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
• 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-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]

Evaluation

Metrics

Information Retrieval

• Dataset: TESTING
• Evaluated with InformationRetrievalEvaluator

Metric	Value
cosine_accuracy@1	0.868
cosine_accuracy@3	0.9183
cosine_accuracy@5	0.9325
cosine_accuracy@10	0.9496
cosine_precision@1	0.868
cosine_precision@3	0.6119
cosine_precision@5	0.4935
cosine_precision@10	0.3476
cosine_recall@1	0.0419
cosine_recall@3	0.0832
cosine_recall@5	0.1074
cosine_recall@10	0.1421
cosine_ndcg@10	0.4493
cosine_mrr@10	0.8964
cosine_map@100	0.1638

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

• 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}
• tp_size: 0
• 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

Click to expand

Epoch	Step	Training Loss	TESTING_cosine_ndcg@10
0.0160	10	20.2777	-
0.0320	20	19.6613	-
0.0481	30	18.8588	-
0.0641	40	17.5525	-
0.0801	50	15.1065	-
0.0961	60	10.8128	-
0.1122	70	7.0698	-
0.1282	80	4.532	-
0.1442	90	3.5143	-
0.1602	100	2.3256	-
0.1762	110	1.4688	-
0.1923	120	1.0081	-
0.2083	130	0.949	-
0.2243	140	0.9709	-
0.2403	150	0.8403	-
0.2564	160	0.8749	-
0.2724	170	0.7955	-
0.2884	180	0.6587	-
0.3044	190	0.5832	-
0.3204	200	0.5376	-
0.3365	210	0.608	-
0.3525	220	0.4639	-
0.3685	230	0.6611	-
0.3845	240	0.5589	-
0.4006	250	0.5845	-
0.4166	260	0.4392	-
0.4326	270	0.4746	-
0.4486	280	0.4517	-
0.4647	290	0.4034	-
0.4807	300	0.4437	-
0.4967	310	0.4339	-
0.5127	320	0.4445	-
0.5287	330	0.3793	-
0.5448	340	0.3591	-
0.5608	350	0.4694	-
0.5768	360	0.4668	-
0.5928	370	0.4121	-
0.6089	380	0.4688	-
0.6249	390	0.387	-
0.6409	400	0.3748	-
0.6569	410	0.2997	-
0.6729	420	0.3756	-
0.6890	430	0.2993	-
0.7050	440	0.3514	-
0.7210	450	0.3646	-
0.7370	460	0.308	-
0.7531	470	0.3612	-
0.7691	480	0.2845	-
0.7851	490	0.2792	-
0.8011	500	0.2204	-
0.8171	510	0.2757	-
0.8332	520	0.2674	-
0.8492	530	0.3753	-
0.8652	540	0.3546	-
0.8812	550	0.3166	-
0.8973	560	0.2656	-
0.9133	570	0.3215	-
0.9293	580	0.2559	-
0.9453	590	0.4629	-
0.9613	600	0.31	-
0.9774	610	0.3601	-
0.9934	620	0.2391	-
1.0	625	-	0.4229
1.0080	630	0.2507	-
1.0240	640	0.1852	-
1.0401	650	0.1836	-
1.0561	660	0.1487	-
1.0721	670	0.1495	-
1.0881	680	0.1567	-
1.1041	690	0.1497	-
1.1202	700	0.1632	-
1.1362	710	0.1997	-
1.1522	720	0.182	-
1.1682	730	0.1884	-
1.1843	740	0.1766	-
1.2003	750	0.1477	-
1.2163	760	0.181	-
1.2323	770	0.092	-
1.2483	780	0.1506	-
1.2644	790	0.1305	-
1.2804	800	0.1533	-
1.2964	810	0.2306	-
1.3124	820	0.1861	-
1.3285	830	0.1157	-
1.3445	840	0.1054	-
1.3605	850	0.1696	-
1.3765	860	0.1327	-
1.3925	870	0.1485	-
1.4086	880	0.1395	-
1.4246	890	0.1021	-
1.4406	900	0.1283	-
1.4566	910	0.102	-
1.4727	920	0.1825	-
1.4887	930	0.1395	-
1.5047	940	0.157	-
1.5207	950	0.1444	-
1.5368	960	0.1317	-
1.5528	970	0.146	-
1.5688	980	0.1809	-
1.5848	990	0.1368	-
1.6008	1000	0.2036	-
1.6169	1010	0.1292	-
1.6329	1020	0.1306	-
1.6489	1030	0.1473	-
1.6649	1040	0.1595	-
1.6810	1050	0.1471	-
1.6970	1060	0.1869	-
1.7130	1070	0.1445	-
1.7290	1080	0.157	-
