Elastic Coding: Robust Maximal Coding Rate Reduction under Label Noise

Maximal Coding Rate Reduction (MCR²) exhibits striking empirical robustness to corrupted labels, yet the source and limits of this robustness remain unclear. We show that label corruption leaves its global expansion term unchanged, while sample-wise normalisation limits the influence of individual examples. Under a balanced union-of-orthogonal-subspaces model, uniformly flipped labels disperse corrupted examples across off-class directions, allowing the clean semantic subspace to remain the leading eigenspace when the flip rate is below $(K-1)/K$. Robustness weakens when corruption concentrates in an off-class subspace strong enough to compete with the clean one. Motivated by a decomposition of the MCR² gradient, we propose **Elastic Coding**, which relaxes class compression when it excessively opposes global expansion. Across datasets with structured and real-world label noise, Elastic Coding achieves the best performance among the compared baselines in most evaluated settings.