@inproceedings{
chen2024meanfield,
title={Mean-Field Analysis for Learning Subspace-Sparse Polynomials with Gaussian Input},
author={Ziang Chen and Rong Ge},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=unA5hxIn6v}
}
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 establish a necessary condition for SGD-learnability, involving both the characteristics of the target function and the expressiveness of the activation function. In addition, we prove that the condition is almost sufficient, in the sense that a condition slightly stronger than the necessary condition can guarantee the exponential decay of the loss functional to zero.
Mean-Field Analysis for Learning Subspace-Sparse Polynomials with Gaussian Input
Ziang Chen Rong Ge