sparse-encoder/example-splade-distilbert-base-uncased-nq

splade-distilbert-base-uncased trained on Natural Questions

This is a SPLADE Sparse Encoder model finetuned from distilbert/distilbert-base-uncased on the natural-questions dataset using the sentence-transformers library. It maps sentences & paragraphs to a 30522-dimensional sparse vector space and can be used for semantic search and sparse retrieval.

Model Details

Model Description

• Model Type: SPLADE Sparse Encoder
• Base model: distilbert/distilbert-base-uncased
• Maximum Sequence Length: 256 tokens
• Output Dimensionality: 30522 dimensions
• Similarity Function: Dot Product
• Training Dataset:
  • natural-questions
• Language: en
• License: apache-2.0

Model Sources

• Documentation: Sentence Transformers Documentation
• Documentation: Sparse Encoder Documentation
• Repository: Sentence Transformers on GitHub
• Hugging Face: Sparse Encoders on Hugging Face

Full Model Architecture

SparseEncoder(
  (0): MLMTransformer({'max_seq_length': 256, 'do_lower_case': False}) with MLMTransformer model: DistilBertForMaskedLM 
  (1): SpladePooling({'pooling_strategy': 'max', 'activation_function': 'relu', 'word_embedding_dimension': 30522})
)

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 SparseEncoder

# Download from the 🤗 Hub
model = SparseEncoder("arthurbresnu/splade-distilbert-base-uncased-nq")
# Run inference
sentences = [
    'is send in the clowns from a musical',
    'Send In the Clowns "Send In the Clowns" is a song written by Stephen Sondheim for the 1973 musical A Little Night Music, an adaptation of Ingmar Bergman\'s film Smiles of a Summer Night. It is a ballad from Act Two, in which the character Desirée reflects on the ironies and disappointments of her life. Among other things, she looks back on an affair years earlier with the lawyer Fredrik, who was deeply in love with her but whose marriage proposals she had rejected. Meeting him after so long, she realizes she is in love with him and finally ready to marry him, but now it is he who rejects her: he is in an unconsummated marriage with a much younger woman. Desirée proposes marriage to rescue him from this situation, but he declines, citing his dedication to his bride. Reacting to his rejection, Desirée sings this song. The song is later reprised as a coda after Fredrik\'s young wife runs away with his son, and Fredrik is finally free to accept Desirée\'s offer.[1]',
    'The Suite Life on Deck The Suite Life on Deck is an American sitcom that aired on Disney Channel from September 26, 2008 to May 6, 2011. It is a sequel/spin-off of the Disney Channel Original Series The Suite Life of Zack & Cody. The series follows twin brothers Zack and Cody Martin and hotel heiress London Tipton in a new setting, the SS Tipton, where they attend classes at "Seven Seas High School" and meet Bailey Pickett while Mr. Moseby manages the ship. The ship travels around the world to nations such as Italy, France, Greece, India, Sweden and the United Kingdom where the characters experience different cultures, adventures, and situations.[1]',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# (3, 30522)

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]

Evaluation

Metrics

Sparse Information Retrieval

• Datasets: NanoMSMARCO, NanoNFCorpus, NanoNQ, NanoClimateFEVER, NanoDBPedia, NanoFEVER, NanoFiQA2018, NanoHotpotQA, NanoMSMARCO, NanoNFCorpus, NanoNQ, NanoQuoraRetrieval, NanoSCIDOCS, NanoArguAna, NanoSciFact and NanoTouche2020
• Evaluated with SparseInformationRetrievalEvaluator

