# FLASH-D: FlashAttention with Hidden Softmax Division

arXiv: https://arxiv.org/abs/2505.14201 · HTML: https://mlsanity.com/paper/2505.14201/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [A Study of BFLOAT16 for Deep Learning Training](https://mlsanity.com/paper/1905.12322/) (2019)
- [FP8 Formats for Deep Learning](https://mlsanity.com/paper/2209.05433/) (2022)
- [Online normalizer calculation for softmax](https://mlsanity.com/paper/1805.02867/) (2018)
- [Self-attention Does Not Need O(n2) Memory](https://mlsanity.com/paper/2112.05682/) (2021)
- [A3: Accelerating Attention Mechanisms in Neural Networks with Approximation](https://mlsanity.com/paper/2002.10941/) (2020)
- [EdgeBERT: Sentence-Level Energy Optimizations for Latency-Aware Multi-Task NLP Inference](https://mlsanity.com/paper/2011.14203/) (2020)
- [FasterViT: Fast Vision Transformers with Hierarchical Attention](https://mlsanity.com/paper/2306.06189/) (2023)
- [PromptBench: A Unified Library for Evaluation of Large Language Models](https://mlsanity.com/paper/2312.07910/) (2023)
- [Hardware Accelerator for Multi-Head Attention and Position-Wise Feed-Forward in the Transformer](https://mlsanity.com/paper/2009.08605/) (2020)
- [X-Former: In-Memory Acceleration of Transformers](https://mlsanity.com/paper/2303.07470/) (2023)
- [ConSmax: Hardware-Friendly Alternative Softmax with Learnable Parameters](https://mlsanity.com/paper/2402.10930/) (2024)
- [Low-rank Attention Side-Tuning for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2402.04009/) (2024)
- [Online Alignment and Addition in Multi-Term Floating-Point Adders](https://mlsanity.com/paper/2410.21959/) (2024)

## Built on by (most cited first, 2 of 2)

- [BLASST: Dynamic BLocked Attention Sparsity via Softmax Thresholding](https://mlsanity.com/paper/2512.12087/) (2025)
- [VFA: Relieving Vector Operations in Flash Attention with Global Maximum Pre-computation](https://mlsanity.com/paper/2604.12798/) (2026)

## Abstract (arXiv)

The transformer's attention mechanism has revolutionized AI and machine learning, with its efficient computation being crucial to its performance. However, calculating attention involves matrix operations interspersed with softmax rescaling, which inherently slows down computation and requires processing the entire input sequence. Building on online softmax computation, FlashAttention integrates softmax calculation with matrix arithmetic, enabling tiled computation independent of sequence length. While optimized for GPUs, FlashAttention's simplicity makes it amenable to direct hardware acceleration. This work re-evaluates the core FlashAttention kernel, presenting FLASH-D a mathematically equivalent, yet simplified, formulation that achieves: (a) hiding softmax division within other non-linear function evaluations; (b) inherently numerically stable computation of exponentials, eliminating the need for maximum value subtraction; and (c) a reduction in computational cost without introducing numerical approximations to the FlashAttention kernel. Importantly, the essential FlashAttention properties that facilitate efficient tiled implementation are fully preserved. Hardware implementation results at 28nm demonstrate that this proposed formulation achieves a 22.8% reduction in area and a 20.3% reduction in power, on average, compared to state-of-the-art parallel hardware architectures without any performance penalty.