Deep neural networks (DNNs) have achieved tremendous success in a variety of applications across many disciplines. Yet, their superior performance comes with the expensive cost of requiring correctly annotated large-scale datasets. Moreover, due to DNNs' rich capacity, errors in training labels can hamper performance. To combat this problem, mean absolute error (MAE) has recently been proposed as a noise-robust alternative to the commonly-used categorical cross entropy (CCE) loss. However, as we show in this paper, MAE can perform poorly with DNNs and large-scale datasets. Here, we present a theoretically grounded set of noise-robust loss functions that can be seen as a generalization of MAE and CCE. Proposed loss functions can be readily applied with any existing DNN architecture and algorithm, while yielding good performance in a wide range of noisy label scenarios. We report results from experiments conducted with CIFAR-10, CIFAR-100 and FASHION-MNIST datasets and synthetically generated noisy labels.

The key insight comes from analyzing the loss function gradients: they are equivalent, except that CCE includes a term that implicitly assigns higher weights to incorrect predictions. This makes training with CCE faster than with MAE but also makes it more susceptible to overfitting label noise. Like CCE, the gradient of Lq loss yields a weighting term but with an exponent parameter that we can choose. When q 0, we get CCE, and when q 1, the weighting term disappears, which is equivalent to MAE. The paper shows that a variant of a known risk bound for MAE under uniform label noise applies to Lq loss as q approaches 1. Experimental results are noticeably strong: Lq consistently outperforms CCE and MAE both and is competitive with several alternative strong baselines.

Deep neural networks (DNNs) have achieved tremendous success in a variety of applications across many disciplines. Yet, their superior performance comes with the expensive cost of requiring correctly annotated large-scale datasets. Moreover, due to DNNs' rich capacity, errors in training labels can hamper performance. To combat this problem, mean absolute error (MAE) has recently been proposed as a noise-robust alternative to the commonly-used categorical cross entropy (CCE) loss. However, as we show in this paper, MAE can perform poorly with DNNs and large-scale datasets. Here, we present a theoretically grounded set of noise-robust loss functions that can be seen as a generalization of MAE and CCE.