Metric	NanoMSMARCO	NanoNFCorpus	NanoNQ	NanoClimateFEVER	NanoDBPedia	NanoFEVER	NanoFiQA2018	NanoHotpotQA	NanoQuoraRetrieval	NanoSCIDOCS	NanoArguAna	NanoSciFact	NanoTouche2020
dot_accuracy@1	0.28	0.38	0.36	0.26	0.62	0.54	0.22	0.74	0.8	0.44	0.1	0.44	0.5714
dot_accuracy@3	0.5	0.46	0.58	0.42	0.82	0.72	0.42	0.9	0.92	0.62	0.52	0.54	0.7959
dot_accuracy@5	0.66	0.52	0.66	0.48	0.86	0.82	0.44	0.9	0.94	0.66	0.66	0.64	0.8367
dot_accuracy@10	0.74	0.62	0.76	0.62	0.92	0.92	0.54	0.98	0.98	0.76	0.78	0.7	0.9796
dot_precision@1	0.28	0.38	0.36	0.26	0.62	0.54	0.22	0.74	0.8	0.44	0.1	0.44	0.5714
dot_precision@3	0.1667	0.32	0.2	0.1533	0.5267	0.24	0.1667	0.42	0.36	0.2733	0.1733	0.2	0.5578
dot_precision@5	0.132	0.292	0.14	0.108	0.464	0.168	0.112	0.284	0.236	0.22	0.132	0.144	0.4735
dot_precision@10	0.074	0.236	0.08	0.078	0.432	0.096	0.072	0.164	0.13	0.164	0.078	0.078	0.3939
dot_recall@1	0.28	0.0242	0.34	0.125	0.0704	0.5267	0.1234	0.37	0.724	0.0917	0.1	0.405	0.0388
dot_recall@3	0.5	0.0531	0.56	0.2017	0.1332	0.6867	0.2904	0.63	0.8613	0.1687	0.52	0.525	0.1084
dot_recall@5	0.66	0.0727	0.64	0.24	0.1783	0.7667	0.3084	0.71	0.906	0.2257	0.66	0.63	0.1584
dot_recall@10	0.74	0.0959	0.72	0.3217	0.3024	0.8767	0.3804	0.82	0.9633	0.3357	0.78	0.68	0.2557
dot_ndcg@10	0.4958	0.2785	0.5342	0.266	0.5285	0.6963	0.2843	0.7251	0.8827	0.3269	0.4417	0.5538	0.4521
dot_mrr@10	0.4185	0.4394	0.4837	0.3618	0.7312	0.6532	0.3184	0.8267	0.8674	0.5352	0.3331	0.5217	0.7053
dot_map@100	0.4294	0.1174	0.4799	0.208	0.3981	0.6384	0.2433	0.6315	0.8507	0.2496	0.3399	0.5177	0.3369
query_active_dims	52.56	62.5	45.64	89.9	48.78	82.72	52.92	69.82	49.62	86.16	119.26	111.38	51.1633
query_sparsity_ratio	0.9983	0.998	0.9985	0.9971	0.9984	0.9973	0.9983	0.9977	0.9984	0.9972	0.9961	0.9964	0.9983
corpus_active_dims	106.134	126.2465	104.3785	107.8876	112.2791	121.6111	104.2389	134.8499	54.1169	115.1506	117.8589	109.9668	122.408
corpus_sparsity_ratio	0.9965	0.9959	0.9966	0.9965	0.9963	0.996	0.9966	0.9956	0.9982	0.9962	0.9961	0.9964	0.996

Sparse Nano BEIR

• Dataset: NanoBEIR_mean
• Evaluated with SparseNanoBEIREvaluator with these parameters:

  {
      "dataset_names": [
          "msmarco",
          "nfcorpus",
          "nq"
      ]
  }
  

Metric	Value
dot_accuracy@1	0.34
dot_accuracy@3	0.5133
dot_accuracy@5	0.6133
dot_accuracy@10	0.7067
dot_precision@1	0.34
dot_precision@3	0.2289
dot_precision@5	0.188
dot_precision@10	0.13
dot_recall@1	0.2147
dot_recall@3	0.371
dot_recall@5	0.4576
dot_recall@10	0.5186
dot_ndcg@10	0.4362
dot_mrr@10	0.4472
dot_map@100	0.3422
query_active_dims	53.5667
query_sparsity_ratio	0.9982
corpus_active_dims	110.0135
corpus_sparsity_ratio	0.9964

Sparse Nano BEIR

• Dataset: NanoBEIR_mean
• Evaluated with SparseNanoBEIREvaluator with these parameters:

  {
      "dataset_names": [
          "climatefever",
          "dbpedia",
          "fever",
          "fiqa2018",
          "hotpotqa",
          "msmarco",
          "nfcorpus",
          "nq",
          "quoraretrieval",
          "scidocs",
          "arguana",
          "scifact",
          "touche2020"
      ]
  }
  

Metric	Value
dot_accuracy@1	0.4424
dot_accuracy@3	0.632
dot_accuracy@5	0.6982
dot_accuracy@10	0.7923
dot_precision@1	0.4424
dot_precision@3	0.2891
dot_precision@5	0.2235
dot_precision@10	0.1597
dot_recall@1	0.2476
dot_recall@3	0.403
dot_recall@5	0.4736
dot_recall@10	0.5594
dot_ndcg@10	0.4974
dot_mrr@10	0.5535
dot_map@100	0.4185
query_active_dims	70.9861
query_sparsity_ratio	0.9977
corpus_active_dims	109.8633
corpus_sparsity_ratio	0.9964

