Related papers: Most Neural Networks Are Almost Learnable

Most Neural Networks Are Almost Learnable

URL: http://arxiv.org/abs/2305.16508v3
Date: Tue, 24 Oct 2023 19:36:51 GMT
Title: Most Neural Networks Are Almost Learnable
Authors: Amit Daniely, Nathan Srebro, Gal Vardi
Abstract summary: We show that for any fixed $epsilon>0$ and depth $i$, there is a poly-time algorithm that learns random Xavier networks of depth $i$. The algorithm runs in time and sample complexity of $(bard)mathrmpoly(epsilon-1)$, where $bar d$ is the size of the network. For some cases of sigmoid and ReLU-like activations the bound can be improved to $(bard)mathrmpolylog(eps
Score: 52.40331776572531
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We present a PTAS for learning random constant-depth networks. We show that for any fixed $\epsilon>0$ and depth $i$, there is a poly-time algorithm that for any distribution on $\sqrt{d} \cdot \mathbb{S}^{d-1}$ learns random Xavier networks of depth $i$, up to an additive error of $\epsilon$. The algorithm runs in time and sample complexity of $(\bar{d})^{\mathrm{poly}(\epsilon^{-1})}$, where $\bar d$ is the size of the network. For some cases of sigmoid and ReLU-like activations the bound can be improved to $(\bar{d})^{\mathrm{polylog}(\epsilon^{-1})}$, resulting in a quasi-poly-time algorithm for learning constant depth random networks.

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