Spectral Neural Network Compression via Discrete Fourier Transform: A Post Hoc and Lightweight Approach

Abstract We introduce a spectral post hoc compression method for neural networks based on Discrete Fourier Transform (DFT) of complex weights. The approach filters low-magnitude frequencies to obtain sparse spectral representations while preserving accuracy. Theoretical results quantify energy preservation and output perturbation. We propose a principled thresholding rule, and demonstrate competitive performance compared to DCT and wavelets. Experiments on MNIST, CIFAR-10 and ResNet show 10–15× compression with negligible loss. Hardware metrics confirm reduced memory usage and improved inference latency. The method is lightweight, requires no retraining , and suits embedded AI.