Preprint

PUBDB-2026-02617

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Selection, Representation, and Execution in Sparse Fourier Neural Operators

Ibrahim, A. Q. (Corresponding author)DESY* ; Burger, M. (Corresponding author)DESY*

2026

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Please use a persistent id in citations: doi:10.3204/PUBDB-2026-02617

Report No.: arXiv:2608.30070

Abstract: Sparse representations are often expected to make models smaller and also reduce inference cost. For Fourier Neural Operators (FNOs), these objectives are not equivalent or do not always align: removing parts of the learned operator can leave the underlying transforms and dense computations unchanged, while changing the grid on which the model is evaluated can introduce overhead of its own. We therefore distinguish sparsity in the representation, in the stored parameters, in the theoretical operation count, and in measured runtime, and present an empirical study of several routes toward sparse FNOs that tests each transition between them separately. Coarsening the execution grid reduces the theoretical cost without reducing measured latency, and adding a correction term recovers accuracy at the cost of making the model slower. Even an 83\% parameter reduction remains slower than the dense baseline under ordinary execution. These results motivate a stricter definition of useful sparsity: the deployed operator must preserve solution accuracy and map its reduced support to a genuinely cheaper execution path.

Keyword(s): Machine Learning (cs.LG) ; Numerical Analysis (math.NA) ; FOS: Computer and information sciences ; FOS: Mathematics ; I.2.6; G.1.8; C.4 ; 68T07, 65M70

Note: 21 pages, 11 figures

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Contributing Institute(s):

1. Computational Imaging (FS-CI)

Research Program(s):

1. 623 - Data Management and Analysis (POF4-623) (POF4-623)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2026

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