Training Sparse Neural Network by Constraining Synaptic Weight on Unit Lp Sphere

TL;DR

This paper introduces a novel method for training sparse neural networks by constraining weights on a unit Lp-sphere, using a new gradient descent algorithm, with theoretical guarantees and practical topology evolution techniques.

Contribution

The paper proposes Lp-spherical gradient descent for constrained optimization, analyzes the effect of p on sparsity, and introduces semi-pruning for effective topology evolution.

Findings

LpSGD converges theoretically and empirically.

The expected sparsity can be predicted under gamma distribution assumptions.

Experimental results validate the effectiveness across benchmark datasets.

Abstract

Sparse deep neural networks have shown their advantages over dense models with fewer parameters and higher computational efficiency. Here we demonstrate constraining the synaptic weights on unit Lp-sphere enables the flexibly control of the sparsity with p and improves the generalization ability of neural networks. Firstly, to optimize the synaptic weights constrained on unit Lp-sphere, the parameter optimization algorithm, Lp-spherical gradient descent (LpSGD) is derived from the augmented Empirical Risk Minimization condition, which is theoretically proved to be convergent. To understand the mechanism of how p affects Hoyer's sparsity, the expectation of Hoyer's sparsity under the hypothesis of gamma distribution is given and the predictions are verified at various p under different conditions. In addition, the "semi-pruning" and threshold adaptation are designed for topology evolution to effectively screen out important connections and lead the neural networks converge from the initial sparsity to the expected sparsity. Our approach is validated by experiments on benchmark datasets covering a wide range of domains. And the theoretical analysis pave the way to future works on training sparse neural networks with constrained optimization.