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---
base_model: dunzhang/stella_en_1.5B_v5
library_name: sentence-transformers
metrics:
- cosine_accuracy@25
- cosine_precision@100
- cosine_precision@200
- cosine_precision@300
- cosine_precision@400
- cosine_precision@500
- cosine_precision@600
- cosine_precision@700
- cosine_precision@800
- cosine_precision@900
- cosine_precision@1000
- cosine_recall@100
- cosine_recall@200
- cosine_recall@300
- cosine_recall@400
- cosine_recall@500
- cosine_recall@600
- cosine_recall@700
- cosine_recall@800
- cosine_recall@900
- cosine_recall@1000
- cosine_ndcg@25
- cosine_mrr@25
- cosine_map@25
- dot_accuracy@25
- dot_precision@100
- dot_precision@200
- dot_precision@300
- dot_precision@400
- dot_precision@500
- dot_precision@600
- dot_precision@700
- dot_precision@800
- dot_precision@900
- dot_precision@1000
- dot_recall@100
- dot_recall@200
- dot_recall@300
- dot_recall@400
- dot_recall@500
- dot_recall@600
- dot_recall@700
- dot_recall@800
- dot_recall@900
- dot_recall@1000
- dot_ndcg@25
- dot_mrr@25
- dot_map@25
pipeline_tag: sentence-similarity
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:3999
- loss:CachedMultipleNegativesSymmetricRankingLoss
widget:
- source_sentence: 'QuestionSummary: Adding and Subtracting Algebraic Fractions
Question: STEP \( 1 \)
Which of the options is a correct first step to express the following as a single
fraction?
\(
\frac{3}{x-2}-\frac{5}{x}
\)
CorrectAnswer: \( \frac{3 x}{x(x-2)}-\frac{5(x-2)}{x(x-2)} \)
Answer: \( \frac{3-5}{x-2-x} \)'
sentences:
- When subtracting fractions, subtracts the numerators and denominators
- Believes that the coefficient of x represents the gradient even when a line is
not in the form y = mx+c
- Confuses factors and multiples
- source_sentence: 'QuestionSummary: Time
Question: Which of the following would correctly calculate the number of seconds
in \( 1 \) day?
CorrectAnswer: \( 24 \times 60 \times 60 \)
Answer: \( 24 \times 60 \)'
sentences:
- Translates rather than reflects across a line of symmetry
- Does not understand the value of zeros as placeholders
- Converted hours to minutes instead of hours to seconds
- source_sentence: 'QuestionSummary: Naming Co-ordinates in 2D
Question: Here are \( 3 \) vertices of a rectangle:
\((-6,-2),(-3,2),(0,0) \text {, }\)
What are the coordinates of the \( 4^{\text {th }} \) vertex?
CorrectAnswer: \( (-3,-4) \)
Answer: \( (-6,-4) \)'
sentences:
- Thinks x = 1 at the x axis
- Does not know how to find the length of a line segment from coordinates
- Believes rounding numbers down would give an overestimate
- source_sentence: 'QuestionSummary: Parts of a Circle
Question: What is the correct name for the line marked on the circle? ![\( \theta
\)]()
CorrectAnswer: Chord
Answer: Radius'
sentences:
- When completing the square, believes the constant in the bracket is double the
coefficient of x
- 'Cannot reflect shape when line of symmetry is diagonal '
- Confuses chord and radius
- source_sentence: "QuestionSummary: Function Machines\nQuestion: Which of the following\
\ pairs of function machines are correct?\nCorrectAnswer: \\(a \\Rightarrow \\\
times2 \\Rightarrow -5\\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow -5 \\Rightarrow\
\ \\times2\\Rightarrow 2(a-5)\\) \nAnswer: \\(a \\Rightarrow \\times2 \\Rightarrow\
\ -5\\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow\
\ 2(a-5)\\) "
sentences:
- Does not follow the arrows through a function machine, changes the order of the
operations asked.
