ModernBERT base

This is a sentence-transformers model finetuned from answerdotai/ModernBERT-base. 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: answerdotai/ModernBERT-base
• Maximum Sequence Length: 8192 tokens
• Output Dimensionality: 768 dimensions
• Similarity Function: Cosine Similarity

• 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-base-finetuned-hard_negatives")
# Run inference
sentences = [
    'What is the error estimate for the eigenfunction approximation in terms of the weak eigenvalue and the norm of the difference between the exact and approximate eigenfunctions?',
    '(\\cite{DangWangXieZhou})\\label{Theorem_Error_Estimate_k}\nLet us define the spectral projection $F_{k,h}^{(\\ell)}: V\\mapsto {\\rm span}\\{u_{1,h}^{(\\ell)}, \\cdots, u_{k,h}^{(\\ell)}\\}$ for any integer $\\ell \\geq 1$ as follows:\n\\begin{eqnarray*}\na(F_{k,h}^{(\\ell)}w, u_{i,h}^{(\\ell)}) = a(w, u_{i,h}^{(\\ell)}), \\ \\ \\ i=1, \\cdots, k\\ \\ {\\rm for}\\ w\\in V.\n\\end{eqnarray*}\nThen the exact eigenfunctions $\\bar u_{1,h},\\cdots, \\bar u_{k,h}$ of (\\ref{Weak_Eigenvalue_Discrete}) and the eigenfunction approximations $u_{1,h}^{(\\ell+1)}$, $\\cdots$,  $u_{k,h}^{(\\ell+1)}$ from Algorithm \\ref{Algorithm_k} with the integer $\\ell > 1$ have the following error estimate:\n\\begin{eqnarray*}\\label{Error_Estimate_Inverse}\n \\left\\|\\bar u_{i,h} - F_{k,h}^{(\\ell+1)}\\bar u_{i,h} \\right\\|_a \\leq\n \\bar\\lambda_{i,h} \\sqrt{1+\\frac{\\eta_a^2(V_H)}{\\bar\\lambda_{1,h}\\big(\\delta_{k,i,h}^{(\\ell+1)}\\big)^2}}\n\\left(1+\\frac{\\bar\\mu_{1,h}}{\\delta_{k,i,h}^{(\\ell)}}\\right)\\eta_a^2(V_H)\\left\\|\\bar u_{i,h} - F_{k,h}^{(\\ell)}\\bar u_{i,h} \\right\\|_a,\n\\end{eqnarray*}\nwhere $\\delta_{k,i,h}^{(\\ell)} $ is defined as follows:\n\\begin{eqnarray*}\n\\delta_{k,i,h}^{(\\ell)} = \\min_{j\\not\\in \\{1, \\cdots, k\\}}\\left|\\frac{1}{\\lambda_{j,h}^{(\\ell)}}-\\frac{1}{\\bar\\lambda_{i,h}}\\right|,\\ \\ \\ i=1, \\cdots, k.\n\\end{eqnarray*}\nFurthermore, the following $\\left\\|\\cdot\\right\\|_b$-norm error estimate holds:\n\\begin{eqnarray*}\n\\left\\|\\bar u_{i,h} -F_{k,h}^{(\\ell+1)}\\bar u_{i,h} \\right\\|_b\\leq \n\\left(1+\\frac{\\bar\\mu_{1,h}}{\\delta_{k,i,h}^{(\\ell+1)}}\\right)\\eta_a(V_H) \\left\\|\\bar u_{i,h} -F_{k,h}^{(\\ell+1)}\\bar u_{i,h}\\right\\|_a.\n\\end{eqnarray*}',
    '\\big[{\\bf Condition $SD1(h)$}\\big]\\label{DefnSD1(h)}\n\nIn \\cite{MDL} an approximation order $O(h^s)$, as $h\\to 0$, is proved, where $h$ is the sampling distance. The achievable order $s$ is of course limited by the smoothness order of the boundaries of $Graph(F)$. Then, the order $s$ depends upon the degree of the polynomials used to approximate the boundary near the neighborhood of points of topology change and upon the degree of splines used at regular regions. \n\nFor example, let us view Step C of the approximation algorithm described in Section 5.2 of \\cite{MDL}. \nIt is assumed that the boundary curves are $C^{2k}$ smooth, and it is implicitly assumed that $h$ is small enough so that there are $2k$ sample points close to the point of topology change, for computing the polynomial $p_{2k-1}$ therein.\nThis condition is related to the more general condition $SD(h)$ and it can serve as a practical way of checking it for the case $d=1$. That is, near a point of topology change, we check whether there are enough sample points for applying the approximation algorithm in \\cite{MDL}. We denote this condition as the $SD1(h)$ condition.',
]
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]

Evaluation

Metrics

Information Retrieval

• Dataset: TESTING
• Evaluated with InformationRetrievalEvaluator

Training Details

Training Dataset

Unnamed Dataset

• Size: 79,876 training samples
• Columns: anchor, positive, and negative
• Approximate statistics based on the first 1000 samples:

  	anchor	positive	negative
  type	string	string	string
  details	min: 9 tokensmean: 38.48 tokensmax: 142 tokens	min: 5 tokensmean: 210.43 tokensmax: 924 tokens	min: 14 tokensmean: 88.74 tokensmax: 516 tokens

• Samples:

  anchor	positive	negative
  What is the limit of the proportion of 1's in the sequence $a_n$ as $n$ approaches infinity, given that $0 \leq 3g_n -2n \leq 4$?	Let $g_n$ be the number of $1$'s in the sequence $a_1 a_2 \cdots a_n$.Then \begin{equation}0 \leq 3g_n -2n \leq 4\label{star}\end{equation}for all $n$, and hence$\lim_{n \rightarrow \infty} g_n/n = 2/3$.\label{thm1}	[] The tree $ \mathcal{T}_{ \infty}$ is the limit in Benjamini--Schramm quenched sense of $ \mathbb{T}_n$ as $n$ goes to infinity.
  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 $g(d,s)$?	\label{ThmConjAreTrue}Conjectures \ref{Conj1} and \ref{Conj2} are true.As a consequence, if either $d=s \geq 1$ or $d \geq 2s+1 \geq 3$, 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 $g(d,s)$.	[{\cite[Corollary 2.2.2 with $p=3$]{BSY}}] 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 $3$.
  \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?}	}\newcommand{\ep}{	\label{prop:coherence} 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 $RX$.

• Loss: MultipleNegativesRankingLoss 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: adamw_torch_fused
• batch_sampler: no_duplicates

All Hyperparameters

• 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: {'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_fused
• 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

Training Logs

• The bold row denotes the saved checkpoint.

Framework Versions

• Python: 3.11.12
• Sentence Transformers: 4.1.0
• Transformers: 4.52.2
• PyTorch: 2.6.0+cu124
• Accelerate: 1.7.0
• 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}
}