# EXAQ: Exponent Aware Quantization For LLMs Acceleration

arXiv: https://arxiv.org/abs/2410.03185 · HTML: https://mlsanity.com/paper/2410.03185/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 28 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Q8BERT: Quantized 8Bit BERT](https://mlsanity.com/paper/1910.06188/) (2019)
- [I-BERT: Integer-only BERT Quantization](https://mlsanity.com/paper/2101.01321/) (2021)
- [A3: Accelerating Attention Mechanisms in Neural Networks with Approximation](https://mlsanity.com/paper/2002.10941/) (2020)
- [FP8-LM: Training FP8 Large Language Models](https://mlsanity.com/paper/2310.18313/) (2023)
- [Softermax: Hardware/Software Co-Design of an Efficient Softmax for Transformers](https://mlsanity.com/paper/2103.09301/) (2021)
- [Accurate Neural Training with 4-bit Matrix Multiplications at Standard Formats](https://mlsanity.com/paper/2112.10769/) (2021)
- [ITA: An Energy-Efficient Attention and Softmax Accelerator for Quantized Transformers](https://mlsanity.com/paper/2307.03493/) (2023)
- [Efficient Softmax Approximation for Deep Neural Networks with Attention Mechanism](https://mlsanity.com/paper/2111.10770/) (2021)

## Built on by (most cited first, 3 of 3)

- [IntAttention: A Fully Integer Attention Pipeline for Efficient Edge Inference](https://mlsanity.com/paper/2511.21513/) (2025)
- [Approximating Softmax in Pretrained LLMs: Model Sensitivity and Kernel Acceleration](https://mlsanity.com/paper/2609.33586/) (2026)
- [Pretraining Transformers with Quantized Softmax in Attention](https://mlsanity.com/paper/2609.33591/) (2026)

## Abstract (arXiv)

Quantization has established itself as the primary approach for decreasing the computational and storage expenses associated with Large Language Models (LLMs) inference. The majority of current research emphasizes quantizing weights and activations to enable low-bit general-matrix-multiply (GEMM) operations, with the remaining non-linear operations executed at higher precision. In our study, we discovered that following the application of these techniques, the primary bottleneck in LLMs inference lies in the softmax layer. The softmax operation comprises three phases: exponent calculation, accumulation, and normalization, Our work focuses on optimizing the first two phases. We propose an analytical approach to determine the optimal clipping value for the input to the softmax function, enabling sub-4-bit quantization for LLMs inference. This method accelerates the calculations of both ex and sum(ex) with minimal to no accuracy degradation. For example, in LLaMA1-30B, we achieve baseline performance with 2-bit quantization on the well-known "Physical Interaction: Question Answering" (PIQA) dataset evaluation. This ultra-low bit quantization allows, for the first time, an acceleration of approximately 4x in the accumulation phase. The combination of accelerating both ex and sum(ex) results in a 36.9% acceleration in the softmax operation.