A faster and simpler algorithm for learning shallow networks

Sitan Chen; Shyam Narayanan

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arXiv · 2307.12496

A faster and simpler algorithm for learning shallow networks

Sitan Chen·Shyam Narayanan

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Abstract

We revisit the well-studied problem of learning a linear combination of $k$ ReLU activations given labeled examples drawn from the standard $d$-dimensional Gaussian measure. Chen et al. [CDG+23] recently gave the first algorithm for this problem to run in $\text{poly}(d,1/\varepsilon)$ time when $k = O(1)$, where $\varepsilon$ is the target error. More precisely, their algorithm runs in time $(d/\varepsilon)^{\mathrm{quasipoly}(k)}$ and learns over multiple stages. Here we show that a much simpler one-stage version of their algorithm suffices, and moreover its runtime is only $(d/\varepsilon)^{O(k^2)}$.

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Sitan Chen, Shyam Narayanan. 2023-07-24. A faster and simpler algorithm for learning shallow networks. https://arxiv.org/abs/2307.12496

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