ProMeCD: Unifying Long-Tailed and Noisy Label Learning via White-Box Control

Real-world data is rarely clean; it is plagued by severe class imbalance (long-tailed distributions) and label corruption. Current solutions lean heavily on "black-box" meta-learning to re-weight samples. However, this paradigm introduces a fatal circular dependency: it relies on pristine, balanced validation sets to guide the optimization, which are essentially non-existent in the wild. We propose ProMeCD, a self-referential framework that breaks this dependency by recasting optimization as an autonomous control problem. Instead of training an opaque neural meta-learner, we employ a transparent proportional-integral controller. The system monitors ``cognitive entropy'' that is a metric derived from von Mises-Fisher gradient statistics to assess learning uncertainty. To resolve the scalar ambiguity between tail and noisy samples, ProMeCD employs a decoupled control strategy: it boosts tail classes via integral accumulation of magnitude deficits when directional consistency is high, while suppressing noise via proportional feedback when consistency collapses. Theoretically, we prove that this mechanism guarantees convergence and formally prevents the minority initial drop, ensuring monotonic improvement for rare classes. Crucially, ProMeCD is fully white-box and validation-free. Experiments on CIFAR-LT, iNaturalist, CIFAR-N, mini WebVision, and Clothing1M confirm that ProMeCD is not merely efficient; it outperforms the recent meta-learner FMW-Net by over 10\% in severe imbalance settings, proving that explicit control theory offers a superior path to handling imperfect data.

Real-world data for AI training is often messy because it contains incorrect labels and extreme rarity where some examples appear far less often than others. Current methods try to fix this by using a second AI system to re-weight the data. However, these methods create a circular problem because they need a perfectly clean dataset to guide the training, which is almost never available in real scenarios. We developed ProMeCD, which is a new framework that manages its own learning process without needing any external clean data. Instead of relying on a hidden AI to make guesses, we used a transparent system based on control theory. Our system monitors internal uncertainty by analyzing the consistency of the learning signals. It identifies rare but consistent examples and increases their importance, while it suppresses chaotic and conflicting noise. This method is self-sufficient and highly efficient. It significantly improves accuracy and outperforms recent state-of-the-art methods by over 10% in challenging settings. By using clear mathematical laws, ProMeCD provides a practical way to build AI that learns effectively from the imperfect data found in everyday life.