{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/q-bert-hessian-based-ultra-low-precision","title":"Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT","arxiv_id":"1909.05840","date":"2019-09-12","proceeding":null,"authors":["Sheng Shen","Zhen Dong","Jiayu Ye","Linjian Ma","Zhewei Yao","Amir Gholami","Michael W. Mahoney","Kurt Keutzer"],"abstract":"Transformer based architectures have become de-facto models used for a range of Natural Language Processing tasks. In particular, the BERT based models achieved significant accuracy gain for GLUE tasks, CoNLL-03 and SQuAD. However, BERT based models have a prohibitive memory footprint and latency. As a result, deploying BERT based models in resource constrained environments has become a challenging task. In this work, we perform an extensive analysis of fine-tuned BERT models using second order Hessian information, and we use our results to propose a novel method for quantizing BERT models to ultra low precision. In particular, we propose a new group-wise quantization scheme, and we use a Hessian based mix-precision method to compress the model further. We extensively test our proposed method on BERT downstream tasks of SST-2, MNLI, CoNLL-03, and SQuAD. We can achieve comparable performance to baseline with at most $2.3\\%$ performance degradation, even with ultra-low precision quantization down to 2 bits, corresponding up to $13\\times$ compression of the model parameters, and up to $4\\times$ compression of the embedding table as well as activations. Among all tasks, we observed the highest performance loss for BERT fine-tuned on SQuAD. By probing into the Hessian based analysis as well as visualization, we show that this is related to the fact that current training/fine-tuning strategy of BERT does not converge for SQuAD.","url_abs":"https://arxiv.org/abs/1909.05840v2","url_pdf":"https://arxiv.org/pdf/1909.05840v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[{"task_slug":"linguistic-acceptability","task_name":"Linguistic Acceptability"},{"task_slug":"natural-language-inference","task_name":"Natural Language Inference"},{"task_slug":"quantization","task_name":"Quantization"},{"task_slug":null,"task_name":"SST-2"},{"task_slug":"semantic-textual-similarity","task_name":"Semantic Textual Similarity"},{"task_slug":"sentiment-analysis","task_name":"Sentiment Analysis"}],"methods":[{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"attention-dropout","method_name":"Attention Dropout"},{"method_slug":"bert","method_name":"BERT"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"linear-warmup-with-linear-decay","method_name":"Linear Warmup With Linear Decay"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"weight-decay","method_name":"Weight Decay"},{"method_slug":"wordpiece","method_name":"WordPiece"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/linguistic-acceptability-on-cola","task":"Linguistic Acceptability","dataset":"CoLA","model":"Q-BERT (Shen et al., 2020)","rank_in_archive_order":23,"of":43,"metrics":{"Accuracy":"65.1"},"uses_additional_data":false},{"leaderboard":"/sota/natural-language-inference-on-multinli","task":"Natural Language Inference","dataset":"MultiNLI","model":"Q-BERT (Shen et al., 2020)","rank_in_archive_order":20,"of":67,"metrics":{"Matched":"87.8"},"uses_additional_data":false},{"leaderboard":"/sota/natural-language-inference-on-qnli","task":"Natural Language Inference","dataset":"QNLI","model":"Q-BERT (Shen et al., 2020)","rank_in_archive_order":22,"of":43,"metrics":{"Accuracy":"93.0"},"uses_additional_data":false},{"leaderboard":"/sota/natural-language-inference-on-rte","task":"Natural Language Inference","dataset":"RTE","model":"Q-BERT (Shen et al., 2020)","rank_in_archive_order":28,"of":90,"metrics":{"Accuracy":"84.7"},"uses_additional_data":false},{"leaderboard":"/sota/semantic-textual-similarity-on-mrpc","task":"Semantic Textual Similarity","dataset":"MRPC","model":"Q-BERT (Shen et al., 2020)","rank_in_archive_order":22,"of":45,"metrics":{"Accuracy":"88.2"},"uses_additional_data":false},{"leaderboard":"/sota/semantic-textual-similarity-on-sts-benchmark","task":"Semantic Textual Similarity","dataset":"STS Benchmark","model":"Q-BERT (Shen et al., 2020)","rank_in_archive_order":13,"of":66,"metrics":{"Pearson Correlation":"0.911"},"uses_additional_data":false},{"leaderboard":"/sota/sentiment-analysis-on-sst-2-binary","task":"Sentiment Analysis","dataset":"SST-2 Binary classification","model":"Q-BERT (Shen et al., 2020)","rank_in_archive_order":31,"of":87,"metrics":{"Accuracy":"94.8"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1909.05840","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}