The classes are airplanes, cars, birds, cats, deer, dogs, frogs, horses, ships, and trucks, and they are all mutually exclusive.

Most existing approaches for dealing with noisy labels broadly fall into two categories: noise-modeling-based methods and memorization-effects-based methods.

For labels taking values in a finite metric space, we introduce techniques new to weak supervision based on pseudo-Euclidean embeddings andtensor decompositions, providing anearly-consistent noise rate estimator.

Based on this observation, we adopt ageneralized version ofthe JensenShannon divergence for multiple distributions to encourage consistency around data points. Using this loss function, we show state-of-the-art results on both synthetic(CIFAR),andreal-world(e.g.WebVision)noisewithvaryingnoiserates.

The challenge of learning with noisy labels is significant in machine learning, as it can severely degrade the performance of prediction models if not addressed properly. This paper introduces a novel framework that conceptualizes noisy label correction as a reinforcement learning (RL) problem. The proposed approach, Reinforcement Learning for Noisy Label Correction (RLNLC), defines a comprehensive state space representing data and their associated labels, an action space that indicates possible label corrections, and a reward mechanism that evaluates the efficacy of label corrections. RLNLC learns a deep feature representation based policy network to perform label correction through reinforcement learning, utilizing an actor-critic method. The learned policy is subsequently deployed to iteratively correct noisy training labels and facilitate the training of the prediction model. The effectiveness of RLNLC is demonstrated through extensive experiments on multiple benchmark datasets, where it consistently outperforms existing state-of-the-art techniques for learning with noisy labels.

This section provides more details on the augmentation process of Figure 1. Testing sets are not involved in our augmentation search process. The testing set is not used. The hyperparameters for re-training used in this paper are listed in Tab. B. Basically, we use the same For those not reported in [7], we refer to [1].

We study language generation in the limit, where an algorithm observes an adversarial enumeration of strings from an unknown target language $K$ and must eventually generate new, unseen strings from $K$. Kleinberg and Mullainathan [KM24] proved that generation is achievable in surprisingly general settings. But their generator suffers from ``mode collapse,'' producing from an ever-smaller subset of the target. To address this, Kleinberg and Wei [KW25] require the generator's output to be ``dense'' in the target language. They showed that generation with density, surprisingly, remains achievable at the same generality. Both results assume perfect data: no noisy insertions and no omissions. This raises a central question: how much contamination can generation tolerate? Recent works made partial progress on this question by studying (non-dense) generation with either finite amounts of noise (but no omissions) or omissions (but no noise). We characterize robustness under contaminated enumerations: 1. Generation under Contamination: Language generation in the limit is achievable for all countable collections iff the fraction of contaminated examples converges to zero. When this fails, we characterize which collections are generable. 2. Dense Generation under Contamination: Dense generation is strictly less robust to contamination than generation. As a byproduct, we resolve an open question of Raman and Raman [ICML25] by showing that generation is possible with only membership oracle access under finitely many contaminated examples. Finally, we introduce a beyond-worst-case model inspired by curriculum learning and prove that dense generation is achievable even with infinite contamination provided the fraction of contaminated examples converges to zero. This suggests curriculum learning may be crucial for learning from noisy web data.