- Has used the wrong data point on the graph
- Incorrectly cancels what they believe is a factor in algebraic fractions
model-index:
- name: SentenceTransformer based on dunzhang/stella_en_1.5B_v5
results:
- task:
type: information-retrieval
name: Information Retrieval
dataset:
name: val
type: val
metrics:
- type: cosine_accuracy@25
value: 0.6946039035591275
name: Cosine Accuracy@25
- type: cosine_precision@100
value: 0.008760045924225027
name: Cosine Precision@100
- type: cosine_precision@200
value: 0.004684270952927668
name: Cosine Precision@200
- type: cosine_precision@300
value: 0.003195560658247226
name: Cosine Precision@300
- type: cosine_precision@400
value: 0.0024339839265212397
name: Cosine Precision@400
- type: cosine_precision@500
value: 0.0019609644087256036
name: Cosine Precision@500
- type: cosine_precision@600
value: 0.0016437045541523154
name: Cosine Precision@600
- type: cosine_precision@700
value: 0.0014187305232081352
name: Cosine Precision@700
- type: cosine_precision@800
value: 0.001244259471871412
name: Cosine Precision@800
- type: cosine_precision@900
value: 0.0011085597652761834
name: Cosine Precision@900
- type: cosine_precision@1000
value: 0.0009977037887485653
name: Cosine Precision@1000
- type: cosine_recall@100
value: 0.8760045924225028
name: Cosine Recall@100
- type: cosine_recall@200
value: 0.9368541905855339
name: Cosine Recall@200
- type: cosine_recall@300
value: 0.9586681974741676
name: Cosine Recall@300
- type: cosine_recall@400
value: 0.9735935706084959
name: Cosine Recall@400
- type: cosine_recall@500
value: 0.9804822043628014
name: Cosine Recall@500
- type: cosine_recall@600
value: 0.9862227324913893
name: Cosine Recall@600
- type: cosine_recall@700
value: 0.9931113662456946
name: Cosine Recall@700
- type: cosine_recall@800
value: 0.9954075774971297
name: Cosine Recall@800
- type: cosine_recall@900
value: 0.9977037887485649
name: Cosine Recall@900
- type: cosine_recall@1000
value: 0.9977037887485649
name: Cosine Recall@1000
- type: cosine_ndcg@25
value: 0.35640204555925886
name: Cosine Ndcg@25
- type: cosine_mrr@25
value: 0.2610487357311384
name: Cosine Mrr@25
- type: cosine_map@25
value: 0.2610487357311386
name: Cosine Map@25
- type: dot_accuracy@25
value: 0.42709529276693453
name: Dot Accuracy@25
- type: dot_precision@100
value: 0.007600459242250287
name: Dot Precision@100
- type: dot_precision@200
value: 0.004328358208955224
name: Dot Precision@200
- type: dot_precision@300
value: 0.003076923076923077
name: Dot Precision@300
- type: dot_precision@400
value: 0.002359357060849598
name: Dot Precision@400
- type: dot_precision@500
value: 0.0019219288174512062
name: Dot Precision@500
- type: dot_precision@600
value: 0.0016188289322617683
name: Dot Precision@600
- type: dot_precision@700
value: 0.0013990487124815481
name: Dot Precision@700
- type: dot_precision@800
value: 0.0012299081515499426
name: Dot Precision@800
- type: dot_precision@900
value: 0.0010970787090190078
name: Dot Precision@900
- type: dot_precision@1000
value: 0.0009896670493685423
name: Dot Precision@1000
- type: dot_recall@100
value: 0.7600459242250287
name: Dot Recall@100
- type: dot_recall@200
value: 0.8656716417910447
name: Dot Recall@200
- type: dot_recall@300
value: 0.9230769230769231
name: Dot Recall@300
- type: dot_recall@400
value: 0.9437428243398392
name: Dot Recall@400
- type: dot_recall@500
value: 0.9609644087256027
name: Dot Recall@500
- type: dot_recall@600
value: 0.9712973593570609
name: Dot Recall@600
- type: dot_recall@700
value: 0.9793340987370838
name: Dot Recall@700
- type: dot_recall@800
value: 0.983926521239954
name: Dot Recall@800
- type: dot_recall@900
value: 0.9873708381171068
name: Dot Recall@900
- type: dot_recall@1000
value: 0.9896670493685419
name: Dot Recall@1000
- type: dot_ndcg@25
value: 0.1952544948998545
name: Dot Ndcg@25
- type: dot_mrr@25
value: 0.13285195280982043
name: Dot Mrr@25
- type: dot_map@25
value: 0.13285195280982032
name: Dot Map@25
---
