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To learn intrinsic low-dimensional structures from high-dimensional data thatmost discriminate between classes, we propose the principle of Maximal CodingRate Reduction ($\text{MCR}^2$), an information-theoretic measure thatmaximizes the coding rate difference between the whole dataset and the sum ofeach individual class. We clarify its relationships with most existingframeworks such as cross-entropy, information bottleneck, information gain,contractive and contrastive learning, and provide theoretical guarantees forlearning diverse and discriminative features. The coding rate can be accuratelycomputed from finite samples of degenerate subspace-like distributions and canlearn intrinsic representations in supervised, self-supervised, andunsupervised settings in a unified manner. Empirically, the representationslearned using this principle alone are significantly more robust to labelcorruptions in classification than those using cross-entropy, and can lead tostate-of-the-art results in clustering mixed data from self-learned invariantfeatures.

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