Training Deep Neural Classifiers with Soft Diamond Regularizers

Abstract

We introduce new soft diamond regularizers that both improve synaptic sparsity and maintain classification accuracy in deep neural networks. These parametrized regularizers outperform the state-of-the-art hard-diamond Laplacian regularizer of Lasso regression and classification. They use thick-tailed symmetric alpha-stable (S S) bell-curve synaptic weight priors that are not Gaussian and so have thicker tails. The geometry of the diamond-shaped constraint set varies from a circle to a star depending on the tail thickness and dispersion of the prior probability density function. Training directly with these priors is computationally intensive because almost all S S probability densities lack a closed form. A precomputed look-up table removed this computational bottleneck. We tested the new soft diamond regularizers with deep neural classifiers on the three datasets CIFAR-10, CIFAR-100, and Caltech-256. The regularizers improved the accuracy of the classifiers. The improvements included 4.57\% on CIFAR-10, 4.27\% on CIFAR-100, and 6.69\% on Caltech-256. They also outperformed L_2 regularizers on all the test cases. Soft diamond regularizers also outperformed L_1 lasso or Laplace regularizers because they better increased sparsity while improving classification accuracy. Soft-diamond priors substantially improved accuracy on CIFAR-10 when combined with dropout, batch, or data-augmentation regularization.

Tasks

Reproductions