the most [[Definition:Significant Figures|significant figures]] that $\\sqrt m$ can have is also $d$.',
    ':$\\displaystyle \\int x \\csc a x \\rd x = \\frac 1 {a^2} \\paren {a x + \\frac {\\paren {a x}^3} {18} + \\frac {7 \\paren {a x}^5} {1800} + \\cdots + \\frac {\\paren {-1}^{n - 1} 2 \\paren {2^{2 n - 1} - 1} B_n \\paren {a x}^{2 n + 1} } {\\paren {2 n + 1}!} + \\cdots} + C$where $B_{2 n}$ is the $2 n$th [[Definition:Bernoulli Numbers|Bernoulli number]].',
    "Let $G$ be a [[Definition:Group|group]].Let $N$ be a [[Definition:Subgroup|subgroup]] of $G$.$N$ is a '''normal subgroup of $G$''' {{iff}}:=== [[Definition:Normal Subgroup/Definition 1|Definition 1]] ==={{:Definition:Normal Subgroup/Definition 1}}=== [[Definition:Normal Subgroup/Definition 2|Definition 2]] ==={{:Definition:Normal Subgroup/Definition 2}}=== [[Definition:Normal Subgroup/Definition 3|Definition 3]] ==={{:Definition:Normal Subgroup/Definition 3}}=== [[Definition:Normal Subgroup/Definition 4|Definition 4]] ==={{:Definition:Normal Subgroup/Definition 4}}=== [[Definition:Normal Subgroup/Definition 5|Definition 5]] ==={{:Definition:Normal Subgroup/Definition 5}}=== [[Definition:Normal Subgroup/Definition 6|Definition 6]] ==={{:Definition:Normal Subgroup/Definition 6}}=== [[Definition:Normal Subgroup/Definition 7|Definition 7]] ==={{:Definition:Normal Subgroup/Definition 7}}",
]
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.*
-->

<!--
## 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

#### train

* Dataset: train
* Size: 21,701 training samples
* Columns: <code>theorems_content</code>, <code>refs_content</code>, and <code>score</code>
* Approximate statistics based on the first 1000 samples:
  |         | theorems_content                                                                     | refs_content                                                                         | score                                                          |
  |:--------|:-------------------------------------------------------------------------------------|:-------------------------------------------------------------------------------------|:---------------------------------------------------------------|
  | type    | string                                                                               | string                                                                               | float                                                          |
  | details | <ul><li>min: 18 tokens</li><li>mean: 131.53 tokens</li><li>max: 256 tokens</li></ul> | <ul><li>min: 11 tokens</li><li>mean: 132.64 tokens</li><li>max: 256 tokens</li></ul> | <ul><li>min: 0.0</li><li>mean: 0.48</li><li>max: 1.0</li></ul> |
* Samples:
  | theorems_content                                                                                                                                                                                                                                                                                                                                                                                                                                                              | refs_content                                                                                                                                                                                                                                                                                                                                                                                                                                                  | score            |
  |:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:-----------------|
  | <code>Let $\left({S, \preceq}\right)$ be an [[Definition:Ordered Set|ordered set]].Let $a, b \in S$.The following are [[Definition:Dual Statement (Order Theory)|dual statements]]::$b \in a^\prec$, the [[Definition:Strict Lower Closure of Element|strict lower closure]] of $a$:$b \in a^\succ$, the [[Definition:Strict Upper Closure of Element|strict upper closure]] of $a$</code>                                                                                    | <code>Let $\left({S, \preccurlyeq}\right)$ be an [[Definition:Ordered Set|ordered set]].Let $a \in S$.The '''strict upper closure of $a$ (in $S$)''' is defined as::$a^\succ := \left\{{b \in S: a \preccurlyeq b \land a \ne b}\right\}$or::$a^\succ := \left\{{b \in S: a \prec b}\right\}$That is, $a^\succ$ is the [[Definition:Set|set]] of all [[Definition:Element|elements]] of $S$ that [[Definition:Strictly Succeed|strictly succeed]] $a$.</code> | <code>1.0</code> |
  | <code>There exists only one [[Definition:Strictly Positive Integer|(strictly) positive integer]] that is exactly twice the [[Definition:Integer Addition|sum]] of its [[Definition:Digit|digits]].</code>                                                                                                                                                                                                                                                                     | <code>Let $n$ be a [[Definition:Number|number]] expressed in a particular [[Definition:Number Base|number base]], $b$ for example.Then $n$ can be expressed as::$\sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0 . r_{-1} r_{-2} \ldots}_b$where::$m$ is such that $b^m \le n < b^{m+1}$;:all the $r_i$ are such that $0 \le r_i < b$.Each of the $r_i$ are known as the '''digits of $n$ (base $b$)'''.</code>                                                      | <code>1.0</code> |
  | <code>Let $p, q \in \R_{\ne 0}$ be non-zero [[Definition:Real Number|real numbers]] with $p < q$.Let $x_1, x_2, \ldots, x_n \ge 0$ be [[Definition:Real Number|real numbers]].If $p < 0$, then we require that $x_1, x_2, \ldots, x_n > 0$.Then the [[Definition:Hölder Mean|Hölder mean]] satisfies the inequality:: $M_p \left({x_1, x_2, \ldots, x_n}\right) \le M_q \left({x_1, x_2, \ldots, x_n}\right)$Equality holds if and only if $x_1 = x_2 = \cdots = x_n$.</code> | <code>:$\map {\dfrac \d {\d x} } {\map {\tanh^{-1} } {\dfrac x a} } = \dfrac a {a^2 - x^2}$where $-a < x < a$.</code>                                                                                                                                                                                                                                                                                                                                         | <code>0.0</code> |
* Loss: [<code>CosineSimilarityLoss</code>](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#cosinesimilarityloss) with these parameters:
  ```json
  {
      "loss_fct": "torch.nn.modules.loss.MSELoss"
  }
  ```

