Label Noise

Increasing the size of overparameterized neural networks has been shown to improve their generalization performance. However, real-world datasets often contain a significant fraction of noisy labels, which can drastically harm the performance of the models trained on them. In this work, we study how neural networks’ test loss changes with model size when the training set contains noisy labels. We show that under a sufficiently large noise-to-sample size ratio, generalization error eventually increases with model size. First, we provide a theoretical analysis on random feature regression and show that this phenomenon occurs as the variance of the generalization loss experiences a second ascent under large noise-to-sample size ratio. Then, we present extensive empirical evidence confirming that our theoretical results hold for neural networks. Furthermore, we empirically observe that the adverse effect of network size is more pronounced when robust training methods are employed to learn from noisy-labeled data. Our results have important practical implications: First, larger models should be employed with extra care, particularly when trained on smaller dataset or using robust learning methods. Second, a large sample size can alleviate the effect of noisy labels and allow larger models to achieve a superior performance even under noise.

Self-supervised Contrastive Learning (CL) has been recently shown to be very effective in preventing deep networks from overfitting noisy labels. Despite its empirical success, the theoretical understanding of the effect of contrastive learning on boosting robustness is very limited. In this work, we rigorously prove that the representation matrix learned by contrastive learning boosts robustness, by having:(i) one prominent singular value corresponding to each sub-class in the data, and significantly smaller remaining singular values; and (ii) a large alignment between the prominent singular vectors and the clean labels of each sub-class. The above properties enable a linear layer trained on such representations to effectively learn the clean labels without overfitting the noise. We further show that the low-rank structure of the Jacobian of deep networks pre-trained with contrastive learning allows them to achieve a superior performance initially, when fine-tuned on noisy labels. Finally, we demonstrate that the initial robustness provided by contrastive learning enables robust training methods to achieve state-of-the-art performance under extreme noise levels, eg, an average of 27.18% and 15.58% increase in accuracy on CIFAR-10 and CIFAR-100 with 80% symmetric noisy labels, and 4.11% increase in accuracy on WebVision.

Modern neural networks have the capacity to overfit noisy labels frequently found in real-world datasets. Although great progress has been made, existing techniques are very limited in providing theoretical guarantees for the performance of the neural networks trained with noisy labels. To tackle this challenge, we propose a novel approach with strong theoretical guarantees for robust training of neural networks trained with noisy labels. The key idea behind our method is to select subsets of clean data points that provide an approximately low-rank Jacobian matrix. We then prove that gradient descent applied to the subsets cannot overfit the noisy labels, without regularization or early stopping. Our extensive experiments corroborate our theory and demonstrate that deep networks trained on our subsets achieve a significantly superior performance, e.g., 7% increase in accuracy on mini Webvision with 50% noisy labels, compared to state-of-the art.