# FourierQK: Spectral Preprocessing of Query-Key Projections Improves Transformer Attention

arXiv: https://arxiv.org/abs/2607.07478 · HTML: https://mlsanity.com/paper/2607.07478/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [FNet: Mixing Tokens with Fourier Transforms](https://mlsanity.com/paper/2105.03824/) (2021)
- [Language Through a Prism: A Spectral Approach for Multiscale Language Representations](https://mlsanity.com/paper/2011.04823/) (2020)
- [Energy-Gated Attention: Spectral Salience as an Inductive Bias for Transformer Attention](https://mlsanity.com/paper/2605.21842/) (2026)
- [Energy-Gated Attention and Wavelet Positional Encoding: Complementary Inductive Biases for Transformer Attention](https://mlsanity.com/paper/2605.26355/) (2026)
- [Beyond Sinusoids: A Morlet Wavelet Framework for Transformer Positional Encoding](https://mlsanity.com/paper/2606.01258/) (2026)
- [Multiscale POD of Transformer Attention Fields: Scale-Selective Analysis via Morlet Scalogram](https://mlsanity.com/paper/2606.06573/) (2026)

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

- [FourierQK: Filter Shape, Admissibility and the Leakage-Coverage Law](https://mlsanity.com/paper/2610.00009/) (2026)

## Abstract (arXiv)

FFT-based spectral preprocessing of learned query-key (Q/K) projections substantially improves transformer attention on character-level language modelling. On TinyShakespeare: a fixed random spectral filter achieves val=1.031 (Delta=+0.443); a single learned frequency at paragraph scale achieves val=0.608 (Delta=+0.867); and four learned frequencies spanning paragraph to word scale achieve val=0.309 (Delta=+1.166), a 79% reduction over standard dot-product attention. The single-frequency result is confirmed across three random seeds (mean val=0.236, std=0.019). The four frequencies converge to a near-geometric multi-scale ordering (49, 27, 10, 6 tokens/cycle) corresponding to paragraph, sub-paragraph, phrase, and word scales. The gain is specific to spectral preprocessing: random orthogonal and non-orthogonal projections of Q/K produce no measurable improvement, suggesting the benefit comes from global frequency-domain mixing rather than metric distortion. All results are verified by a shuffled-validation diagnostic against positional leakage. Causal filters (Gaussian, Mexican Hat, Morlet) do not improve over standard attention at character-level tokenisation: the bilateral FFT kernel is structurally non-causal, coupling every position to future tokens. This defines an architectural boundary between bilateral spectral attention (this paper) and genuinely causal spectral attention at word-scale tokenisation (companion paper MorletQK). This work is architecturally distinct from FNet (Lee-Thorp et al., 2021), which replaces attention with Fourier mixing of token embeddings. Here, spectral preprocessing applies only to Q/K projections while the full attention score structure is preserved.