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

Metric	Value
cosine_accuracy@1	0.8599
cosine_accuracy@3	0.9113
cosine_accuracy@5	0.9272
cosine_accuracy@10	0.9432
cosine_precision@1	0.8599
cosine_precision@3	0.6012
cosine_precision@5	0.4809
cosine_precision@10	0.3352
cosine_recall@1	0.0415
cosine_recall@3	0.0813
cosine_recall@5	0.1041
cosine_recall@10	0.1366
cosine_ndcg@10	0.4373
cosine_mrr@10	0.8887
cosine_map@100	0.1552

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 tokens mean: 38.48 tokens max: 142 tokens	min: 5 tokens mean: 210.43 tokens max: 924 tokens	min: 14 tokens mean: 88.74 tokens max: 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

Click to expand

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