Soft Diamond Regularizers for Deep Learning

TL;DR

This paper introduces a new family of soft diamond regularizers based on alpha-stable distributions, which improve deep learning performance and sparsity, outperforming existing regularizers in image classification and language translation tasks.

Contribution

The paper proposes a novel soft diamond regularizer using alpha-stable distributions, addressing computational challenges with a look-up table, and demonstrates its effectiveness in deep learning applications.

Findings

Improved accuracy and sparsity in image classifiers.

Outperformed Laplacian regularizer in tests.

Effective in German-English translation tasks.

Abstract

This chapter presents the new family of soft diamond synaptic regularizers based on thick-tailed symmetric alpha stable $S{\alpha}S$ probability bell curves. These new parametrized weight priors improved deep-learning performance on image and language-translation test sets and increased the sparsity of the trained weights. They outperformed the state-of-the-art hard-diamond Laplacian regularizer of sparse lasso regression and classification. The $S{\alpha}S$ synaptic weight priors have power-law bell-curve tails that are thicker than the thin exponential tails of Gaussian bell curves that underly ridge regularizers. Their tails get thicker as the $\alpha$ parameter decreases. These thicker tails model more impulsive behavior and allow for occasional distant search in synaptic weight spaces of extremely high dimension. The geometry of their constraint sets has a diamond shape. The shape varies from a circle to a star or diamond that depends on the $\alpha$ tail thickness and dispersion of the $S{\alpha}S$ weight prior. These $S{\alpha}S$ bell curves lack a closed form in general and this makes direct training computationally intensive. We removed this computational bottleneck by using a precomputed look-up table. We tested the soft diamond regularizers with deep neural classifiers on both image test sets and German-to-English language translation. The image simulations used the three datasets CIFAR-10, CIFAR-100, and Caltech-256. The regularizers improved the accuracy and sparsity of the classifiers. We also tested with deep neural machine-translation models on the IWSLT-2016 Evaluation dataset for German-to-English text translation. They also outperformed ridge regularizers and lasso regularizers. These findings recommend the sub-Cauchy $\alpha = 0.5$ soft diamond regularizer as a competitive and sparse regularizer for large-scale machine learning.