Training Details

Training Dataset

natural-questions

• Dataset: natural-questions at f9e894e
• Size: 99,000 training samples
• Columns: query and answer
• Approximate statistics based on the first 1000 samples:

  	query	answer
  type	string	string
  details	min: 10 tokens mean: 11.71 tokens max: 26 tokens	min: 4 tokens mean: 131.81 tokens max: 450 tokens

• Samples:

  query	answer
  who played the father in papa don't preach	Alex McArthur Alex McArthur (born March 6, 1957) is an American actor.
  where was the location of the battle of hastings	Battle of Hastings The Battle of Hastings[a] was fought on 14 October 1066 between the Norman-French army of William, the Duke of Normandy, and an English army under the Anglo-Saxon King Harold Godwinson, beginning the Norman conquest of England. It took place approximately 7 miles (11 kilometres) northwest of Hastings, close to the present-day town of Battle, East Sussex, and was a decisive Norman victory.
  how many puppies can a dog give birth to	Canine reproduction The largest litter size to date was set by a Neapolitan Mastiff in Manea, Cambridgeshire, UK on November 29, 2004; the litter was 24 puppies.[22]

• Loss: SpladeLoss with these parameters:

  {
      "loss": "SparseMultipleNegativesRankingLoss(scale=1.0, similarity_fct='dot_score')",
      "lambda_corpus": 3e-05,
      "lambda_query": 5e-05
  }
  

Evaluation Dataset

natural-questions

• Dataset: natural-questions at f9e894e
• Size: 1,000 evaluation samples
• Columns: query and answer
• Approximate statistics based on the first 1000 samples:

  	query	answer
  type	string	string
  details	min: 10 tokens mean: 11.69 tokens max: 23 tokens	min: 15 tokens mean: 134.01 tokens max: 512 tokens

• Samples:

  query	answer
  where is the tiber river located in italy	Tiber The Tiber (/ˈtaɪbər/, Latin: Tiberis,[1] Italian: Tevere [ˈteːvere])[2] is the third-longest river in Italy, rising in the Apennine Mountains in Emilia-Romagna and flowing 406 kilometres (252 mi) through Tuscany, Umbria and Lazio, where it is joined by the river Aniene, to the Tyrrhenian Sea, between Ostia and Fiumicino.[3] It drains a basin estimated at 17,375 square kilometres (6,709 sq mi). The river has achieved lasting fame as the main watercourse of the city of Rome, founded on its eastern banks.
  what kind of car does jay gatsby drive	Jay Gatsby At the Buchanan home, Jordan Baker, Nick, Jay, and the Buchanans decide to visit New York City. Tom borrows Gatsby's yellow Rolls Royce to drive up to the city. On the way to New York City, Tom makes a detour at a gas station in "the Valley of Ashes", a run-down part of Long Island. The owner, George Wilson, shares his concern that his wife, Myrtle, may be having an affair. This unnerves Tom, who has been having an affair with Myrtle, and he leaves in a hurry.
  who sings if i can dream about you	I Can Dream About You "I Can Dream About You" is a song performed by American singer Dan Hartman on the soundtrack album of the film Streets of Fire. Released in 1984 as a single from the soundtrack, and included on Hartman's album I Can Dream About You, it reached number 6 on the Billboard Hot 100.[1]

• Loss: SpladeLoss with these parameters:

  {
      "loss": "SparseMultipleNegativesRankingLoss(scale=1.0, similarity_fct='dot_score')",
      "lambda_corpus": 3e-05,
      "lambda_query": 5e-05
  }
  

Training Hyperparameters

Non-Default Hyperparameters

• eval_strategy: steps
• per_device_train_batch_size: 12
• per_device_eval_batch_size: 12
• learning_rate: 2e-05
• num_train_epochs: 1
• bf16: True
• load_best_model_at_end: True
• batch_sampler: no_duplicates

All Hyperparameters

Click to expand

• overwrite_output_dir: False
• do_predict: False
• eval_strategy: steps
• prediction_loss_only: True
• per_device_train_batch_size: 12
• per_device_eval_batch_size: 12
• 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: 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: 1
• max_steps: -1
• lr_scheduler_type: linear
• lr_scheduler_kwargs: {}
• warmup_ratio: 0.0
• 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: 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}
• 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
• 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
• dispatch_batches: None
• split_batches: 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

