SentenceTransformer based on sentence-transformers/all-MiniLM-L6-v2

This is a sentence-transformers model finetuned from sentence-transformers/all-MiniLM-L6-v2. It maps sentences & paragraphs to a 384-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: sentence-transformers/all-MiniLM-L6-v2
Maximum Sequence Length: 384 tokens
Output Dimensionality: 384 dimensions
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': 384, 'do_lower_case': False}) with Transformer model: BertModel 
  (1): Pooling({'word_embedding_dimension': 384, '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): 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("Lysandrec/MNLP_M2_document_encoder")
# Run inference
sentences = [
    'For some constant $b$, if the minimum value of \\[f(x)=\\dfrac{x^2-2x+b}{x^2+2x+b}\\] is $\\tfrac12$, what is the maximum value of $f(x)$?',
    "<page_title> Second degree polynomial </page_title> <path> Quadratic_function > Graph of the univariate function > Vertex > Maximum and minimum points </path> <section_title> Maximum and minimum points </section_title> <content> Using calculus, the vertex point, being a maximum or minimum of the function, can be obtained by finding the roots of the derivative: f ( x ) = a x 2 + b x + c ⇒ f ′ ( x ) = 2 a x + b {\\displaystyle f(x)=ax^{2}+bx+c\\quad \\Rightarrow \\quad f'(x)=2ax+b} x is a root of f '(x) if f '(x) = 0 resulting in x = − b 2 a {\\displaystyle x=-{\\frac {b}{2a}}} with the corresponding function value f ( x ) = a ( − b 2 a ) 2 + b ( − b 2 a ) + c = c − b 2 4 a , {\\displaystyle f(x)=a\\left(-{\\frac {b}{2a}}\\right)^{2}+b\\left(-{\\frac {b}{2a}}\\right)+c=c-{\\frac {b^{2}}{4a}},} so again the vertex point coordinates, (h, k), can be expressed as ( − b 2 a , c − b 2 4 a ) . {\\displaystyle \\left(-{\\frac {b}{2a}},c-{\\frac {b^{2}}{4a}}\\right).} </content>",
    '<page_title> Lagrangian multiplier </page_title> <path> Lagrange_multiplier > Examples > Example 1 </path> <section_title> Example 1 </section_title> <content> Evaluating the objective function f at these points yields f ( 2 2 , 2 2 ) = 2 , f ( − 2 2 , − 2 2 ) = − 2 . {\\displaystyle f\\left({\\tfrac {\\sqrt {2\\ }}{2}},{\\tfrac {\\sqrt {2\\ }}{2}}\\right)={\\sqrt {2\\ }}\\ ,\\qquad f\\left(-{\\tfrac {\\sqrt {2\\ }}{2}},-{\\tfrac {\\sqrt {2\\ }}{2}}\\right)=-{\\sqrt {2\\ }}~.} Thus the constrained maximum is 2 {\\displaystyle \\ {\\sqrt {2\\ }}\\ } and the constrained minimum is − 2 {\\displaystyle -{\\sqrt {2}}} . </content>',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 384]

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]

Training Details

Training Dataset

Unnamed Dataset

This training dataset was synthetically generated. For each question from the source Q/A dataset (Lysandrec/MNLP_M2_rag_dataset), relevant passages were retrieved from a large document corpus (Lysandrec/MNLP_M2_rag_documents).

A positive_passage was identified from the retrieved candidates, typically one containing the answer to the question. If no definitive positive was found, the top retrieved passage was often selected.
Hard_negative_passages were selected from other highly-ranked (but not positive) retrieved documents for the same question.
Random_negative_passages were sampled from the broader document corpus, ensuring they differed from the selected positive and hard negative passages. This process resulted in triplets of (query, positive_passage, negative_passage) used for training.

Size: 100,000 training samples
Columns: query (a question), positive_passage (a good retrieved document), and negative_passage (a bad example of a retrieved document)

Approximate statistics based on the first 1000 samples:

	query	positive_passage	negative_passage
type	string	string	string
details	min: 13 tokens mean: 64.12 tokens max: 214 tokens	min: 64 tokens mean: 205.95 tokens max: 384 tokens	min: 63 tokens mean: 178.5 tokens max: 384 tokens

Samples:

query	positive_passage	negative_passage
`The average of first five prime numbers greater than 61 is?<br>A. A)32.2<br>B. B)32.98<br>C. C)74.6<br>D. D)32.8<br>E. E)32.4`	<page_title> 61 (number) </page_title> <path> 61_(number) > In mathematics </path> <section_title> In mathematics </section_title> <content> 61 is: the 18th prime number. a twin prime with 59. a cuban prime of the form p = x3 − y3/x − y, where x = y + 1. the smallest proper prime, a prime p which ends in the digit 1 in base 10 and whose reciprocal in base 10 has a repeating sequence with length p − 1. In such primes, each digit 0, 1, ..., 9 appears in the repeating sequence the same number of times as does each other digit (namely, p − 1/10 times). </content>	<page_title> Astatine </page_title> <path> Element_85 > Characteristics > Chemical </path> <section_title> Chemical </section_title> <content> In comparison, the value of Cl (349) is 6.4% higher than F (328); Br (325) is 6.9% less than Cl; and I (295) is 9.2% less than Br. The marked reduction for At was predicted as being due to spin–orbit interactions. The first ionization energy of astatine is about 899 kJ mol−1, which continues the trend of decreasing first ionization energies down the halogen group (fluorine, 1681; chlorine, 1251; bromine, 1140; iodine, 1008). </content>
`A charitable association sold an average of 66 raffle tickets per member. Among the female members, the average was 70 raffle tickets. The male to female ratio of the association is 1:2. What was the average number E of tickets sold by the male members of the association<br>A. A)50<br>B. B)56<br>C. C)58<br>D. D)62<br>E. E)66`	`<page_title> RSA number </page_title> <path> RSA_numbers </path> <section_title> Summary </section_title> <content> Cash prizes of varying size, up to US$200,000 (and prizes up to $20,000 awarded), were offered for factorization of some of them. The smallest RSA number was factored in a few days. Most of the numbers have still not been factored and many of them are expected to remain unfactored for many years to come. </content>`	<page_title> Peer learning </page_title> <path> Peer_learning > Connections with other practices > Connectivism </path> <section_title> Connectivism </section_title> <content> Yochai Benkler explains how the now-ubiquitous computer helps us produce and process knowledge together with others in his book, The Wealth of Networks. George Siemens argues in Connectivism: A Learning Theory for the Digital Age, that technology has changed the way we learn, explaining how it tends to complicate or expose the limitations of the learning theories of the past. In practice, the ideas of connectivism developed in and alongside the then-new social formation, "massive open online courses" or MOOCs. Connectivism proposes that the knowledge we can access by virtue of our connections with others is just as valuable as the information carried inside our minds. </content>
`Find prime numbers $a, b, c, d, e$ such that $a^4 + b^4 + c^4 + d^4 + e^4 = abcde$.`	<page_title> Pythagorean triangle </page_title> <path> Primitive_Pythagorean_triple > Special cases and related equations > The Jacobi–Madden equation </path> <section_title> The Jacobi–Madden equation </section_title> <content> The equation, a 4 + b 4 + c 4 + d 4 = ( a + b + c + d ) 4 {\displaystyle a^{4}+b^{4}+c^{4}+d^{4}=(a+b+c+d)^{4}} is equivalent to the special Pythagorean triple, ( a 2 + a b + b 2 ) 2 + ( c 2 + c d + d 2 ) 2 = ( ( a + b ) 2 + ( a + b ) ( c + d ) + ( c + d ) 2 ) 2 {\displaystyle (a^{2}+ab+b^{2})^{2}+(c^{2}+cd+d^{2})^{2}=((a+b)^{2}+(a+b)(c+d)+(c+d)^{2})^{2}} There is an infinite number of solutions to this equation as solving for the variables involves an elliptic curve. Small ones are, a , b , c , d = − 2634 , 955 , 1770 , 5400 {\displaystyle a,b,c,d=-2634,955,1770,5400} a , b , c , d = − 31764 , 7590 , 27385 , 48150 {\displaystyle a,b,c,d=-31764,7590,27385,48150} </content>	` Pythagorean triple Descartes' Circle Theorem For the case of Descartes' circle theorem where all variables are squares, 2 ( a 4 + b 4 + c 4 + d 4 ) = ( a 2 + b 2 + c 2 + d 2 ) 2 {\displaystyle 2(a^{4}+b^{4}+c^{4}+d^{4})=(a^{2}+b^{2}+c^{2}+d^{2})^{2}} Euler showed this is equivalent to three simultaneous Pythagorean triples, ( 2 a b ) 2 + ( 2 c d ) 2 = ( a 2 + b 2 − c 2 − d 2 ) 2 {\displaystyle (2ab)^{2}+(2cd)^{2}=(a^{2}+b^{2}-c^{2}-d^{2})^{2}} ( 2 a c ) 2 + ( 2 b d ) 2 = ( a 2 − b 2 + c 2 − d 2 ) 2 {\displaystyle (2ac)^{2}+(2bd)^{2}=(a^{2}-b^{2}+c^{2}-d^{2})^{2}} ( 2 a d ) 2 + ( 2 b c ) 2 = ( a 2 − b 2 − c 2 + d 2 ) 2 {\displaystyle (2ad)^{2}+(2bc)^{2}=(a^{2}-b^{2}-c^{2}+d^{2})^{2}} There is also an infinite number of solutions, and for the special case when a + b = c {\displaystyle a+b=c} , then the equation simplifi...

Loss: TripletLoss with these parameters:

{
    "distance_metric": "TripletDistanceMetric.EUCLIDEAN",
    "triplet_margin": 5
}

Training Hyperparameters

Non-Default Hyperparameters

per_device_train_batch_size: 64
per_device_eval_batch_size: 64
num_train_epochs: 1
multi_dataset_batch_sampler: round_robin

All Hyperparameters

Click to expand

overwrite_output_dir: False
do_predict: False
eval_strategy: no
prediction_loss_only: True
per_device_train_batch_size: 64
per_device_eval_batch_size: 64
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
num_train_epochs: 1
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}
tp_size: 0
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: None
hub_always_push: False
gradient_checkpointing: False
gradient_checkpointing_kwargs: None
include_inputs_for_metrics: False
include_for_metrics: []
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
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
average_tokens_across_devices: False
prompts: None
batch_sampler: batch_sampler
multi_dataset_batch_sampler: round_robin

Training Logs

Epoch	Step	Training Loss
0.3199	500	4.0855
0.6398	1000	3.9274
0.9597	1500	3.9199

Framework Versions

Python: 3.12.8
Sentence Transformers: 3.4.1
Transformers: 4.51.3
PyTorch: 2.5.1+cu124
Accelerate: 1.3.0
Datasets: 3.2.0
Tokenizers: 0.21.0

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",
}

TripletLoss

@misc{hermans2017defense,
    title={In Defense of the Triplet Loss for Person Re-Identification},
    author={Alexander Hermans and Lucas Beyer and Bastian Leibe},
    year={2017},
    eprint={1703.07737},
    archivePrefix={arXiv},
    primaryClass={cs.CV}
}

Lysandrec
/

MNLP_M2_document_encoder