Hybrid Dealiasing and Implicit Packing for Real Convolutions
arXiv:2608.14497
2026
Memory
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper gives a concrete FFT factorization that performs the effect of zero-padding without storing the padded array, by splitting indices into short radix blocks and evaluating the padded transform through smaller inner sums. This is directly transferable to FFT-based long convolutions in spectral neural layers, neural operators, and very long sequence models, where temporary zero-padded tensors can dominate memory traffic. Its second asset is implicit real-to-complex packing: real inputs can share one complex transform while conjugate symmetry supplies the missing frequency information. The most promising engineering path is a drop-in FFT convolution kernel that combines tiled implicit padding with real packing and benchmarks wall-clock time, peak memory, and gradients against standard FFT implementations.
Ideas from this paper
✗ Failed on benchmark
2026
Replace explicit zero-padding before FFT convolution by the paper's mixed-radix decomposition, which injects zeros through bounded tile sums and never allocates the padded input. The resulting transform is mathematically identical to the length-M transform of the explicitly padded signal, while reducing temporary storage and potentially memory bandwidth.
Useful7/10
Difficulty7/10
Novelty6/10
Unverified
2026
Pack two real tensors into the real and imaginary components of one complex tensor, perform one complex transform, and recover both real spectra through conjugate symmetry. Combine this with implicit padding so separate padded real arrays and transform workspaces are not allocated.
Useful6/10
Difficulty6/10
Novelty5/10