# SentenceTransformer based on dunzhang/stella_en_1.5B_v5
This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [dunzhang/stella_en_1.5B_v5](https://huggingface.co./dunzhang/stella_en_1.5B_v5). It maps sentences & paragraphs to a 1024-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:** [dunzhang/stella_en_1.5B_v5](https://huggingface.co./dunzhang/stella_en_1.5B_v5) <!-- at revision d03be74b361d4eb24f42a2fe5bd2e29917df4604 -->
- **Maximum Sequence Length:** 512 tokens
- **Output Dimensionality:** 1024 tokens
- **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: Qwen2Model
(1): Pooling({'word_embedding_dimension': 1536, '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): Dense({'in_features': 1536, 'out_features': 1024, 'bias': True, 'activation_function': 'torch.nn.modules.linear.Identity'})
)
```
## 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("sentence_transformers_model_id")
# Run inference
sentences = [
'QuestionSummary: Function Machines\nQuestion: Which of the following pairs of function machines are correct?\nCorrectAnswer: \\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow -5 \\Rightarrow \\times2\\Rightarrow 2(a-5)\\) \nAnswer: \\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow 2a-5\\) \n\n\\(a \\Rightarrow \\times2 \\Rightarrow -5\\Rightarrow 2(a-5)\\) ',
'Does not follow the arrows through a function machine, changes the order of the operations asked.',
'Incorrectly cancels what they believe is a factor in algebraic fractions',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 1024]
# 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
#### Information Retrieval
* Dataset: `val`
* Evaluated with [<code>InformationRetrievalEvaluator</code>](https://sbert.net/docs/package_reference/sentence_transformer/evaluation.html#sentence_transformers.evaluation.InformationRetrievalEvaluator)
| Metric | Value |
|:----------------------|:----------|
| cosine_accuracy@25 | 0.6946 |
| cosine_precision@100 | 0.0088 |
| cosine_precision@200 | 0.0047 |
| cosine_precision@300 | 0.0032 |
| cosine_precision@400 | 0.0024 |
| cosine_precision@500 | 0.002 |
| cosine_precision@600 | 0.0016 |
| cosine_precision@700 | 0.0014 |
| cosine_precision@800 | 0.0012 |
| cosine_precision@900 | 0.0011 |
| cosine_precision@1000 | 0.001 |
| cosine_recall@100 | 0.876 |
| cosine_recall@200 | 0.9369 |
| cosine_recall@300 | 0.9587 |
| cosine_recall@400 | 0.9736 |
| cosine_recall@500 | 0.9805 |
| cosine_recall@600 | 0.9862 |
| cosine_recall@700 | 0.9931 |
| cosine_recall@800 | 0.9954 |
| cosine_recall@900 | 0.9977 |
| cosine_recall@1000 | 0.9977 |
| cosine_ndcg@25 | 0.3564 |
| cosine_mrr@25 | 0.261 |
| **cosine_map@25** | **0.261** |
| dot_accuracy@25 | 0.4271 |
| dot_precision@100 | 0.0076 |
| dot_precision@200 | 0.0043 |
| dot_precision@300 | 0.0031 |
| dot_precision@400 | 0.0024 |
| dot_precision@500 | 0.0019 |
| dot_precision@600 | 0.0016 |
| dot_precision@700 | 0.0014 |
| dot_precision@800 | 0.0012 |
| dot_precision@900 | 0.0011 |
| dot_precision@1000 | 0.001 |
| dot_recall@100 | 0.76 |
| dot_recall@200 | 0.8657 |
| dot_recall@300 | 0.9231 |
| dot_recall@400 | 0.9437 |
| dot_recall@500 | 0.961 |
| dot_recall@600 | 0.9713 |
| dot_recall@700 | 0.9793 |
| dot_recall@800 | 0.9839 |
| dot_recall@900 | 0.9874 |
| dot_recall@1000 | 0.9897 |
| dot_ndcg@25 | 0.1953 |
| dot_mrr@25 | 0.1329 |
| dot_map@25 | 0.1329 |
<!--
## 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: 3,999 training samples
* Columns: <code>anchor</code> and <code>positive</code>
* Approximate statistics based on the first 1000 samples:
| | anchor | positive |
|:--------|:------------------------------------------------------------------------------------|:----------------------------------------------------------------------------------|
| type | string | string |
| details | <ul><li>min: 30 tokens</li><li>mean: 87.03 tokens</li><li>max: 363 tokens</li></ul> | <ul><li>min: 4 tokens</li><li>mean: 13.84 tokens</li><li>max: 42 tokens</li></ul> |
* Samples:
| anchor | positive |
|:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| <code>QuestionSummary: Simplifying Algebraic Fractions<br>Question: Simplify the following, if possible: \( \frac{m^{2}+2 m-3}{m-3} \)<br>CorrectAnswer: Does not simplify<br>Answer: \( m+1 \)</code> | <code>Does not know that to factorise a quadratic expression, to find two numbers that add to give the coefficient of the x term, and multiply to give the non variable term<br></code> |
| <code>QuestionSummary: Range and Interquartile Range from a List of Data<br>Question: Tom and Katie are discussing the \( 5 \) plants with these heights:<br>\( 24 \mathrm{~cm}, 17 \mathrm{~cm}, 42 \mathrm{~cm}, 26 \mathrm{~cm}, 13 \mathrm{~cm} \)<br>Tom says if all the plants were cut in half, the range wouldn't change.<br>Katie says if all the plants grew by \( 3 \mathrm{~cm} \) each, the range wouldn't change.<br>Who do you agree with?<br>CorrectAnswer: Only<br>Katie<br>Answer: Only<br>Tom</code> | <code>Believes if you changed all values by the same proportion the range would not change</code> |
| <code>QuestionSummary: Properties of Quadrilaterals<br>Question: The angles highlighted on this rectangle with different length sides can never be... ![A rectangle with the diagonals drawn in. The angle on the right hand side at the centre is highlighted in red and the angle at the bottom at the centre is highlighted in yellow.]()<br>CorrectAnswer: \( 90^{\circ} \)<br>Answer: acute</code> | <code>Does not know the properties of a rectangle</code> |
* Loss: [<code>CachedMultipleNegativesSymmetricRankingLoss</code>](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#cachedmultiplenegativessymmetricrankingloss) with these parameters:
```json
{
"scale": 20.0,
"similarity_fct": "cos_sim",
"mini_batch_size": 1
}
```
### Training Hyperparameters
#### Non-Default Hyperparameters
- `eval_strategy`: steps
- `per_device_train_batch_size`: 1372
- `per_device_eval_batch_size`: 1372
- `learning_rate`: 4e-05
- `num_train_epochs`: 5
- `warmup_ratio`: 0.1
- `save_only_model`: True
- `bf16`: True
- `load_best_model_at_end`: True
- `batch_sampler`: no_duplicates
#### 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`: 1372
- `per_device_eval_batch_size`: 1372
- `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`: 4e-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`: 5
- `max_steps`: -1
- `lr_scheduler_type`: linear
- `lr_scheduler_kwargs`: {}
- `warmup_ratio`: 0.1
- `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`: True
- `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`: True
- `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`: True
- `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`: False
- `resume_from_checkpoint`: None
- `hub_model_id`: None
- `hub_strategy`: every_save
- `hub_private_repo`: False
- `hub_always_push`: False
- `gradient_checkpointing`: False
- `gradient_checkpointing_kwargs`: None
- `include_inputs_for_metrics`: False
- `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
- `batch_sampler`: no_duplicates
- `multi_dataset_batch_sampler`: proportional
</details>
### Training Logs
| Epoch | Step | Training Loss | val_cosine_map@25 |
|:-------:|:-----:|:-------------:|:-----------------:|
| 0.3333 | 1 | 2.2717 | 0.1775 |
| 0.6667 | 2 | 2.1785 | 0.2300 |
| 1.0 | 3 | 1.4112 | 0.2651 |
| 1.3333 | 4 | 1.1861 | 0.2726 |
| 1.6667 | 5 | 0.8742 | 0.2813 |
| 2.0 | 6 | 0.8327 | 0.2818 |
| 2.3333 | 7 | 0.7626 | 0.2777 |
| 2.6667 | 8 | 0.5767 | 0.2752 |
| **3.0** | **9** | **0.493** | **0.2698** |
| 3.3333 | 10 | 0.5174 | 0.2654 |
| 3.6667 | 11 | 0.3906 | 0.2655 |
| 4.0 | 12 | 0.419 | 0.2627 |
| 4.3333 | 13 | 0.4394 | 0.2625 |
| 4.6667 | 14 | 0.5449 | 0.2612 |
| 5.0 | 15 | 0.3731 | 0.2610 |
* The bold row denotes the saved checkpoint.
### Framework Versions
- Python: 3.10.13
- Sentence Transformers: 3.1.1
- Transformers: 4.45.1
- PyTorch: 2.2.0
- Accelerate: 0.34.2
- Datasets: 3.0.1
- Tokenizers: 0.20.0
## 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",
}
```
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