ModernBERT-small-1.5-Retrieval-BEIR-Tuned

This is a sentence-transformers model trained on the msmarco, gooaq and natural_questions datasets. It maps sentences & paragraphs to a 384-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
  • Maximum Sequence Length: 1024 tokens
  • Output Dimensionality: 384 dimensions
  • Similarity Function: Cosine Similarity
  • Training Datasets:
  • Language: en
  • License: apache-2.0

Model Sources

Full Model Architecture

SentenceTransformer(
  (0): Transformer({'max_seq_length': 1024, 'do_lower_case': False, 'architecture': 'ModernBertModel'})
  (1): Pooling({'word_embedding_dimension': 384, '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})
)

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("sentence_transformers_model_id")
# Run inference
sentences = [
    'who is catch me if you can based on',
    'Catch Me If You Can Catch Me If You Can is a 2002 American biographical crime film directed and produced by Steven Spielberg from a screenplay by Jeff Nathanson. The film is based on the life of Frank Abagnale, who, before his 19th birthday, successfully performed cons worth millions of dollars by posing as a Pan American World Airways pilot, a Georgia doctor and a Louisiana parish prosecutor. His primary crime was check fraud; he became so experienced that the FBI eventually turned to him for help in catching other checking forgers. The film stars Leonardo DiCaprio and Tom Hanks, with Christopher Walken, Martin Sheen, and Nathalie Baye in supporting roles.',
    "Colonial Brazil In contrast to the neighboring Spanish possessions, which had several viceroyalties with jurisdiction initially over New Spain (Mexico) and Peru, and in the eighteenth century expanded to viceroyalties of Rio de la Plata and New Granada, the Portuguese colony of Brazil was settled mainly in the coastal area by the Portuguese and a large black slave population working sugar plantations and mines. The boom and bust economic cycles were linked to export products. Brazil's sugar age, with the development of plantation slavery, merchants serving as middle men between production sites, Brazilian ports, and Europe was undermined by the growth of the sugar industry in the Caribbean on islands that European powers seized from Spain. Gold and diamonds were discovered and mined in southern Brazil through the end of the colonial era. Brazilian cities were largely port cities and the colonial administrative capital was moved several times in response to the rise and fall of export products' importance. Unlike Spanish America that fragmented in many republics, Brazil remained as a single administrative unit with a monarch, giving rise to the largest country in Latin America. Like Spanish America with European Spanish, Brazil had linguistic integrity of Portuguese. Both Spanish America and Brazil were Roman Catholic.",
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 384]

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities)
# tensor([[ 1.0000,  0.5555, -0.1763],
#         [ 0.5555,  1.0000, -0.0652],
#         [-0.1763, -0.0652,  1.0000]])

Evaluation

Metrics

Information Retrieval

Metric NanoMSMARCO NanoNQ NanoHotpotQA
cosine_accuracy@1 0.08 0.16 0.52
cosine_accuracy@3 0.3 0.32 0.72
cosine_accuracy@5 0.36 0.44 0.78
cosine_accuracy@10 0.5 0.6 0.84
cosine_precision@1 0.08 0.16 0.52
cosine_precision@3 0.1 0.1067 0.2933
cosine_precision@5 0.072 0.088 0.192
cosine_precision@10 0.05 0.06 0.118
cosine_recall@1 0.08 0.14 0.26
cosine_recall@3 0.3 0.29 0.44
cosine_recall@5 0.36 0.4 0.48
cosine_recall@10 0.5 0.55 0.59
cosine_ndcg@10 0.2775 0.3273 0.5098
cosine_mrr@10 0.208 0.2773 0.6255
cosine_map@100 0.2278 0.2638 0.4239

Nano BEIR

  • Dataset: NanoBEIR_mean
  • Evaluated with NanoBEIREvaluator with these parameters:
    {
        "dataset_names": [
            "MSMARCO",
            "NQ",
            "HotpotQA"
        ]
    }
    
Metric Value
cosine_accuracy@1 0.2533
cosine_accuracy@3 0.4467
cosine_accuracy@5 0.5267
cosine_accuracy@10 0.6467
cosine_precision@1 0.2533
cosine_precision@3 0.1667
cosine_precision@5 0.1173
cosine_precision@10 0.076
cosine_recall@1 0.16
cosine_recall@3 0.3433
cosine_recall@5 0.4133
cosine_recall@10 0.5467
cosine_ndcg@10 0.3715
cosine_mrr@10 0.3703
cosine_map@100 0.3052

