Neural Networks are Integrable

Yucong Liu

Neural Networks are Integrable

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arxiv 2310.14394 v2 pith:7U6UCH2K submitted 2023-10-22 math.NA cs.NA

Yucong Liu This is my paper · ORCID

classification math.NAcs.NA

keywords integrationnetworksneuralaccuracyachievedalgorithmapproachapproximation

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In this study, we explore the integration of Neural Networks, a powerful class of functions known for their exceptional approximation capabilities. Our primary emphasis is on the integration of multi-layer Neural Networks, a challenging task within this domain. To tackle this challenge, we introduce a novel numerical method that consist of a forward algorithm and a corrective procedure. Our experimental results demonstrate the accuracy achieved through our integration approach.

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Computational Math with Neural Networks is Hard
math.NA 2025-05 conditional novelty 7.0 of 10

Under SETH, approximating integrals, Poisson solutions, or matrix-vector products for neural network inputs requires runtime at least accuracy^{-1+o(1)}.

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