Deep Noise Label Learning via Effective Rank Reduction

Learning with noisy labels in large-scale classification re-mains challenging. Existing forward-correction methods estimate class-dependent label noise via a transition matrix, but this matrix is typ-ically assumed to be full-rank and unconstrained. However, real-worldlabel noise is typically structured and exhibits low-rank properties dueto semantic clustering, especially when the number of classes is large.This mismatch between modeling assumptions and the intrinsic struc-ture of label noise leads to unstable optimization and degraded general-ization performance. Motivated by this observation, we propose a novelLow-Effective-Rank Noisy-Label Learning (LENL) framework, whichexplicitly constrains the transition matrix via nuclear-norm regulariza-tion. This low-rank inductive bias captures structured confusion pat-terns while suppressing spurious noise modes, yielding both statisticalefficiency and improved generalization. We further provide theoreticalanalysis establishing the benefits of rank-constrained estimation understructured noise assumptions. To enable stable and scalable optimiza-tion, we introduce a Newton–Schulz optimizer tailored for label-noiselearning, which approximates the nuclear norm through decomposition-free iterative updates, avoiding the numerical instability and computa-tional overhead of explicit singular value decomposition. Extensive exper-iments on CIFAR-100, CIFAR-100N, ImageNet-1K, and Noisy Ostracodsdemonstrate consistent and significant improvements over state-of-the-art label-noise learning methods.