Master-thesis-NAP/ModernBERT-DAPT-Embed-DAPT-Math-v2

ModernBERT DAPT Embed DAPT Math

This is a sentence-transformers model finetuned from Master-thesis-NAP/ModernBert-DAPT-math. 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: Master-thesis-NAP/ModernBert-DAPT-math <!-- at revision a30384f91d764c272e6b740c256d5581325ea4bb -->
• —Maximum Sequence Length: 8192 tokens
• —Output Dimensionality: 768 dimensions
• —Similarity Function: Cosine Similarity <!-- - Training Dataset: Unknown -->
• —Language: en
• —License: apache-2.0

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': 8192, 'do_lower_case': False}) with Transformer model: ModernBertModel 
  (1): Pooling({'word_embedding_dimension': 768, '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("Master-thesis-NAP/ModernBERT-DAPT-Embed-DAPT-Math-v2")
# Run inference
sentences = [
    'What is the meaning of the identity containment $1_x:x\\to x$ in the context of the bond system?',
    "A \\emph{bond system} is a tuple $(B,C,s,t,1,\\cdot)$, where $B$ is a set of \\emph{bonds}, $C$ is a set of \\emph{content} relations, and $s,t:C\\to B$ are \\emph{source} and \\emph{target} functions. For $c\\in C$ with $s(c)=x$ and $t(c)=y$, we write $x\\xrightarrow{c}y$ or $c:x\\to y$, indicating that $x$ \\emph{contains} $y$. Each bond $x\\in B$ has an \\emph{identity} containment $1_x:x\\to x$, meaning every bond trivially contains itself. For $c:x\\to y$ and $c':y\\to z$, their composition is $cc':x\\to z$. These data must satisfy:\n    \\begin{enumerate}\n        \\item Identity laws: For each $c:x\\to y$, $1_x c= c=c1_y$\n        \\item Associativity: For $c:x\\to y$, $c':y\\to z$, $c'':z\\to w$, $c(c'c'')=(cc')c''$\n        \\item Anti-symmetry: For $c:x\\to y$ and $c':y\\to x$, $x=y$\n        \\item Left cancellation: For $c,c':x\\to y$ and $c'':y\\to z$, if $cc''=c'c''$, then $c=c'$\n    \\end{enumerate}",
    '\\label{lem:opt_lin}\nConsider the optimization problem\n\\begin{equation}\\label{eq:max_tr_lem}\n\\begin{aligned}\n    \\max_{\\bs{U}}&\\;\\; \\Re\\{\\mrm{tr}(\\bs{U}^\\mrm{H}\\bs{B}) \\}\\\\\n    \\mrm{s.t. \\;\\;}& \\bs{U}\\in \\mathcal{U}(N),\n\\end{aligned}\n\\end{equation}\nwhere $\\bs{B}$ may be an arbitrary $N\\times N$ matrix with singular value decomposition (SVD) $\\bs{B}=\\bs{U}_{\\bs{B}}\\bs{S}_{\\bs{B}}\\bs{V}_{\\bs{B}}^\\mrm{H}$. The solution to \\eqref{eq:max_tr_lem} is given by\n\\begin{equation}\\label{eq:sol_max}\n    \\bs{U}_\\mrm{opt} = \\bs{U}_{\\bs{B}}^\\mrm{H}\\bs{V}_{\\bs{B}}.\n\\end{equation}\n\\begin{skproof}\n    A formal proof, which may be included in the extended version, can be obtained by defining the Riemannian gradient over the unitary group and finding the stationary point where it vanishes. However, an intuitive argument is that the solution to \\eqref{eq:max_tr_lem} is obtained by positively combining the singular values of $\\bs{B}$, leading to \\eqref{eq:sol_max}.\n\\end{skproof}',
]
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]

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Downstream Usage (Sentence Transformers)

