# AFPQ: Asymmetric Floating Point Quantization for LLMs

arXiv: https://arxiv.org/abs/2311.01792 · HTML: https://mlsanity.com/paper/2311.01792/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 24 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## Builds on (most cited first, 20 of 20)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [WizardCoder: Empowering Code Large Language Models with Evol-Instruct](https://mlsanity.com/paper/2306.08568/) (2023)
- [ZeroQuant: Efficient and Affordable Post-Training Quantization for Large-Scale Transformers](https://mlsanity.com/paper/2206.01861/) (2022)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [SpQR: A Sparse-Quantized Representation for Near-Lossless LLM Weight Compression](https://mlsanity.com/paper/2306.03078/) (2023)
- [The case for 4-bit precision: k-bit Inference Scaling Laws](https://mlsanity.com/paper/2212.09720/) (2022)
- [ZeroQuant-FP: A Leap Forward in LLMs Post-Training W4A8 Quantization Using Floating-Point Formats](https://mlsanity.com/paper/2307.09782/) (2023)
- [Integer or Floating Point? New Outlooks for Low-Bit Quantization on Large Language Models](https://mlsanity.com/paper/2305.12356/) (2023)

## Built on by (most cited first, 7 of 7)

- [AMXFP4: Taming Activation Outliers with Asymmetric Microscaling Floating-Point for 4-bit LLM Inference](https://mlsanity.com/paper/2411.09909/) (2024)
- [HQ-DiT: Efficient Diffusion Transformer with FP4 Hybrid Quantization](https://mlsanity.com/paper/2405.19751/) (2024)
- [Rotate, Clip, and Partition: Towards W2A4KV4 Quantization by Integrating Rotation and Learnable Non-uniform Quantizer](https://mlsanity.com/paper/2502.15779/) (2025)
- [FPQVAR: Floating Point Quantization for Visual Autoregressive Model with FPGA Hardware Co-design](https://mlsanity.com/paper/2505.16335/) (2025)
- [OffQ: Taming Structured Outliers in LLM Quantization by Offsetting](https://mlsanity.com/paper/2606.07116/) (2026)
- [Benford's Law as a Distributional Prior for Post-Training Quantization of Large Language Models](https://mlsanity.com/paper/2602.00165/) (2026)
- [GyRot: Leveraging Hidden Synergy between Rotation and Fine-grained Group Quantization for Low-bit LLM Inference](https://mlsanity.com/paper/2607.27694/) (2026)

## Abstract (arXiv)

Large language models (LLMs) show great performance in various tasks, but face deployment challenges from limited memory capacity and bandwidth. Low-bit weight quantization can save memory and accelerate inference. Although floating-point (FP) formats show good performance in LLM quantization, they tend to perform poorly with small group sizes or sub-4 bits. We find the reason is that the absence of asymmetry in previous FP quantization makes it unsuitable for handling asymmetric value distribution of LLM weight tensors. In this work, we propose asymmetric FP quantization (AFPQ), which sets separate scales for positive and negative values. Our method leads to large accuracy improvements and can be easily plugged into other quantization methods, including GPTQ and AWQ, for better performance. Besides, no additional storage is needed compared with asymmetric integer (INT) quantization. The code is available at https://github.com/zhangsichengsjtu/AFPQ.