# CAT: Circular-Convolutional Attention for Sub-Quadratic Transformers

arXiv: https://arxiv.org/abs/2504.06704 · HTML: https://mlsanity.com/paper/2504.06704/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 33 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [MetaFormer Is Actually What You Need for Vision](https://mlsanity.com/paper/2111.11418/) (2021)
- [Long-Term Feature Banks for Detailed Video Understanding](https://mlsanity.com/paper/1812.05038/) (2018)
- [An Empirical Study of Mamba-based Language Models](https://mlsanity.com/paper/2406.07887/) (2024)
- [The Hedgehog & the Porcupine: Expressive Linear Attentions with Softmax Mimicry](https://mlsanity.com/paper/2402.04347/) (2024)

## Abstract (arXiv)

Transformers have driven remarkable breakthroughs in natural language processing and computer vision, yet their standard attention mechanism still imposes O(N^2) complexity, hindering scalability to longer sequences. We introduce Circular-convolutional ATtention (CAT), a Fourier-based approach that efficiently applies circular convolutions to reduce complexity without sacrificing representational power. CAT achieves O(NlogN) computations, requires fewer learnable parameters by streamlining fully connected layers, and introduces no additional heavy operations, resulting in consistent accuracy improvements and about a 10% speedup in naive PyTorch implementations. Based on the Engineering-Isomorphic Transformers (EITs) framework, CAT's design not only offers practical efficiency and ease of implementation, but also provides insights to guide the development of future high-performance Transformer architectures. Finally, our ablation studies highlight the key conditions underlying CAT's success, shedding light on broader principles for scalable attention mechanisms.