Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction

TL;DR

This paper introduces the Maximal Coding Rate Reduction principle, an information-theoretic approach that learns low-dimensional, discriminative data representations, improving robustness and clustering performance across various learning settings.

Contribution

It formalizes the MCR^2 principle, connecting it with existing frameworks, and demonstrates its effectiveness in learning diverse, robust representations in supervised, self-supervised, and unsupervised contexts.

Findings

Learned representations are more robust to label noise.

Achieves state-of-the-art clustering results.

Provides theoretical guarantees for feature diversity and discrimination.

Abstract

To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction ($\text{MCR}^2$), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.