### Evaluation Dataset

#### train

* Dataset: train
* Size: 5,387 evaluation samples
* Columns: <code>theorems_content</code>, <code>refs_content</code>, and <code>score</code>
* Approximate statistics based on the first 1000 samples:
  |         | theorems_content                                                                     | refs_content                                                                         | score                                                         |
  |:--------|:-------------------------------------------------------------------------------------|:-------------------------------------------------------------------------------------|:--------------------------------------------------------------|
  | type    | string                                                                               | string                                                                               | float                                                         |
  | details | <ul><li>min: 22 tokens</li><li>mean: 136.05 tokens</li><li>max: 256 tokens</li></ul> | <ul><li>min: 12 tokens</li><li>mean: 130.19 tokens</li><li>max: 256 tokens</li></ul> | <ul><li>min: 0.0</li><li>mean: 0.5</li><li>max: 1.0</li></ul> |
* Samples:
  | theorems_content                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        | refs_content                                                                                                                                                                                                                                                                                                                                                                                                                                      | score            |
  |:----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:-----------------|
  | <code>Let $G$ be a [[Definition:Group|group]] whose [[Definition:Identity Element|identity]] is $e$.Let $N$ be a [[Definition:Normal Subgroup|normal subgroup]] of $G$.Let $a \in G$.Then::$\paren {a N}^n$ is the [[Definition:Identity Element|identity]] of the [[Definition:Quotient Group|quotient group]] $G / N${{iff}}::$a^n \in N$</code>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      | <code>Let $G$ be a [[Definition:Group|group]].Let $N$ be a [[Definition:Normal Subgroup|normal subgroup]] of $G$.Then the [[Definition:Left Coset Space|left coset space]] $G / N$ is a [[Definition:Group|group]], where the [[Definition:Group Operation|group operation]] is defined as::$\paren {a N} \paren {b N} = \paren {a b} N$$G / N$ is called the '''quotient group of $G$ by $N$'''.</code>                                          | <code>1.0</code> |
  | <code>Let $\omega$ be the [[Definition:Natural Numbers|set of natural numbers]] defined as the [[Definition:Von Neumann Construction of Natural Numbers|von Neumann construction]].Let $m, n \in \omega$.Then::$m < n \iff m \in n$That is, every [[Definition:Natural Numbers|natural number]] is the [[Definition:Set|set]] of all smaller [[Definition:Natural Numbers|natural numbers]].</code>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     | <code>Let $S \subseteq \R$ be a [[Definition:Countable Set|countable set]].Then $\lambda \left({S}\right) = 0$, where $\lambda$ is [[Definition:Lebesgue Measure|Lebesgue measure]].That is, $S$ is a [[Definition:Null Set|$\lambda$-null set]].</code>                                                                                                                                                                                          | <code>0.0</code> |
