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abstract indexed · arXiv 2609.20483 · updated 2026-10-18

Scaling Fourier-Based Sparse Matrix Analysis on GPUs

First page of Scaling Fourier-Based Sparse Matrix Analysis on GPUs
From the original paper · arXiv 2609.20483Page 1. Select the image to read the PDF.

The method replaces dense cuFFT-based spectral analysis of large sparse matrices (e.g., GNN adjacency matrices) with a lossless binary-sparse FFT pipeline, optionally followed by sampled-grid (Elastic BS-FFT) or density-map spatial compression. It costs implementation complexity for a custom sparse FFT pipeline, and the compression variants trade spectral fidelity (up to 11.56% feature error) for computation time. It can fail if downstream uses require exact spectra (only BS-FFT is lossless), if matrices are not binary/sparse enough to benefit, or if the workload is outside graph spectral analysis where the technique has no application.

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Binary-sparse FFT for spectral analysis of sparse matrices
published
2026-09-17

This is a specialized GPU kernel technique for spectral analysis of graph adjacency matrices, which is only relevant if the reader runs GNN workloads that need spectral signatures, so it should be monitored rather than adopted for general LLM production.

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  1. claim 01Paperraft inference
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    The method replaces dense cuFFT-based spectral analysis of large sparse matrices (e.g., GNN adjacency matrices) with a lossless binary-sparse FFT pipeline, optionally followed by sampled-grid (Elastic BS-FFT) or density-map spatial compression. It costs implementation complexity for a custom sparse FFT pipeline, and the compression variants trade spectral fidelity (up to 11.56% feature error) for computation time. It can fail if downstream uses require exact spectra (only BS-FFT is lossless), if matrices are not binary/sparse enough to benefit, or if the workload is outside graph spectral analysis where the technique has no application.

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  2. claim 02Paperraft inference

    BS-FFT reduces GPU memory use by 2.9-11.6x relative to dense cuFFT and completes all 15 GNN adjacency matrices where dense cuFFT completes 6 on a 40 GB A100; the compression variants reduce GPU computation time by 2.0-1466.4x with 0.16%-11.56% spectral feature error.

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