1.7450	1090	0.1382	-
1.7611	1100	0.157	-
1.7771	1110	0.1073	-
1.7931	1120	0.0864	-
1.8091	1130	0.1312	-
1.8252	1140	0.1644	-
1.8412	1150	0.1366	-
1.8572	1160	0.1257	-
1.8732	1170	0.127	-
1.8892	1180	0.1494	-
1.9053	1190	0.1516	-
1.9213	1200	0.1709	-
1.9373	1210	0.1717	-
1.9533	1220	0.1044	-
1.9694	1230	0.1551	-
1.9854	1240	0.1303	-
2.0	1250	0.1081	0.4392
2.0160	1260	0.0572	-
2.0320	1270	0.0504	-
2.0481	1280	0.0535	-
2.0641	1290	0.0512	-
2.0801	1300	0.0539	-
2.0961	1310	0.0462	-
2.1122	1320	0.0611	-
2.1282	1330	0.0989	-
2.1442	1340	0.0462	-
2.1602	1350	0.061	-
2.1762	1360	0.0557	-
2.1923	1370	0.0622	-
2.2083	1380	0.0744	-
2.2243	1390	0.0531	-
2.2403	1400	0.0507	-
2.2564	1410	0.0533	-
2.2724	1420	0.0676	-
2.2884	1430	0.0706	-
2.3044	1440	0.0452	-
2.3204	1450	0.0415	-
2.3365	1460	0.0562	-
2.3525	1470	0.0487	-
2.3685	1480	0.0614	-
2.3845	1490	0.045	-
2.4006	1500	0.0529	-
2.4166	1510	0.048	-
2.4326	1520	0.059	-
2.4486	1530	0.0593	-
2.4647	1540	0.0631	-
2.4807	1550	0.0506	-
2.4967	1560	0.058	-
2.5127	1570	0.0896	-
2.5287	1580	0.0522	-
2.5448	1590	0.035	-
2.5608	1600	0.0677	-
2.5768	1610	0.0538	-
2.5928	1620	0.0485	-
2.6089	1630	0.0575	-
2.6249	1640	0.0571	-
2.6409	1650	0.0761	-
2.6569	1660	0.0582	-
2.6729	1670	0.0366	-
2.6890	1680	0.0445	-
2.7050	1690	0.0519	-
2.7210	1700	0.0506	-
2.7370	1710	0.0637	-
2.7531	1720	0.0618	-
2.7691	1730	0.0433	-
2.7851	1740	0.0503	-
2.8011	1750	0.0541	-
2.8171	1760	0.0443	-
2.8332	1770	0.0634	-
2.8492	1780	0.0586	-
2.8652	1790	0.0497	-
2.8812	1800	0.0444	-
2.8973	1810	0.0397	-
2.9133	1820	0.0483	-
2.9293	1830	0.0441	-
2.9453	1840	0.0758	-
2.9613	1850	0.0988	-
2.9774	1860	0.0566	-
2.9934	1870	0.0497	-
3.0	1875	-	0.4466
3.0080	1880	0.0388	-
3.0240	1890	0.0278	-
3.0401	1900	0.0231	-
3.0561	1910	0.0482	-
3.0721	1920	0.0416	-
3.0881	1930	0.052	-
3.1041	1940	0.0403	-
3.1202	1950	0.0384	-
3.1362	1960	0.0288	-
3.1522	1970	0.0368	-
3.1682	1980	0.0301	-
3.1843	1990	0.029	-
3.2003	2000	0.0332	-
3.2163	2010	0.0307	-
3.2323	2020	0.0502	-
3.2483	2030	0.0474	-
3.2644	2040	0.0383	-
3.2804	2050	0.0392	-
3.2964	2060	0.0308	-
3.3124	2070	0.0479	-
3.3285	2080	0.0448	-
3.3445	2090	0.0478	-
3.3605	2100	0.0249	-
3.3765	2110	0.03	-
3.3925	2120	0.0284	-
3.4086	2130	0.0323	-
3.4246	2140	0.0379	-
3.4406	2150	0.0221	-
3.4566	2160	0.0354	-
3.4727	2170	0.0332	-
3.4887	2180	0.0287	-
3.5047	2190	0.0382	-
3.5207	2200	0.0342	-
3.5368	2210	0.0381	-
3.5528	2220	0.056	-
3.5688	2230	0.0426	-
3.5848	2240	0.0465	-
3.6008	2250	0.0372	-
3.6169	2260	0.0345	-
3.6329	2270	0.0459	-
3.6489	2280	0.0368	-
3.6649	2290	0.0349	-
3.6810	2300	0.059	-
3.6970	2310	0.0275	-
3.7130	2320	0.0305	-
3.7290	2330	0.0406	-
3.7450	2340	0.0456	-
3.7611	2350	0.0311	-
3.7771	2360	0.0428	-
3.7931	2370	0.0308	-
3.8091	2380	0.0345	-
3.8252	2390	0.0378	-
3.8412	2400	0.0322	-
3.8572	2410	0.0236	-
3.8732	2420	0.0383	-
3.8892	2430	0.0295	-
3.9053	2440	0.0273	-
3.9213	2450	0.0286	-
3.9373	2460	0.0366	-
3.9533	2470	0.0285	-
3.9694	2480	0.0335	-
3.9854	2490	0.0278	-
3.995	2496	-	0.4493

• The bold row denotes the saved checkpoint.

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}
}