ModernBERT DAPT Embed DAPT Math

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")
# 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]

Evaluation

Metrics

Information Retrieval

Dataset: TESTING
Evaluated with InformationRetrievalEvaluator

Metric	Value
cosine_accuracy@1	0.8649
cosine_accuracy@3	0.9143
cosine_accuracy@5	0.9287
cosine_accuracy@10	0.9458
cosine_precision@1	0.8649
cosine_precision@3	0.6053
cosine_precision@5	0.4861
cosine_precision@10	0.3406
cosine_recall@1	0.0418
cosine_recall@3	0.0822
cosine_recall@5	0.1057
cosine_recall@10	0.1394
cosine_ndcg@10	0.4427
cosine_mrr@10	0.8928
cosine_map@100	0.1599

Training Details

Training Dataset

Unnamed Dataset

Size: 79,876 training samples
Columns: anchor and positive
Approximate statistics based on the first 1000 samples:
anchor positive
type string string
details
min: 9 tokens
mean: 38.48 tokens
max: 142 tokens

min: 5 tokens
mean: 210.43 tokens
max: 924 tokens

	anchor	positive
type	string	string
details	min: 9 tokens mean: 38.48 tokens max: 142 tokens	min: 5 tokens mean: 210.43 tokens max: 924 tokens

Samples:

anchor	positive
`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}`
`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 $g(d,s)$.`
`\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}{`

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