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This article explains the Fourier transform of power-law functions, focusing on the interesting case of 1/f noise and the symmetry between time and frequency domains.
This paper characterizes the error that arises when substituting the Hadamard transform (which diagonalizes dyadic convolution) for the DFT (which diagonalizes circular convolution), identifying universal zero-error positions, a nearly full-rank error operator, and a closed-form expression for expected error magnitude governed by a single alignment scalar.
An in-depth exploration of the Fourier transform, starting from Fourier series and extending to non-periodic functions, with interactive visualizations and mathematical derivation.
This paper presents Accelerated Fourier SAT (AFSAT), a GPU-accelerated solver for pseudo-Boolean satisfiability based on continuous local search. It improves upon prior proof-of-concept implementations by supporting heterogeneous constraints and leveraging JAX for parallel computation.
Mix-MoE proposes a mixed Mixture-of-Experts framework with specialized expert groups and Fourier-transform-enhanced routing to mitigate parameter interference in multilingual machine translation, achieving significant improvements over baselines.