# Exact Causal Attention with 10% Fewer Operations

arXiv: https://arxiv.org/abs/2510.05175 · HTML: https://mlsanity.com/paper/2510.05175/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 35 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 26 of 26)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Efficient Transformers: A Survey](https://mlsanity.com/paper/2009.06732/) (2020)
- [Efficiently Scaling Transformer Inference](https://mlsanity.com/paper/2211.05102/) (2022)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [Generating Wikipedia by Summarizing Long Sequences](https://mlsanity.com/paper/1801.10198/) (2018)
- [Query-Key Normalization for Transformers](https://mlsanity.com/paper/2010.04245/) (2020)
- [Flex Attention: A Programming Model for Generating Optimized Attention Kernels](https://mlsanity.com/paper/2412.05496/) (2024)
- [Data Movement Is All You Need: A Case Study on Optimizing Transformers](https://mlsanity.com/paper/2007.00072/) (2020)
- [Monarch: Expressive Structured Matrices for Efficient and Accurate Training](https://mlsanity.com/paper/2204.00595/) (2022)
- [Multi-task Sequence to Sequence Learning](https://mlsanity.com/paper/1511.06114/) (2015)
- [Tensor Product Attention Is All You Need](https://mlsanity.com/paper/2501.06425/) (2025)
- [Lean Attention: Hardware-Aware Scalable Attention Mechanism for the Decode-Phase of Transformers](https://mlsanity.com/paper/2405.10480/) (2024)
- [Hardware-Efficient Attention for Fast Decoding](https://mlsanity.com/paper/2505.21487/) (2025)
- [Fast and Practical Strassen's Matrix Multiplication using FPGAs](https://mlsanity.com/paper/2406.02088/) (2024)
- [Changing Base Without Losing Pace: A GPU-Efficient Alternative to MatMul in DNNs](https://mlsanity.com/paper/2503.12211/) (2025)

## Abstract (arXiv)

We present Exact Causal Attention (ECA), a Strassen-style algorithm that computes exact Causal Attention using 10% fewer operations. ECA improves a special class of matrix multiplications where either one operand or the output matrix is upper- or lower-triangular. This includes all matrix multiplication operations in the forward and backward pass of Causal Attention, such as masked product Mask(QKT). ECA is built upon algebraic identities discovered via machine learning and combinatorial search. We note that ECA cannot accelerate fused kernels such as FlashAttention on GPU. This is because ECA requires materialization of large intermediate expressions in the memory, while FlashAttention does not. However, it provides an alternative approach for compute-bound applications and can potentially be useful in scenarios with FLOPs considerations.