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Evaluation

Metrics

Information Retrieval

• —Dataset: TESTING
• —Evaluated with <code>InformationRetrievalEvaluator</code>

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Training Details

Training Dataset

Unnamed Dataset

• —Size: 79,876 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: 9 tokens</li><li>mean: 38.48 tokens</li><li>max: 142 tokens</li></ul> | <ul><li>min: 5 tokens</li><li>mean: 210.43 tokens</li><li>max: 924 tokens</li></ul> |
• —Samples: | anchor | positive | |:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | <code>What is the limit of the proportion of 1's in the sequence $an$ as $n$ approaches infinity, given that $0 \leq 3gn -2n \leq 4$?</code> | <code>Let $gn$ be the number of $1$'s in the sequence $a1 a2 \cdots an$.<br>Then <br>\begin{equation}<br>0 \leq 3gn -2n \leq 4<br>\label{star}<br>\end{equation}<br>for all $n$, and hence<br>$\lim{n \rightarrow \infty} gn/n = 2/3$.<br>\label{thm1}</code> | | <code>Does the statement of \textbf{ThmConjAreTrue} imply that the maximum genus of a locally Cohen-Macaulay curve in $\mathbb{P}^3{\mathbb{C}}$ of degree $d$ that does not lie on a surface of degree $s-1$ is always equal to $g(d,s)$?</code> | <code>\label{ThmConjAreTrue}<br>Conjectures \ref{Conj1} and \ref{Conj2} are true.<br>As a consequence, <br>if either $d=s \geq 1$ or $d \geq 2s+1 \geq 3$, <br>the maximum genus of a locally Cohen-Macaulay curve in $\mathbb{P}^3_{\mathbb{C}}$ of degree $d$ that does not lie on a surface of degree $s-1$ is equal to $g(d,s)$.</code> | | <code>\\emph{Is the statement \emph{If $X$ is a compact Hausdorff space, then $X$ is normal}, proven in the first isomorphism theorem for topological groups, or is it a well-known result in topology?}</code> | <code>}<br>\newcommand{\ep}{</code> |
• —Loss: <code>MultipleNegativesRankingLoss</code> with these parameters:

  {
      "scale": 20.0,
      "similarity_fct": "cos_sim"
  }

Training Hyperparameters

Non-Default Hyperparameters

• —eval_strategy: epoch
• —per_device_train_batch_size: 16
• —per_device_eval_batch_size: 16
• —gradient_accumulation_steps: 8
• —learning_rate: 2e-05
• —num_train_epochs: 4
• —lr_scheduler_type: cosine
• —warmup_ratio: 0.1
• —bf16: True
• —tf32: True
• —load_best_model_at_end: True
• —optim: adamwtorchfused
• —batch_sampler: no_duplicates

All Hyperparameters

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

• —overwrite_output_dir: False
• —do_predict: False
• —eval_strategy: epoch
• —prediction_loss_only: True
• —per_device_train_batch_size: 16
• —per_device_eval_batch_size: 16
• —per_gpu_train_batch_size: None
• —per_gpu_eval_batch_size: None
• —gradient_accumulation_steps: 8
• —eval_accumulation_steps: None
• —torch_empty_cache_steps: None
• —learning_rate: 2e-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: 4
• —max_steps: -1
• —lr_scheduler_type: cosine
• —lr_scheduler_kwargs: {}
• —warmup_ratio: 0.1
• —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: True
• —fp16: False
• —fp16_opt_level: O1
• —half_precision_backend: auto
• —bf16_full_eval: False
• —fp16_full_eval: False
• —tf32: True
• —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: True
• —ignore_data_skip: False
• —fsdp: []
• —fsdp_min_num_params: 0
• —fsdp_config: {'minnumparams': 0, 'xla': False, 'xlafsdpv2': False, 'xlafsdpgrad_ckpt': False}
• —tp_size: 0
• —fsdp_transformer_layer_cls_to_wrap: None
• —accelerator_config: {'splitbatches': False, 'dispatchbatches': None, 'evenbatches': True, 'useseedablesampler': True, 'nonblocking': False, 'gradientaccumulationkwargs': None}
• —deepspeed: None
• —label_smoothing_factor: 0.0
• —optim: adamwtorchfused
• —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: no_duplicates
• —multi_dataset_batch_sampler: proportional

</details>

Training Logs

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

• —The bold row denotes the saved checkpoint. </details>

Framework Versions

• —Python: 3.11.12
• —Sentence Transformers: 4.1.0
• —Transformers: 4.51.3
• —PyTorch: 2.6.0+cu124
• —Accelerate: 1.6.0
• —Datasets: 2.14.4
• —Tokenizers: 0.21.1

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}
}

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