Epoch	Step	Training Loss	Validation Loss	NanoMSMARCO_dot_ndcg@10	NanoNFCorpus_dot_ndcg@10	NanoNQ_dot_ndcg@10	NanoBEIR_mean_dot_ndcg@10	NanoClimateFEVER_dot_ndcg@10	NanoDBPedia_dot_ndcg@10	NanoFEVER_dot_ndcg@10	NanoFiQA2018_dot_ndcg@10	NanoHotpotQA_dot_ndcg@10	NanoQuoraRetrieval_dot_ndcg@10	NanoSCIDOCS_dot_ndcg@10	NanoArguAna_dot_ndcg@10	NanoSciFact_dot_ndcg@10	NanoTouche2020_dot_ndcg@10
0.0242	200	6.3626	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.0485	400	0.0957	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.0727	600	0.0927	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.0970	800	0.0588	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.1212	1000	0.0408	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.1455	1200	0.0515	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.1697	1400	0.0517	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.1939	1600	0.0213	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.2	1650	-	0.0520	0.4929	0.2618	0.4572	0.4040	-	-	-	-	-	-	-	-	-	-
0.2182	1800	0.019	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.2424	2000	0.0333	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.2667	2200	0.0282	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.2909	2400	0.0418	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.3152	2600	0.0386	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.3394	2800	0.0289	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.3636	3000	0.0242	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.3879	3200	0.0335	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.4	3300	-	0.0360	0.4715	0.2808	0.5340	0.4288	-	-	-	-	-	-	-	-	-	-
0.4121	3400	0.0264	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.4364	3600	0.0331	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.4606	3800	0.0339	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.4848	4000	0.0225	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.5091	4200	0.0164	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.5333	4400	0.0247	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.5576	4600	0.0213	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.5818	4800	0.0187	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.6	4950	-	0.0217	0.4901	0.2930	0.5072	0.4301	-	-	-	-	-	-	-	-	-	-
0.6061	5000	0.0153	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.6303	5200	0.0186	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.6545	5400	0.0096	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.6788	5600	0.0115	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.7030	5800	0.0255	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.7273	6000	0.0219	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.7515	6200	0.033	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.7758	6400	0.0199	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.8	6600	0.0175	0.0224	0.4700	0.2743	0.5136	0.4193	-	-	-	-	-	-	-	-	-	-
0.8242	6800	0.0236	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.8485	7000	0.0145	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.8727	7200	0.0372	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.8970	7400	0.0107	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.9212	7600	0.0131	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.9455	7800	0.0127	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.9697	8000	0.0207	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
0.9939	8200	0.0217	-	-	-	-	-	-	-	-	-	-	-	-	-	-	-
1.0	8250	-	0.0219	0.4958	0.2785	0.5342	0.4362	-	-	-	-	-	-	-	-	-	-
-1	-1	-	-	0.4958	0.2785	0.5342	0.4974	0.2660	0.5285	0.6963	0.2843	0.7251	0.8827	0.3269	0.4417	0.5538	0.4521

• The bold row denotes the saved checkpoint.

Environmental Impact

Carbon emissions were measured using CodeCarbon.

• Energy Consumed: 0.040 kWh
• Carbon Emitted: 0.002 kg of CO2
• Hours Used: 0.322 hours

Training Hardware

• On Cloud: No
• GPU Model: 1 x NVIDIA GeForce RTX 3070 Ti Laptop GPU
• CPU Model: AMD Ryzen 9 6900HX with Radeon Graphics
• RAM Size: 30.61 GB

Framework Versions

• Python: 3.12.9
• Sentence Transformers: 4.2.0.dev0
• Transformers: 4.50.3
• PyTorch: 2.6.0+cu124
• Accelerate: 1.6.0
• Datasets: 3.5.0
• 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",
}

SpladeLoss

@misc{formal2022distillationhardnegativesampling,
      title={From Distillation to Hard Negative Sampling: Making Sparse Neural IR Models More Effective},
      author={Thibault Formal and Carlos Lassance and Benjamin Piwowarski and Stéphane Clinchant},
      year={2022},
      eprint={2205.04733},
      archivePrefix={arXiv},
      primaryClass={cs.IR},
      url={https://arxiv.org/abs/2205.04733},
}

SparseMultipleNegativesRankingLoss

@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}
}

FlopsLoss

@article{paria2020minimizing,
    title={Minimizing flops to learn efficient sparse representations},
    author={Paria, Biswajit and Yeh, Chih-Kuan and Yen, Ian EH and Xu, Ning and Ravikumar, Pradeep and P{'o}czos, Barnab{'a}s},
    journal={arXiv preprint arXiv:2004.05665},
    year={2020}
    }