Samples With Low Loss Curvature Improve Data Efficiency

In this paper, we study the second order properties of the loss of trained deep neural networks with respect to the training data points to understand the curvature of the loss surface in the vicinity of these points. We find that there is an unexpected concentration of samples with very low curvature. We note that these low curvature samples are largely consistent across completely different architectures, and identifiable in the early epochs of training. We show that the curvature relates to the 'cleanliness' of the data points, with low curvatures samples corresponding to clean, higher clarity samples, representative of their category. Alternatively, high curvature samples are often occluded, have conflicting features and visually atypical of their category. Armed with this insight, we introduce SLo-Curves, a novel coreset identification and training algorithm. SLo-curves identifies the samples with low curvatures as being more data-efficient and trains on them with an additional regularizer that penalizes high curvature of the loss surface in their vicinity. We demonstrate the efficacy of SLo-Curves on CIFAR-10 and CIFAR-100 datasets, where it outperforms state of the art coreset selection methods at small coreset sizes by up to 9%. The identified coresets generalize across architectures, and hence can be pre-computed to generate condensed versions of datasets for use in downstream tasks.