Training Details

Training Datasets

msmarco

  • Dataset: msmarco at 28ff31e
  • Size: 17,307,990 training samples
  • Columns: anchor, positive, and negative
  • Approximate statistics based on the first 1000 samples:
    anchor positive negative
    type string string string
    details
    • min: 5 tokens
    • mean: 9.57 tokens
    • max: 16 tokens
    • min: 44 tokens
    • mean: 83.39 tokens
    • max: 211 tokens
    • min: 24 tokens
    • mean: 83.62 tokens
    • max: 268 tokens
  • Samples:
    anchor positive negative
    what are the liberal arts? liberal arts. 1. the academic course of instruction at a college intended to provide general knowledge and comprising the arts, humanities, natural sciences, and social sciences, as opposed to professional or technical subjects. The liberal arts education at the secondary school level prepares the student for higher education at a university. They are thus meant for the more academically minded students. In addition to the usual curriculum, students of a liberal arts education often study Latin and Ancient Greek. Some liberal arts education provide general education, others have a specific focus.
    what are the liberal arts? liberal arts. 1. the academic course of instruction at a college intended to provide general knowledge and comprising the arts, humanities, natural sciences, and social sciences, as opposed to professional or technical subjects. Liberal Arts. Upon completion of the Liberal Arts degree, students will be able to express ideas in coherent, creative, and appropriate forms, orally and in writing. Students will be able to apply their reading abilities in order to interconnect an understanding of resources to academic, professional, and personal interests.
    what are the liberal arts? liberal arts. 1. the academic course of instruction at a college intended to provide general knowledge and comprising the arts, humanities, natural sciences, and social sciences, as opposed to professional or technical subjects. Rather than preparing students for a specific career, liberal arts programs focus on cultural literacy and hone communication and analytical skills. They often cover various disciplines, ranging from the humanities to social sciences. 1 Program Levels in Liberal Arts: Associate degree, Bachelor's degree, Master's degree.
  • Loss: CachedMultipleNegativesRankingLoss with these parameters:
    {
        "scale": 20.0,
        "similarity_fct": "cos_sim",
        "mini_batch_size": 64
    }
    

gooaq

  • Dataset: gooaq at b089f72
  • Size: 3,012,496 training samples
  • Columns: anchor and positive
  • Approximate statistics based on the first 1000 samples:
    anchor positive
    type string string
    details
    • min: 8 tokens
    • mean: 12.19 tokens
    • max: 22 tokens
    • min: 13 tokens
    • mean: 58.34 tokens
    • max: 124 tokens
  • Samples:
    anchor positive
    is toprol xl the same as metoprolol? Metoprolol succinate is also known by the brand name Toprol XL. It is the extended-release form of metoprolol. Metoprolol succinate is approved to treat high blood pressure, chronic chest pain, and congestive heart failure.
    are you experienced cd steve hoffman? The Are You Experienced album was apparently mastered from the original stereo UK master tapes (according to Steve Hoffman - one of the very few who has heard both the master tapes and the CDs produced over the years). ... The CD booklets were a little sparse, but at least they stayed true to the album's original design.
    how are babushka dolls made? Matryoshka dolls are made of wood from lime, balsa, alder, aspen, and birch trees; lime is probably the most common wood type. ... After cutting, the trees are stripped of most of their bark, although a few inner rings of bark are left to bind the wood and keep it from splitting.
  • Loss: CachedMultipleNegativesSymmetricRankingLoss with these parameters:
    {
        "scale": 20.0,
        "similarity_fct": "cos_sim",
        "mini_batch_size": 64
    }
    

