# EFQ-Softmax: Exp-Free Quantization for Softmax

arXiv: https://arxiv.org/abs/2609.09721 · HTML: https://mlsanity.com/paper/2609.09721/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 25 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [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)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Towards VQA Models That Can Read](https://mlsanity.com/paper/1904.08920/) (2019)
- [OK-VQA: A Visual Question Answering Benchmark Requiring External Knowledge](https://mlsanity.com/paper/1906.00067/) (2019)
- [Modeling Context in Referring Expressions](https://mlsanity.com/paper/1608.00272/) (2016)
- [Generation and Comprehension of Unambiguous Object Descriptions](https://mlsanity.com/paper/1511.02283/) (2015)
- [A Diagram Is Worth A Dozen Images](https://mlsanity.com/paper/1603.07396/) (2016)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [FP8 Formats for Deep Learning](https://mlsanity.com/paper/2209.05433/) (2022)
- [SageAttention: Accurate 8-Bit Attention for Plug-and-play Inference Acceleration](https://mlsanity.com/paper/2410.02367/) (2024)
- [Microscaling Data Formats for Deep Learning](https://mlsanity.com/paper/2310.10537/) (2023)
- [SageAttention3: Microscaling FP4 Attention for Inference and An Exploration of 8-Bit Training](https://mlsanity.com/paper/2505.11594/) (2025)

## Abstract (arXiv)

Low-bit attention accelerates Transformer inference by moving the QK^top and PV matrix multiplications to FP8 or FP4 matrix engines. However, the softmax path often evaluates shifted-score exponentials in higher precision, forms a temporary probability block, and quantizes it before low-bit PV multiplication. This exp-then-quantize path creates a mismatch between a high-precision probability producer and a low-bit matrix consumer. We propose EFQ-Softmax (Exp-Free Quantization for Softmax), a low-bit probability-generation method that directly maps shifted attention scores to block-scaled E2M1 operands. For each microscaling block, EFQ-Softmax selects an exponent-only scale from the local maximum, maps the shifted scores to a normalized residual domain, and generates nonnegative E2M1 probability codes using a single affine rule. The resulting operand is used consistently in both the widetildePV numerator update and the widetildeP1 denominator update. The FlashAttention-style row-maximum update, historical rescaling, high-precision accumulation, and final normalization remain unchanged. We evaluate end-to-end quality on Qwen3-8B, Qwen3-VL-8B-Instruct, and WAN2.2-TI2V-5B, and separately measure kernel-level performance on the A5 vector unit. EFQ-Softmax improves the Qwen3-8B seven-task mean from 0.6749 with MXFP4 to 0.6773 and the Qwen3-VL nine-task mean from 0.7826 to 0.8000. On WAN2.2, it maintains temporal consistency and visual quality comparable to the FP16 and MXFP4 baselines under VBench. On the A5 vector unit, EFQ-Softmax reduces the vector-stage latency of the fused probability-generation kernel by 40.33% on average across sequence lengths from 16K to 128K. These results show that direct low-bit probability generation can replace the conventional exp-then-quantize path while preserving end-to-end model quality.