A Provably Correct Algorithm for Deep Learning that Actually Works

TL;DR

This paper introduces a provably correct layer-by-layer training algorithm for deep convolutional networks based on a generative model, demonstrating both theoretical convergence and practical effectiveness on CIFAR.

Contribution

It presents a novel, theoretically grounded training algorithm for deep networks that combines gradient updates with clustering, supported by convergence analysis and empirical validation.

Findings

Algorithm converges under certain generative assumptions.

Achieves performance comparable to standard CNN training on CIFAR.

Provides new proof techniques of independent interest.

Abstract

We describe a layer-by-layer algorithm for training deep convolutional networks, where each step involves gradient updates for a two layer network followed by a simple clustering algorithm. Our algorithm stems from a deep generative model that generates mages level by level, where lower resolution images correspond to latent semantic classes. We analyze the convergence rate of our algorithm assuming that the data is indeed generated according to this model (as well as additional assumptions). While we do not pretend to claim that the assumptions are realistic for natural images, we do believe that they capture some true properties of real data. Furthermore, we show that our algorithm actually works in practice (on the CIFAR dataset), achieving results in the same ballpark as that of vanilla convolutional neural networks that are being trained by stochastic gradient descent. Finally, our proof techniques may be of independent interest.