Shallow neural networks learn low-degree spherical polynomials with feature learning

Researchers have developed a novel approach using shallow neural networks with learnable channel attention to efficiently learn low-degree spherical polynomials. This method significantly improves sample complexity compared to existing methods, requiring only $n \text{ \textasymp } \Theta(d^{\ell_0}/\eps)$ samples. The process involves two stages: first, a channel selection algorithm identifies the degree of the target function, and second, standard gradient descent trains the network using the selected channels. This work marks a significant advancement in achieving minimax optimal risk bounds for finite-width neural networks capable of feature learning. AI

IMPACT Introduces a novel method for learning spherical polynomials with improved sample complexity, potentially impacting fields requiring spherical data analysis.

RANK_REASON This is a research paper published on arXiv detailing a new theoretical result in machine learning.

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