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: 5
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: 5
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	0.3382
2.2831	1000	0.1004
3.4247	1500	0.0386
4.5662	2000	0.0133

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}
}