metadata

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 model finetuned from 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
Maximum Sequence Length: 512 tokens
Output Dimensionality: 768 tokens
Similarity Function: Cosine Similarity

Model Sources

Documentation: Sentence Transformers Documentation
Repository: Sentence Transformers on GitHub
Hugging Face: Sentence Transformers on Hugging Face

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:

pip install -U sentence-transformers

Then you can load this model and run inference.

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

	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? ###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? ###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 with these parameters:

{
    "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

Training Logs

Epoch	Step	Training Loss
1.1416	500	0.341
2.2831	1000	0.1082
3.4247	1500	0.0485
4.5662	2000	0.0226
5.7078	2500	0.0133
6.8493	3000	0.0066
7.9909	3500	0.0042
9.1324	4000	0.0017

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

@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

@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}
}