natural_questions

  • Dataset: natural_questions at f9e894e
  • Size: 100,231 training samples
  • Columns: anchor and positive
  • Approximate statistics based on the first 1000 samples:
    anchor positive
    type string string
    details
    • min: 10 tokens
    • mean: 12.47 tokens
    • max: 23 tokens
    • min: 17 tokens
    • mean: 138.32 tokens
    • max: 556 tokens
  • Samples:
    anchor positive
    when did richmond last play in a preliminary final Richmond Football Club Richmond began 2017 with 5 straight wins, a feat it had not achieved since 1995. A series of close losses hampered the Tigers throughout the middle of the season, including a 5-point loss to the Western Bulldogs, 2-point loss to Fremantle, and a 3-point loss to the Giants. Richmond ended the season strongly with convincing victories over Fremantle and St Kilda in the final two rounds, elevating the club to 3rd on the ladder. Richmond's first final of the season against the Cats at the MCG attracted a record qualifying final crowd of 95,028; the Tigers won by 51 points. Having advanced to the first preliminary finals for the first time since 2001, Richmond defeated Greater Western Sydney by 36 points in front of a crowd of 94,258 to progress to the Grand Final against Adelaide, their first Grand Final appearance since 1982. The attendance was 100,021, the largest crowd to a grand final since 1986. The Crows led at quarter time and led by as many as 13, but the Tig...
    who sang what in the world's come over you Jack Scott (singer) At the beginning of 1960, Scott again changed record labels, this time to Top Rank Records.[1] He then recorded four Billboard Hot 100 hits – "What in the World's Come Over You" (#5), "Burning Bridges" (#3) b/w "Oh Little One" (#34), and "It Only Happened Yesterday" (#38).[1] "What in the World's Come Over You" was Scott's second gold disc winner.[6] Scott continued to record and perform during the 1960s and 1970s.[1] His song "You're Just Gettin' Better" reached the country charts in 1974.[1] In May 1977, Scott recorded a Peel session for BBC Radio 1 disc jockey, John Peel.
    who produces the most wool in the world Wool Global wool production is about 2 million tonnes per year, of which 60% goes into apparel. Wool comprises ca 3% of the global textile market, but its value is higher owing to dying and other modifications of the material.[1] Australia is a leading producer of wool which is mostly from Merino sheep but has been eclipsed by China in terms of total weight.[30] New Zealand (2016) is the third-largest producer of wool, and the largest producer of crossbred wool. Breeds such as Lincoln, Romney, Drysdale, and Elliotdale produce coarser fibers, and wool from these sheep is usually used for making carpets.
  • Loss: CachedMultipleNegativesSymmetricRankingLoss with these parameters:
    {
        "scale": 20.0,
        "similarity_fct": "cos_sim",
        "mini_batch_size": 64
    }
    

Training Hyperparameters

Non-Default Hyperparameters

  • eval_strategy: steps
  • per_device_train_batch_size: 256
  • weight_decay: 0.01
  • num_train_epochs: 1
  • lr_scheduler_type: cosine
  • warmup_ratio: 0.1
  • bf16: True
  • bf16_full_eval: True
  • load_best_model_at_end: True

All Hyperparameters

Click to expand
  • overwrite_output_dir: False
  • do_predict: False
  • eval_strategy: steps
  • prediction_loss_only: True
  • per_device_train_batch_size: 256
  • per_device_eval_batch_size: 8
  • per_gpu_train_batch_size: None
  • per_gpu_eval_batch_size: None
  • gradient_accumulation_steps: 1
  • eval_accumulation_steps: None
  • torch_empty_cache_steps: None
  • learning_rate: 5e-05
  • weight_decay: 0.01
  • adam_beta1: 0.9
  • adam_beta2: 0.999
  • adam_epsilon: 1e-08
  • max_grad_norm: 1.0
  • num_train_epochs: 1
  • 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: True
  • fp16_full_eval: False
  • tf32: None
  • 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
  • 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
  • hub_revision: None
  • 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
  • liger_kernel_config: None
  • eval_use_gather_object: False
  • average_tokens_across_devices: False
  • prompts: None
  • batch_sampler: batch_sampler
  • multi_dataset_batch_sampler: proportional
  • router_mapping: {}
  • learning_rate_mapping: {}

