# Softmax Attention with Constant Cost per Token

arXiv: https://arxiv.org/abs/2404.05843 · HTML: https://mlsanity.com/paper/2404.05843/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 16 references that are in the map.
- First posted on arXiv 8 Apr 2024.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [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)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Repeat After Me: Transformers are Better than State Space Models at Copying](https://mlsanity.com/paper/2402.01032/) (2024)
- [Parallelizing Linear Recurrent Neural Nets Over Sequence Length](https://mlsanity.com/paper/1709.04057/) (2017)
- [An Attention Free Transformer](https://mlsanity.com/paper/2105.14103/) (2021)
- [GateLoop: Fully Data-Controlled Linear Recurrence for Sequence Modeling](https://mlsanity.com/paper/2311.01927/) (2023)

## Built on by (most cited first, 1 of 1)

- [ELSA: Exact Linear-Scan Attention for Fast and Memory-Light Vision Transformers](https://mlsanity.com/paper/2604.23798/) (2026)

## Abstract (arXiv)

We propose a simple modification to the conventional attention mechanism applied by Transformers: Instead of quantifying pairwise query-key similarity with scaled dot-products, we quantify it with the logarithms of scaled dot-products of exponentials. Our modification linearizes attention with exponential kernel feature maps, whose corresponding feature function is infinite dimensional. We show that our modification is expressible as a composition of log-sums of exponentials, with a latent space of constant size, enabling application with constant time and space complexity per token. We implement our modification, verify that it works in practice, and conclude that it is a promising alternative to conventional attention.