In label-noise learning, the noise transition matrix reveals how an instance transitions from its clean label to its noisy label. Accurately estimating an instance's noise transition matrix is crucial for estimating its clean label.

Label noise widely exists in large-scale image datasets.

The accuracy of machine learning interatomic potentials suffers from reference data that contains numerical noise. Often originating from unconverged or inconsistent electronic-structure calculations, this noise is challenging to identify. Existing mitigation strategies such as manual filtering or iterative refinement of outliers, require either substantial expert effort or multiple expensive retraining cycles, making them difficult to scale to large datasets. Here, we introduce an on-the-fly outlier detection scheme that automatically down-weights noisy samples, without requiring additional reference calculations. By tracking the loss distribution via an exponential moving average, this unsupervised method identifies outliers throughout a single training run. We show that this approach prevents overfitting and matches the performance of iterative refinement baselines with significantly reduced overhead. The method's effectiveness is demonstrated by recovering accurate physical observables for liquid water from unconverged reference data, including diffusion coefficients. Furthermore, we validate its scalability by training a foundation model for organic chemistry on the SPICE dataset, where it reduces energy errors by a factor of three. This framework provides a simple, automated solution for training robust models on imperfect datasets across dataset sizes.

While impressive, most of these tasks can be easily performed by an intelligent human.

Deep double descent is one of the key phenomena underlying the generalization capability of deep learning models. In this study, epoch-wise double descent, which is delayed generalization following overfitting, was empirically investigated by focusing on the evolution of internal structures. Fully connected neural networks of three different sizes were trained on the CIFAR-10 dataset with 30% label noise. By decomposing the loss curves into signal contributions from clean and noisy training data, the epoch-wise evolutions of internal signals were analyzed separately. Three main findings were obtained from this analysis. First, the model achieved strong re-generalization on test data even after perfectly fitting noisy training data during the double descent phase, corresponding to a "benign overfitting" state. Second, noisy data were learned after clean data, and as learning progressed, their corresponding internal activations became increasingly separated in outer layers; this enabled the model to overfit only noisy data. Third, a single, very large activation emerged in the shallow layer across all models; this phenomenon is referred as "outliers," "massive activations," and "super activations" in recent large language models and evolves with re-generalization. These empirical findings directly link the recent key phenomena of "deep double descent," "benign over-fitting," and "large activation", and support the proposal of a novel scenario for understanding deep double descent. Artificial intelligence technologies have undergone remarkable development in recent years, introducing substantial transformation to social structures and influencing various academic fields. Although these models form the core of such technologies, the fundamental principles underlying their high generalization capability when trained on real-world data remain poorly understood. Recent numerical experiments have empirically revealed various intriguing phenomena related to this gap.

In label-noise learning, the noise transition matrix reveals how an instance transitions from its clean label to its noisy label. Accurately estimating an instance's noise transition matrix is crucial for estimating its clean label. However, when only a noisy dataset is available, noise transition matrices can be estimated only for some special instances. To leverage these estimated transition matrices to help estimate the transition matrices of other instances, it is essential to explore relations between the matrices of these special instances and those of others. Existing studies typically build the relation by explicitly defining the similarity between the estimated noise transition matrices of special instances and those of other instances.

We present the Noisy Ostracods, a noisy dataset for genus and species classificationof crustacean ostracods with specialists' annotations. Over the 71466 specimenscollected, 5.58% of them are estimated to be noisy (possibly problematic) at genuslevel. The dataset is created to addressing a real-world challenge: creating aclean fine-grained taxonomy dataset. The Noisy Ostracods dataset has diversenoises from multiple sources. Firstly, the noise is open-set, including new classesdiscovered during curation that were not part of the original annotation. Thedataset has pseudo-classes, where annotators misclassified samples that shouldbelong to an existing class into a new pseudo-class.

We study benign overfitting in two-layer ReLU networks trained using gradient descent and hinge loss on noisy data for binary classification. In particular, we consider linearly separable data for which a relatively small proportion of labels are corrupted or flipped. We identify conditions on the margin of the clean data that give rise to three distinct training outcomes: benign overfitting, in which zero loss is achieved and with high probability test data is classified correctly; overfitting, in which zero loss is achieved but test data is misclassified with probability lower bounded by a constant; and non-overfitting, in which clean points, but not corrupt points, achieve zero loss and again with high probability test data is classified correctly. Our analysis provides a fine-grained description of the dynamics of neurons throughout training and reveals two distinct phases: in the first phase clean points achieve close to zero loss, in the second phase clean points oscillate on the boundary of zero loss while corrupt points either converge towards zero loss or are eventually zeroed by the network. We prove these results using a combinatorial approach that involves bounding the number of clean versus corrupt updates during these phases of training.

We study a completion problem of broad practical interest: the reconstruction of a low-rank symmetric tensor from highly incomplete and randomly corrupted observations of its entries. While a variety of prior work has been dedicated to this problem, prior algorithms either are computationally too expensive for large-scale applications, or come with sub-optimal statistical guarantees. Focusing on ``incoherent'' and well-conditioned tensors of a constant CP rank, we propose a two-stage nonconvex algorithm --- (vanilla) gradient descent following a rough initialization --- that achieves the best of both worlds. Specifically, the proposed nonconvex algorithm faithfully completes the tensor and retrieves all low-rank tensor factors within nearly linear time, while at the same time enjoying near-optimal statistical guarantees (i.e.~minimal sample complexity and optimal $\ell_2$ and $\ell_{\infty}$ statistical accuracy). The insights conveyed through our analysis of nonconvex optimization might have implications for other tensor estimation problems.

Deep neural networks (DNNs) have achieved remarkable success in a variety of computer vision tasks, where massive labeled images are routinely required for model optimization. Yet, the data collected from the open world are unavoidably polluted by noise, which may significantly undermine the efficacy of the learned models. Various attempts have been made to reliably train DNNs under data noise, but they separately account for either the noise existing in the labels or that existing in the images. A naive combination of the two lines of works would suffer from the limitations in both sides, and miss the opportunities to handle the two kinds of noise in parallel. This works provides a first, unified framework for reliable learning under the joint (image, label)-noise. Technically, we develop a confidence-based sample filter to progressively filter out noisy data without the need of pre-specifying noise ratio. Then, we penalize the model uncertainty of the detected noisy data instead of letting the model continue over-fitting the misleading information in them. Experimental results on various challenging synthetic and real-world noisy datasets verify that the proposed method can outperform competing baselines in the aspect of classification performance.