Training Logs

Click to expand
Epoch Step Training Loss NanoMSMARCO_cosine_ndcg@10 NanoNQ_cosine_ndcg@10 NanoHotpotQA_cosine_ndcg@10 NanoBEIR_mean_cosine_ndcg@10
-1 -1 - 0.2397 0.3332 0.4767 0.3499
0.0063 500 1.6152 - - - -
0.0125 1000 1.6149 - - - -
0.0188 1500 1.5833 - - - -
0.0251 2000 1.58 0.2449 0.3259 0.4793 0.3500
0.0313 2500 1.5475 - - - -
0.0376 3000 1.5432 - - - -
0.0439 3500 1.5067 - - - -
0.0501 4000 1.4909 0.2474 0.3124 0.4786 0.3461
0.0564 4500 1.4532 - - - -
0.0627 5000 1.425 - - - -
0.0689 5500 1.4394 - - - -
0.0752 6000 1.42 0.2532 0.3149 0.4895 0.3525
0.0815 6500 1.3737 - - - -
0.0878 7000 1.3755 - - - -
0.0940 7500 1.3194 - - - -
0.1003 8000 1.3143 0.2660 0.3163 0.4823 0.3548
0.1066 8500 1.3038 - - - -
0.1128 9000 1.2815 - - - -
0.1191 9500 1.2291 - - - -
0.1254 10000 1.24 0.2687 0.3407 0.4876 0.3657
0.1316 10500 1.2383 - - - -
0.1379 11000 1.2116 - - - -
0.1442 11500 1.1967 - - - -
0.1504 12000 1.1712 0.2697 0.3436 0.4888 0.3674
0.1567 12500 1.1781 - - - -
0.1630 13000 1.1798 - - - -
0.1692 13500 1.1486 - - - -
0.1755 14000 1.156 0.2761 0.3490 0.4895 0.3716
0.1818 14500 1.1622 - - - -
0.1880 15000 1.1638 - - - -
0.1943 15500 1.1447 - - - -
0.2006 16000 1.1353 0.2783 0.3427 0.4967 0.3726
0.2068 16500 1.1397 - - - -
0.2131 17000 1.1346 - - - -
0.2194 17500 1.1345 - - - -
0.2256 18000 1.13 0.2697 0.3424 0.5051 0.3724
0.2319 18500 1.1145 - - - -
0.2382 19000 1.1215 - - - -
0.2445 19500 1.1193 - - - -
0.2507 20000 1.1329 0.2795 0.3363 0.4992 0.3717
0.2570 20500 1.1239 - - - -
0.2633 21000 1.0929 - - - -
0.2695 21500 1.1079 - - - -
0.2758 22000 1.1192 0.2792 0.3278 0.5054 0.3708
0.2821 22500 1.1252 - - - -
0.2883 23000 1.1089 - - - -
0.2946 23500 1.1032 - - - -
0.3009 24000 1.0974 0.2769 0.3372 0.5043 0.3728
0.3071 24500 1.1129 - - - -
0.3134 25000 1.0901 - - - -
0.3197 25500 1.1087 - - - -
0.3259 26000 1.0921 0.2769 0.3349 0.5038 0.3719
0.3322 26500 1.0881 - - - -
0.3385 27000 1.0984 - - - -
0.3447 27500 1.105 - - - -
0.3510 28000 1.1022 0.2766 0.3353 0.5043 0.3721
0.3573 28500 1.0925 - - - -
0.3635 29000 1.1009 - - - -
0.3698 29500 1.1043 - - - -
0.3761 30000 1.0893 0.2772 0.3279 0.5055 0.3702
0.3823 30500 1.1084 - - - -
0.3886 31000 1.0885 - - - -
0.3949 31500 1.1046 - - - -
0.4012 32000 1.0925 0.2775 0.3273 0.5052 0.3700
0.4074 32500 1.1126 - - - -
0.4137 33000 1.0946 - - - -
0.4200 33500 1.0979 - - - -
0.4262 34000 1.0852 0.2775 0.3273 0.5098 0.3715
0.4325 34500 1.0925 - - - -
0.4388 35000 1.0919 - - - -
0.4450 35500 1.0878 - - - -
0.4513 36000 1.0775 0.2781 0.3273 0.5098 0.3717
0.4576 36500 1.0898 - - - -
0.4638 37000 1.0858 - - - -
0.4701 37500 1.0822 - - - -
0.4764 38000 1.0831 0.2849 0.3273 0.5098 0.3740
0.4826 38500 1.0886 - - - -
0.4889 39000 1.089 - - - -
0.4952 39500 1.0986 - - - -
0.5014 40000 1.0885 0.2775 0.3276 0.5101 0.3717
0.5077 40500 1.0903 - - - -
0.5140 41000 1.0883 - - - -
0.5202 41500 1.1009 - - - -
0.5265 42000 1.0909 0.2781 0.3276 0.5101 0.3719
0.5328 42500 1.0843 - - - -
0.5390 43000 1.086 - - - -
0.5453 43500 1.0762 - - - -
