Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction (2006.08558v1)

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.

• The paper introduces the MCR² principle, an info-theoretic measure that enhances class discrimination and representation diversity.
• The approach unifies supervised, self-supervised, and unsupervised learning by providing a robust alternative to conventional cross-entropy loss.
• Experiments confirm that MCR² yields more interpretable and resilient features, especially in noisy and corrupted label scenarios.

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

The paper presents a novel approach for learning low-dimensional intrinsic structures in high-dimensional data, focusing on maximizing class discriminativeness. The authors propose a principle of Maximal Coding Rate Reduction (MCR$^2$), which is a measure to exploit the difference between the coding rate of a complete dataset and the sum of the individual coding rates of each class. This principle is grounded in information theory and aims to unify several existing paradigms in machine learning by providing a framework with theoretical guarantees for learning discriminative and diverse representations.

The main contributions of this research can be summarized as follows:

1. Introduction of MCR$^2$ Principle: MCR$^2$ is an information-theoretic formulation that seeks to maximize the reduction in coding rate when mapping data into low-dimensional representations. This principle contrasts the typical use of cross-entropy loss, focusing on capturing intrinsic data structures rather than just fitting labels.
2. Unified Framework: MCR$^2$ can be applied to supervised, self-supervised, and unsupervised learning scenarios. Unlike task-specific metrics like cross-entropy, it provides a task-agnostic measure of representation effectiveness, offering robustness to label noise and enhancing interpretability.
3. Theoretical Insights: The authors provide theoretical analyses that demonstrate how the optimal representations obtained by MCR$^2$ are both discriminative between classes and diverse within them. The representations naturally promote orthogonality among different classes and push for maximal subspace dimensions, aligning with the goal of learning robust and generalizable features.
4. Experimental Validation: The paper presents empirical results showing that the MCR$^2$ framework yields representations that outperform traditional methods like cross-entropy loss in robustness, especially when dealing with corrupted labels. The method also shows state-of-the-art performance in clustering tasks when combined with self-supervised learning setups.
5. Implications and Future Work: The results imply significant potential for MCR$^2$ in improving feature learning and representation robustness in varied machine learning applications. The research opens up pathways to further exploration in optimizing deep learning architectures and training dynamics to harness the full power of this principle.

The MCR$^2$ principle provides a compelling alternative to prevailing methods, emphasizing learning features that are not only useful for current tasks but retain the richness and diversity needed for future adaptability and tasks across different domains. Future research could explore more extensive applications of MCR$^2$ across various data types and tasks, along with developing more sophisticated models to better capture the principle's benefits.

Through this work, the authors have not only advanced theoretical understanding but have also provided practical tools to significantly enhance machine learning models’ capabilities in handling diverse and noisy datasets, marking a step forward in the quest for more robust and interpretable machine learning paradigms.