README.md

---
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:3503
- loss:MultipleNegativesRankingLoss
base_model: jinaai/jina-embeddings-v3
widget:
- source_sentence: '###Question###:Factorising into a Double Bracket-Factorise a quadratic
    expression in the form x² + bx - c-If

    \(

    m^{2}+5 m-14 \equiv(m+a)(m+b)

    \)

    then \( a \times b= \)

    ###Correct Answer###:\( -14 \)

    ###Misconcepted Incorrect answer###:\( 5 \)'
  sentences:
  - Does not know that units of volume are usually cubed
  - Believes the coefficent of x in an expanded quadratic comes from multiplying the
    two numbers in the brackets
  - Does not copy a given method accurately
- source_sentence: '###Question###:Rounding to the Nearest Whole (10, 100, etc)-Round
    non-integers to the nearest 10-What is \( \mathbf{8 6 9 8 . 9} \) rounded to the
    nearest ten?

    ###Correct Answer###:\( 8700 \)

    ###Misconcepted Incorrect answer###:\( 8699 \)'
  sentences:
  - Rounds to the wrong degree of accuracy (rounds too much)
  - 'Believes division is commutative '
  - Believes that a number divided by itself equals 0
- source_sentence: '###Question###:Simultaneous Equations-Solve linear simultaneous
    equations requiring a scaling of both expressions-If five cups of tea and two
    cups of coffee cost \( £ 3.70 \), and two cups of tea and five cups of coffee
    cost \( £ 4.00 \), what is the cost of a cup of tea and a cup of coffee?

    ###Correct Answer###:Tea \( =50 \mathrm{p} \) coffee \( =60 p \)

    ###Misconcepted Incorrect answer###:\( \begin{array}{l}\text { Tea }=0.5 \\ \text
    { coffee }=0.6\end{array} \)'
  sentences:
  - Misinterprets the meaning of angles on a straight line angle fact
  - Does not include units in answer.
  - Believes midpoint calculation is just half of the difference
- source_sentence: '###Question###:Quadratic Sequences-Find the nth term rule for
    ascending quadratic sequences in the form ax² + bx + c-\(

    6,14,28,48,74, \ldots

    \)


    When calculating the nth-term rule of this sequence, what should replace the triangle?


    nth-term rule: \( 3 n^{2} \)\( \color{red}\triangle \)  \(n\) \( \color{purple}\square
    \)


    ###Correct Answer###:\( -1 \)

    (or just a - sign)

    ###Misconcepted Incorrect answer###:\[

    +1

    \]

    (or just a + sign)'
  sentences:
  - 'When finding the differences between terms in a sequence, believes they can do
    so from right to left '
  - When solving an equation forgets to eliminate the coefficient in front of the
    variable in the last step
  - Believes parallelogram is the term used to describe two lines at right angles
- source_sentence: '###Question###:Written Multiplication-Multiply 2 digit integers
    by 2 digit integers using long multiplication-Which working out is correct for
    $72 \times 36$?

    ###Correct Answer###:![ Long multiplication for 72 multiplied by 36 with correct
    working and correct final answer. First row of working is correct: 4 3 2. Second
    row of working is correct: 2 1 6 0. Final answer is correct: 2 5 9 2.]()

    ###Misconcepted Incorrect answer###:![ Long multiplication for 72 multiplied by
    36 with incorrect working and incorrect final answer. First row of working is
    incorrect: 4 2 2. Second row of working is incorrect: 2 7. Final answer is incorrect:
    4 4 9.]()'
  sentences:
  - When solving an equation forgets to eliminate the coefficient in front of the
    variable in the last step
  - Thinks a variable next to a number means addition rather than multiplication
  - When two digits multiply to 10 or more during a multiplication problem, does not
    add carried value to the preceding digit
pipeline_tag: sentence-similarity
library_name: sentence-transformers
---