  | <code>Let $\CC$ be a [[Definition:Cartesian Plane|Cartesian plane]].Let $S$ be a [[Definition:Set|set]] of [[Definition:Point|points]] in $\CC$.Let $F$ be the smallest [[Definition:Field (Abstract Algebra)|field]] containing all the [[Definition:Cartesian Coordinate System|coordinates]] of the [[Definition:Point|points]] in $S$.Let $P = \tuple {a, b}$ be a [[Definition:Point|point]] in $\CC$.Then::$P$ is [[Definition:Constructible Point in Plane|constructible]] from $S$ using a [[Definition:Compass and Straightedge Construction|compass and straightedge construction]]{{iff}}::the [[Definition:Cartesian Coordinate System|coordinates]] of $P$ are contained in a [[Definition:Finite Field Extension|finite extension]] $K$ of $F$ whose [[Definition:Degree of Field Extension|degree]] is given by:::$\index K F = 2^m$:for some $m \in \Z_{\ge 0}$.</code> | <code>Let $\mathcal L$ be a [[Definition:Formal Language|formal language]] used in the field of [[:Definition:Symbolic Logic|symbolic logic]].Then the [[Definition:Well-Formed Formula|well-formed formulas]] of $\mathcal L$ are often referred to as '''logical formulas'''.They are symbolic representations of [[Definition:Statement|statements]], and often of [[Definition:Compound Statement|compound statements]] in particular.</code> | <code>0.0</code> |
* Loss: [<code>CosineSimilarityLoss</code>](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#cosinesimilarityloss) with these parameters:
  ```json
  {
      "loss_fct": "torch.nn.modules.loss.MSELoss"
  }
  ```

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

- `eval_strategy`: epoch
- `push_to_hub`: True
- `hub_model_id`: TONKKrongyuth/finetune-all-minilm-I6-v2-proofwiki_w-theorem

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

- `overwrite_output_dir`: False
- `do_predict`: False
- `eval_strategy`: epoch
- `prediction_loss_only`: True
- `per_device_train_batch_size`: 8
- `per_device_eval_batch_size`: 8
- `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`: 1.0
- `num_train_epochs`: 3
- `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}
- `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`: True
- `resume_from_checkpoint`: None
- `hub_model_id`: TONKKrongyuth/finetune-all-minilm-I6-v2-proofwiki_w-theorem
- `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
- `dispatch_batches`: None
- `split_batches`: 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`: batch_sampler
- `multi_dataset_batch_sampler`: proportional

</details>

### Training Logs
| Epoch | Step | Training Loss | train loss |
|:-----:|:----:|:-------------:|:----------:|
| 1.0   | 2713 | 0.037         | 0.0280     |
| 2.0   | 5426 | 0.0185        | 0.0271     |
| 3.0   | 8139 | 0.0109        | 0.0259     |


### Framework Versions
- Python: 3.11.11
- Sentence Transformers: 3.4.1
- Transformers: 4.48.3
- PyTorch: 2.6.0+cu124
- Accelerate: 1.3.0
- Datasets: 3.3.2
- 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",
}
```

<!--
## Glossary

*Clearly define terms in order to be accessible across audiences.*
-->

<!--
## Model Card Authors

*Lists the people who create the model card, providing recognition and accountability for the detailed work that goes into its construction.*
-->

<!--
## Model Card Contact

*Provides a way for people who have updates to the Model Card, suggestions, or questions, to contact the Model Card authors.*
-->