5 papers
Training Transformers in Cosine Coefficient Space
Mohamed Amine Bergach
Linear layers hold most of a transformer's parameters. We replace each linear layer with one that stores out of two-dimensional DCT coefficients per weight matrix and reco…
Shortest-Path FFT: Optimal SIMD Instruction Scheduling via Graph Search
Mohamed Amine Bergach
An -point FFT admits many valid implementations that differ in radix choice, stage ordering, and register-blocking strategy. These alternatives use different SIMD instruction mi…
From 8 Seconds to 370ms: Kernel-Fused SAR Imaging on Apple Silicon via Single-Dispatch FFT Pipelines
Mohamed Amine Bergach
We present the first kernel-fused SAR Range Doppler pipeline on any GPU platform. By fusing FFT, matched-filter multiply, and IFFT into a single Metal compute dispatch -- keeping a…
Dual-Select FMA Butterfly for FFT: Eliminating Twiddle Factor Singularities with Bounded Precomputed Ratios
Mohamed Amine Bergach
The fused multiply-add (FMA) instruction enables the radix-2 FFT butterfly to be computed in 6~FMA operations -- the proven minimum. The classical factorization by Linzer and Feig~…
Beating vDSP: A 138 GFLOPS Radix-8 Stockham FFT on Apple Silicon via Two-Tier Register-Threadgroup Memory Decomposition
Mohamed Amine Bergach
We present an optimized Fast Fourier Transform (FFT) implementation for Apple Silicon GPUs, achieving 138.45~GFLOPS for complex single-precision transforms -- a 29\% i…