A faster and simpler algorithm for learning shallow networks

• URL: http://arxiv.org/abs/2307.12496v1
• Date: Mon, 24 Jul 2023 03:04:10 GMT
• Title: A faster and simpler algorithm for learning shallow networks
• Authors: Sitan Chen, Shyam Narayanan
• Abstract summary: We revisit the well-studied problem of learning a linear combination of $k$ ReLU activations given labeled examples. Here we show that a simpler one-stage version of their algorithm suffices, and moreover its runtime is only $(d/varepsilon)O(k2)$.
• Score: 10.595936992218856
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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