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

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")
# Run inference
sentences = [
    "Does Werner-Young's inequality imply that the convolution of two $L^p$ spaces is always $L^r$ for $1 < r < \\infty$?",
    "[Werner-Young's inequality]\\label{Young op-op}\nSuppose $S\\in \\cS^p$ and $T\\in \\cS^q$ with $1+r^{-1}=p^{-1}+q^{-1}$.\nThen $S\\star T\\in L^r(\\R^{2d})$ and\n\\begin{align*}\n    \\|S\\star T\\|_{L^{r}}\\leq \\|S\\|_{\\cS^p}\\|T\\|_{\\cS^q}.\n\\end{align*}",
    '$\\cE^{(0)}_{p,\\alpha}$ satisfies the second Beurling-Deny criterion.  If $1 < p_- \\leq p_+ < \\infty$, it is reflexive and satisfies the $\\Delta_2$-condition.  \n %',
]
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>, <code>positive</code>, and <code>negative</code>
• —Approximate statistics based on the first 1000 samples: | | anchor | positive | negative | |:--------|:-----------------------------------------------------------------------------------|:------------------------------------------------------------------------------------|:------------------------------------------------------------------------------------| | type | string | 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> | <ul><li>min: 14 tokens</li><li>mean: 91.02 tokens</li><li>max: 481 tokens</li></ul> |
• —Samples: | anchor | positive | negative | |:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | <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>\label{thm:boundsinitial}<br> Let $\seqq{s}$ be a sequence of rank $r$ for which the roots of the characteristic polynomial are all different. Then, for any positive integer $M$, the rank of $\seq{s^M}$ is at most<br> \begin{align}<br> \rank s^M \leq \binom{M+r-1}{M}.<br> \end{align}</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>[{\cite[Corollary 2.2.2 with $p=3$]{BSY}}]<br> Let $S$ be a non-trivial Severi-Brauer surface over a perfect field $\textbf{k}$. Then $S$ does not contain points of degree $d$, where $d$ is not divisible by $3$. On the other hand $S$ contains a point of degree $3$.</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> | <code>\label{prop:coherence}<br> If $X$ is a qcqs scheme, then $RX$ is coherent in the sense that the set of quasi-compact open subsets of $RX$ is closed under finite intersections and forms a basis for the topology of $RX$.</code> |
• —Loss: <code>TripletLoss</code> with these parameters:

  {
      "distance_metric": "TripletDistanceMetric.COSINE",
      "triplet_margin": 0.1
  }

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",
}

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}
}

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