# Beyond Self Attention: A Subquadratic Fourier Wavelet Transformer with Multi Modal Fusion

arXiv: https://arxiv.org/abs/2111.15473 · HTML: https://mlsanity.com/paper/2111.15473/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 25 Nov 2021.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Nystr"omformer: A Nystr"om-Based Algorithm for Approximating Self-Attention](https://mlsanity.com/paper/2102.03902/) (2021)
- [A Neural Attention Model for Abstractive Sentence Summarization](https://mlsanity.com/paper/1509.00685/) (2015)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [PubMed 200k RCT: a Dataset for Sequential Sentence Classification in Medical Abstracts](https://mlsanity.com/paper/1710.06071/) (2017)

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

- [Legal-HNet: Mixing Legal Long-Context Tokens with Hartley Transform](https://mlsanity.com/paper/2311.05089/) (2023)

## Abstract (arXiv)

We revisit the use of spectral techniques to replaces the attention mechanism in Transformers through Fourier Transform based token mixing, and present a comprehensive and novel reformulation of this technique in next generation transformer models. We provide expanded literature context, detailed mathematical formulations of Fourier mixing and causal masking, and introduce a novel MultiDomain Fourier Wavelet Attention(MDFWA) that integrates frequency and time localized transforms to capture both global and local dependencies efficiently. We derive the complexity bounds, gradient formulas, and show that MDFWA achieves sub quadratic time and memory cost while improving expressive power. We validate our design on an abstractive summarization task using PubMed dataset, by enhancing the proposed approach with learned frequency bases, adaptive scale selection, and multi-modal extensions.