Provable Bounds for Learning Some Deep Representations

TL;DR

This paper presents algorithms with provable guarantees for learning a broad class of deep neural networks modeled as generative graphs with random weights, using layerwise learning and correlation-based inference.

Contribution

It introduces a novel layerwise learning algorithm with provable guarantees for almost all networks in a specified class of deep generative models.

Findings

Algorithms learn networks with polynomial runtime.

Sample complexity is quadratic or cubic.

Reveals structural properties of neural networks with random weights.

Abstract

We give algorithms with provable guarantees that learn a class of deep nets in the generative model view popularized by Hinton and others. Our generative model is an $n$ node multilayer neural net that has degree at most $n^{\gamma}$ for some $\gamma <1$ and each edge has a random edge weight in $[-1,1]$. Our algorithm learns {\em almost all} networks in this class with polynomial running time. The sample complexity is quadratic or cubic depending upon the details of the model. The algorithm uses layerwise learning. It is based upon a novel idea of observing correlations among features and using these to infer the underlying edge structure via a global graph recovery procedure. The analysis of the algorithm reveals interesting structure of neural networks with random edge weights.