# SentenceTransformer based on jinaai/jina-embeddings-v3

This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [jinaai/jina-embeddings-v3](https://huggingface.co/jinaai/jina-embeddings-v3). 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:** [jinaai/jina-embeddings-v3](https://huggingface.co/jinaai/jina-embeddings-v3) <!-- at revision 62a81741b58448ed8f691764cec7aa5d3c045e4c -->
- **Maximum Sequence Length:** 8194 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(
  (transformer): Transformer(
    (auto_model): XLMRobertaLoRA(
      (roberta): XLMRobertaModel(
        (embeddings): XLMRobertaEmbeddings(
          (word_embeddings): ParametrizedEmbedding(
            250002, 1024, padding_idx=1
            (parametrizations): ModuleDict(
              (weight): ParametrizationList(
                (0): LoRAParametrization()
              )
            )
          )
          (token_type_embeddings): ParametrizedEmbedding(
            1, 1024
            (parametrizations): ModuleDict(
              (weight): ParametrizationList(
                (0): LoRAParametrization()
              )
            )
          )
        )
        (emb_drop): Dropout(p=0.1, inplace=False)
        (emb_ln): LayerNorm((1024,), eps=1e-05, elementwise_affine=True)
        (encoder): XLMRobertaEncoder(
          (layers): ModuleList(
            (0-23): 24 x Block(
              (mixer): MHA(
                (rotary_emb): RotaryEmbedding()
                (Wqkv): ParametrizedLinearResidual(
                  in_features=1024, out_features=3072, bias=True
                  (parametrizations): ModuleDict(
                    (weight): ParametrizationList(
                      (0): LoRAParametrization()
                    )
                  )
                )
                (inner_attn): FlashSelfAttention(
                  (drop): Dropout(p=0.1, inplace=False)
                )
                (inner_cross_attn): FlashCrossAttention(
                  (drop): Dropout(p=0.1, inplace=False)
                )
                (out_proj): ParametrizedLinear(
                  in_features=1024, out_features=1024, bias=True
                  (parametrizations): ModuleDict(
                    (weight): ParametrizationList(
                      (0): LoRAParametrization()
                    )
                  )
                )
              )
              (dropout1): Dropout(p=0.1, inplace=False)
              (drop_path1): StochasticDepth(p=0.0, mode=row)
              (norm1): LayerNorm((1024,), eps=1e-05, elementwise_affine=True)
              (mlp): Mlp(
                (fc1): ParametrizedLinear(
                  in_features=1024, out_features=4096, bias=True
                  (parametrizations): ModuleDict(
                    (weight): ParametrizationList(
                      (0): LoRAParametrization()
                    )
                  )
                )
                (fc2): ParametrizedLinear(
                  in_features=4096, out_features=1024, bias=True
                  (parametrizations): ModuleDict(
                    (weight): ParametrizationList(
                      (0): LoRAParametrization()
                    )
                  )
                )
              )
              (dropout2): Dropout(p=0.1, inplace=False)
              (drop_path2): StochasticDepth(p=0.0, mode=row)
              (norm2): LayerNorm((1024,), eps=1e-05, elementwise_affine=True)
            )
          )
        )
        (pooler): XLMRobertaPooler(
          (dense): ParametrizedLinear(
            in_features=1024, out_features=1024, bias=True
            (parametrizations): ModuleDict(
              (weight): ParametrizationList(
                (0): LoRAParametrization()
              )
            )
          )
          (activation): Tanh()
        )
      )
    )
  )
  (pooler): Pooling({'word_embedding_dimension': 1024, '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})
  (normalizer): 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("sentence_transformers_model_id")
# Run inference
sentences = [
    '###Question###:Written Multiplication-Multiply 2 digit integers by 2 digit integers using long multiplication-Which working out is correct for $72 \\times 36$?\n###Correct Answer###:![ Long multiplication for 72 multiplied by 36 with correct working and correct final answer. First row of working is correct: 4 3 2. Second row of working is correct: 2 1 6 0. Final answer is correct: 2 5 9 2.]()\n###Misconcepted Incorrect answer###:![ Long multiplication for 72 multiplied by 36 with incorrect working and incorrect final answer. First row of working is incorrect: 4 2 2. Second row of working is incorrect: 2 7. Final answer is incorrect: 4 4 9.]()',
    'When two digits multiply to 10 or more during a multiplication problem, does not add carried value to the preceding digit',
    'Thinks a variable next to a number means addition rather than multiplication',
]
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]
```

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

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## Training Details

### Training Dataset

#### Unnamed Dataset


* Size: 3,503 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: 59 tokens</li><li>mean: 131.26 tokens</li><li>max: 449 tokens</li></ul> | <ul><li>min: 6 tokens</li><li>mean: 17.43 tokens</li><li>max: 46 tokens</li></ul> |
* Samples:
  | anchor                                                                                                                                                                                                                                                                                                                                                                                                                                                                | positive                                                                                     |
  |:----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------------------|
  | <code>###Question###:Area of Simple Shapes-Calculate the area of a parallelogram where the dimensions are given in the same units-What is the area of this shape? ![A parallelogram drawn on a square grid in purple with an area of 9 square units. The base is length 3 squares and the perpendicular height is also length 3 squares.]()<br>###Correct Answer###:\( 9 \)<br>###Misconcepted Incorrect answer###:\( 12 \)</code>                                    | <code>Counts half-squares as full squares when calculating area on a square grid</code>      |
  | <code>###Question###:Substitution into Formula-Substitute into simple formulae given in words-A theme park charges \( £ 8 \) entry fee and then \( £ 3 \) for every ride you go on.<br>Heena goes on \( 5 \) rides.<br>How much does she pay in total?<br>###Correct Answer###:\( £ 23 \)<br>###Misconcepted Incorrect answer###:\( £ 55 \)</code>                                                                                                                    | <code>Combines variables with constants when writing a formula from a given situation</code> |
  | <code>###Question###:Trial and Improvement and Iterative Methods-Use area to write algebraic expressions-The area of the rectangle on the right is \( 8 \mathrm{~cm}^{2} \).<br><br>Which of the following equations can we write from the information given? ![A rectangle with the short side labelled \(x\) and the opposite side labelled \(x^2 + 9\).]()<br>###Correct Answer###:\( x^{3}+9 x=8 \)<br>###Misconcepted Incorrect answer###:\( x^{3}+9=8 \)</code> | <code>Only multiplies the first term in the expansion of a bracket</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

- `num_train_epochs`: 10
- `push_to_hub`: True
- `batch_sampler`: no_duplicates

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

- `overwrite_output_dir`: False
- `do_predict`: False
- `eval_strategy`: no
- `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`: 10
- `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`: 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 |
|:------:|:----:|:-------------:|
| 1.1416 | 500  | 0.3244        |
| 2.2831 | 1000 | 0.1048        |
| 3.4247 | 1500 | 0.0394        |
| 4.5662 | 2000 | 0.0211        |
| 5.7078 | 2500 | 0.0145        |
| 6.8493 | 3000 | 0.0114        |
| 7.9909 | 3500 | 0.0106        |
| 9.1324 | 4000 | 0.0092        |


### Framework Versions
- Python: 3.10.12
- Sentence Transformers: 3.1.1
- Transformers: 4.45.2
- PyTorch: 2.5.1+cu121
- Accelerate: 1.1.1
- Datasets: 3.1.0
- Tokenizers: 0.20.3

## 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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