---
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:3503
- loss:MultipleNegativesRankingLoss
base_model: BAAI/bge-base-en-v1.5
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 BAAI/bge-base-en-v1.5
This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [BAAI/bge-base-en-v1.5](https://huggingface.co/BAAI/bge-base-en-v1.5). It maps sentences & paragraphs to a 768-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:** [BAAI/bge-base-en-v1.5](https://huggingface.co/BAAI/bge-base-en-v1.5)
- **Maximum Sequence Length:** 512 tokens
- **Output Dimensionality:** 768 tokens
- **Similarity Function:** Cosine Similarity
### 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': True}) with Transformer model: BertModel
(1): Pooling({'word_embedding_dimension': 768, 'pooling_mode_cls_token': True, 'pooling_mode_mean_tokens': False, '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("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, 768]
# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]
```
## Training Details
### Training Dataset
#### Unnamed Dataset
* Size: 3,503 training samples
* Columns: anchor and positive
* Approximate statistics based on the first 1000 samples:
| | anchor | positive |
|:--------|:-------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------|
| type | string | string |
| details | - min: 60 tokens
- mean: 122.66 tokens
- max: 415 tokens
| - min: 6 tokens
- mean: 14.9 tokens
- max: 39 tokens
|
* Samples:
| anchor | positive |
|:----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------------------|
| ###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.]()
###Correct Answer###:\( 9 \)
###Misconcepted Incorrect answer###:\( 12 \) | Counts half-squares as full squares when calculating area on a square grid |
| ###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.
Heena goes on \( 5 \) rides.
How much does she pay in total?
###Correct Answer###:\( £ 23 \)
###Misconcepted Incorrect answer###:\( £ 55 \) | Combines variables with constants when writing a formula from a given situation |
| ###Question###:Trial and Improvement and Iterative Methods-Use area to write algebraic expressions-The area of the rectangle on the right is \( 8 \mathrm{~cm}^{2} \).
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 \(x^2 + 9\).]()
###Correct Answer###:\( x^{3}+9 x=8 \)
###Misconcepted Incorrect answer###:\( x^{3}+9=8 \) | Only multiplies the first term in the expansion of a bracket |
* Loss: [MultipleNegativesRankingLoss](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
- `fp16`: True
- `push_to_hub`: True
- `batch_sampler`: no_duplicates
#### All Hyperparameters
Click to expand
- `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`: True
- `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