0.5516 44000 1.0781 0.2781 0.3276 0.5101 0.3719
0.5579 44500 1.0952 - - - -
0.5641 45000 1.0814 - - - -
0.5704 45500 1.0815 - - - -
0.5767 46000 1.0889 0.2849 0.3276 0.5101 0.3742
0.5829 46500 1.087 - - - -
0.5892 47000 1.0786 - - - -
0.5955 47500 1.0846 - - - -
0.6017 48000 1.095 0.2849 0.3273 0.5101 0.3741
0.6080 48500 1.0839 - - - -
0.6143 49000 1.0899 - - - -
0.6205 49500 1.0903 - - - -
0.6268 50000 1.0915 0.2775 0.3273 0.5098 0.3715
0.6331 50500 1.0764 - - - -
0.6393 51000 1.1006 - - - -
0.6456 51500 1.0968 - - - -
0.6519 52000 1.084 0.2849 0.3273 0.5101 0.3741
0.6581 52500 1.0892 - - - -
0.6644 53000 1.09 - - - -
0.6707 53500 1.0946 - - - -
0.6769 54000 1.0861 0.2775 0.3273 0.5098 0.3715
0.6832 54500 1.0962 - - - -
0.6895 55000 1.0841 - - - -
0.6958 55500 1.0894 - - - -
0.7020 56000 1.082 0.2775 0.3273 0.5098 0.3715
0.7083 56500 1.0939 - - - -
0.7146 57000 1.096 - - - -
0.7208 57500 1.1048 - - - -
0.7271 58000 1.0853 0.2849 0.3273 0.5098 0.3740
0.7334 58500 1.0893 - - - -
0.7396 59000 1.0946 - - - -
0.7459 59500 1.0985 - - - -
0.7522 60000 1.099 0.2849 0.3273 0.5098 0.3740
0.7584 60500 1.0972 - - - -
0.7647 61000 1.0812 - - - -
0.7710 61500 1.0744 - - - -
0.7772 62000 1.0781 0.2775 0.3273 0.5101 0.3716
0.7835 62500 1.0823 - - - -
0.7898 63000 1.0819 - - - -
0.7960 63500 1.0911 - - - -
0.8023 64000 1.1069 0.2775 0.3273 0.5098 0.3715
0.8086 64500 1.0786 - - - -
0.8148 65000 1.0872 - - - -
0.8211 65500 1.0776 - - - -
0.8274 66000 1.0849 0.2849 0.3273 0.5098 0.3740
0.8336 66500 1.0778 - - - -
0.8399 67000 1.0972 - - - -
0.8462 67500 1.0835 - - - -
0.8525 68000 1.0927 0.2849 0.3273 0.5098 0.3740
0.8587 68500 1.082 - - - -
0.8650 69000 1.0742 - - - -
0.8713 69500 1.0886 - - - -
0.8775 70000 1.0828 0.2775 0.3273 0.5098 0.3715
0.8838 70500 1.0863 - - - -
0.8901 71000 1.0905 - - - -
0.8963 71500 1.0856 - - - -
0.9026 72000 1.0946 0.2775 0.3273 0.5098 0.3715
0.9089 72500 1.102 - - - -
0.9151 73000 1.0819 - - - -
0.9214 73500 1.0884 - - - -
0.9277 74000 1.0888 0.2775 0.3273 0.5098 0.3715
0.9339 74500 1.0756 - - - -
0.9402 75000 1.0767 - - - -
0.9465 75500 1.0821 - - - -
0.9527 76000 1.0891 0.2775 0.3273 0.5098 0.3715
0.9590 76500 1.0923 - - - -
0.9653 77000 1.0765 - - - -
0.9715 77500 1.075 - - - -
0.9778 78000 1.0902 0.2775 0.3273 0.5098 0.3715
0.9841 78500 1.0833 - - - -
0.9903 79000 1.0746 - - - -
0.9966 79500 1.0872 - - - -
  • The bold row denotes the saved checkpoint.

Framework Versions

  • Python: 3.11.13
  • Sentence Transformers: 5.0.0
  • Transformers: 4.53.1
  • PyTorch: 2.7.1+cu128
  • Accelerate: 1.8.1
  • Datasets: 4.0.0
  • Tokenizers: 0.21.2

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",
}

CachedMultipleNegativesRankingLoss

@misc{gao2021scaling,
    title={Scaling Deep Contrastive Learning Batch Size under Memory Limited Setup},
    author={Luyu Gao and Yunyi Zhang and Jiawei Han and Jamie Callan},
    year={2021},
    eprint={2101.06983},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}
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