# Q-BERT: Hessian Based Ultra Low Precision Quantization of BERT

arXiv: https://arxiv.org/abs/1909.05840 · HTML: https://mlsanity.com/paper/1909.05840/

## Key facts

- Cited by 359 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2019.

## Built on by (most cited first, 30 of 359)

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- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [FlexGen: High-Throughput Generative Inference of Large Language Models with a Single GPU](https://mlsanity.com/paper/2303.06865/) (2023)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [DeepSpeed-MoE: Advancing Mixture-of-Experts Inference and Training to Power Next-Generation AI Scale](https://mlsanity.com/paper/2201.05596/) (2022)
- [EAGLE-2: Faster Inference of Language Models with Dynamic Draft Trees](https://mlsanity.com/paper/2406.16858/) (2024)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [EAGLE-3: Scaling up Inference Acceleration of Large Language Models via Training-Time Test](https://mlsanity.com/paper/2503.01840/) (2025)
- [LLM-QAT: Data-Free Quantization Aware Training for Large Language Models](https://mlsanity.com/paper/2305.17888/) (2023)
- [Pre-Trained Models: Past, Present and Future](https://mlsanity.com/paper/2106.07139/) (2021)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [SqueezeLLM: Dense-and-Sparse Quantization](https://mlsanity.com/paper/2306.07629/) (2023)
- [Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2106.14156/) (2021)
- [Post-training Quantization on Diffusion Models](https://mlsanity.com/paper/2211.15736/) (2022)
- [I-BERT: Integer-only BERT Quantization](https://mlsanity.com/paper/2101.01321/) (2021)
- [ZeroGen: Efficient Zero-shot Learning via Dataset Generation](https://mlsanity.com/paper/2202.07922/) (2022)
- [LoftQ: LoRA-Fine-Tuning-Aware Quantization for Large Language Models](https://mlsanity.com/paper/2310.08659/) (2023)
- [Outlier Suppression: Pushing the Limit of Low-bit Transformer Language Models](https://mlsanity.com/paper/2209.13325/) (2022)
- [PTQ4ViT: Post-training quantization for vision transformers with twin uniform quantization](https://mlsanity.com/paper/2111.12293/) (2021)
- [Structured Pruning Learns Compact and Accurate Models](https://mlsanity.com/paper/2204.00408/) (2022)
- [Speculative Decoding with Big Little Decoder](https://mlsanity.com/paper/2302.07863/) (2023)
- [A Fast Post-Training Pruning Framework for Transformers](https://mlsanity.com/paper/2204.09656/) (2022)
- [QA-LoRA: Quantization-Aware Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2309.14717/) (2023)
- [FQ-ViT: Post-Training Quantization for Fully Quantized Vision Transformer](https://mlsanity.com/paper/2111.13824/) (2021)
- [Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing](https://mlsanity.com/paper/2306.12929/) (2023)
- [Understanding and Overcoming the Challenges of Efficient Transformer Quantization](https://mlsanity.com/paper/2109.12948/) (2021)
- [Learned Token Pruning for Transformers](https://mlsanity.com/paper/2107.00910/) (2021)

## Abstract (arXiv)

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× compression of the model parameters, and up to 4× 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.