Problem
Research questions and friction points this paper is trying to address.
MCR^2
Out-of-Distribution Generalisation
Distribution Shift
Invariant Risk Minimisation
Risk Extrapolation
On the Limits of Maximal Coding Rate Reduction for Out-of-Distribution Generalisation
🤖 AI Summary
研究探讨了MCR^2在分布外泛化中的局限性，指出其可能因环境特征不稳定导致预测失败，并提出需要新的假设或学习原则来确保跨环境的稳定预测。
📝 Abstract
Substantial efforts have been devoted to making deep learning objectives, representations, and architectures interpretable, with the goal of improving the safety, robustness, and generalisation of learning systems in diverse real-world applications. The recently proposed maximal coding rate reduction ($\mathrm{MCR}^{2}$) offers a promising information-theoretic framework for learning structured, discriminative representations of class-wise submanifolds and has inspired interpretable white-box architectures. However, we observe that $\mathrm{MCR}^{2}$ can completely fail under distribution shift, motivating our study of its out-of-distribution (OOD) generalisation limits. We establish two limitations of $\mathrm{MCR}^{2}$ for OOD generalisation. First, the $\mathrm{MCR}^{2}$ objective alone can admit complete prediction failure: a representation based entirely on unstable environmental features can achieve the global coding optimum yet fail completely after correlation reversal, despite an available perfectly stable feature. This exact-optimum example includes test inputs that cannot occur during training. Even when every possible test input can also occur during training, coding quality can be arbitrarily close to optimal while prediction error is arbitrarily close to 100%. Second, directly incorporating the invariance principle underlying widely successful invariant risk minimisation (IRM) and risk extrapolation (REx) does not eliminate this failure. The failing representation admits the same optimal coding operator across training environments, showing that shared coding optimality does not ensure stable prediction. Reliable OOD guarantees for $\mathrm{MCR}^{2}$ therefore require additional new assumptions or learning principles that establish stable predictive relationships across environments.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Maximal Coding Rate Reduction
Out-of-Distribution Generalisation
Invariant Risk Minimisation
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