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Mean-Field Analysis for Learning Subspace-Sparse Polynomials with Gaussian Input
Feb. 15, 2024, 5:41 a.m. | Ziang Chen, Rong Ge
cs.LG updates on arXiv.org arxiv.org
Abstract: In this work, we study the mean-field flow for learning subspace-sparse polynomials using stochastic gradient descent and two-layer neural networks, where the input distribution is standard Gaussian and the output only depends on the projection of the input onto a low-dimensional subspace. We propose a basis-free generalization of the merged-staircase property in Abbe et al. (2022) and establish a necessary condition for the SGD-learnability. In addition, we prove that the condition is almost sufficient, in …
abstract analysis arxiv cs.lg distribution flow free gradient layer low mean networks neural networks projection standard stochastic study type work
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