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