The ability of overparameterized deep networks to interpolate noisy data, while at the same time showing good generalization performance, has been recently characterized in terms of the double descent curve for the test error. Common intuition from polynomial regression suggests that overparameterized networks are able to sharply interpolate noisy data, without considerably deviating from the ground-truth signal, thus preserving generalization ability. At present, a precise characterization of the relationship between interpolation and generalization for deep networks is missing. In this work, we quantify sharpness of fit of the training data interpolated by neural network functions, by studying the loss landscape w.r.t. to the input variable locally to each training point, over volumes around cleanly- and noisily-labelled training samples, as we systematically increase the number of model parameters and training epochs. Our findings show that loss sharpness in the input space follows both model- and epoch-wise double descent, with worse peaks observed around noisy labels. While small interpolating models sharply fit both clean and noisy data, large interpolating models express a smooth loss landscape, where noisy targets are predicted over large volumes around training data points, in contrast to existing intuition.

Prior works have found it beneficial to combine provably noise-robust loss functions e.g. mean absolute error (MAE) with standard categorical loss function e.g. crossentropy (CE) to improve their learnability. Here, we propose to use Jensen-Shannondivergence as a noise-robust loss function and show that it interestingly interpolatebetween CE and MAE with a controllable mixing parameter. Furthermore, wemake a crucial observation that CE exhibits lower consistency around noisy datapoints. Based on this observation, we adopt a generalized version of the Jensen-Shannon divergence for multiple distributions to encourage consistency arounddata points. Using this loss function, we show state-of-the-art results on bothsynthetic (CIFAR), and real-world (e.g. WebVision) noise with varying noise rates.

A natural way of estimating heteroscedastic label noise in regression is to model the observed (potentially noisy) target as a sample from a normal distribution, whose parameters can be learned by minimizing the negative log-likelihood. This formulation has desirable loss attenuation properties, as it reduces the contribution of high-error examples. Intuitively, this behavior can improve robustness against label noise by reducing overfitting. We propose an extension of this simple and probabilistic approach to classification that has the same desirable loss attenuation properties. Furthermore, we discuss and address some practical challenges of this extension. We evaluate the effectiveness of the method by measuring its robustness against label noise in classification. We perform enlightening experiments exploring the inner workings of the method, including sensitivity to hyperparameters, ablation studies, and other insightful analyses.

Deep neural networks and large-scale datasets have revolutionized the field of machine learning. However, these large networks are susceptible to overfitting to label noise, resulting in reduced generalization. To address this challenge, two promising approaches have emerged: i) loss reweighting, which reduces the influence of noisy examples on the training loss, and ii) label correction that replaces noisy labels with estimated true labels. These directions have been pursued separately or combined as independent methods, lacking a unified approach. In this work, we present a unified method that seamlessly combines loss reweighting and label correction to enhance robustness against label noise in classification tasks. Specifically, by leveraging ideas from compositional data analysis in statistics, we frame the problem as a regression task, where loss reweighting and label correction can naturally be achieved with a shifted Gaussian label noise model. Our unified approach achieves strong performance compared to recent baselines on several noisy labelled datasets. We believe this work is a promising step towards robust deep learning in the presence of label noise. Our code is available at: https://github.com/ErikEnglesson/SGN.