FourierQK: Filter Shape, Admissibility and the Leakage-Coverage Law

תקציר מקורי באנגליתarXiv:2610.00009v1 Announce Type: new Abstract: Frequency-collapse attention [Zeris, 2026e] achieves large gains over standard dot-product attention by replacing the Q/K dot product with a bandpass-filtered inner product at a learned frequency. A natural follow-up question is: which filter shape works best, and why? We test five hypotheses about filter properties -- DC suppression, Nyquist suppression, bandwidth, centre frequency, and multi-scale coverage -- using a controlled ablation on character-level language modelling (TinyShakespeare, 6-layer GPT). Our main findings are: (1) DC and Nyquist components are actively harmful (val ~= 2.0, equivalent to phase randomisation), confirming that oscillatory bandpass structure is essential, not just any low-dimensional spectral summary; (2) the