Data Pruning via Moving-one-Sample-out

In this paper, we propose a novel data-pruning approach called moving-one-sampleout (MoSo), which aims to identify and remove the least informative samples from the training set. The core insight behind MoSo is to determine the importance of each sample by assessing its impact on the optimal empirical risk. This is achieved by measuring the extent to which the empirical risk changes when a particular sample is excluded from the training set. Instead of using the computationally expensive leaving-one-out-retraining procedure, we propose an efficient first-order approximator that only requires gradient information from different training stages. The key idea behind our approximation is that samples with gradients that are consistently aligned with the average gradient of the training set are more informative and should receive higher scores, which could be intuitively understood as follows: if the gradient from a specific sample is consistent with the average gradient vector, it implies that optimizing the network using the sample will yield a similar effect on all remaining samples. Experimental results demonstrate that MoSo effectively mitigates severe performance degradation at high pruning ratios and achieves satisfactory performance across various settings. Existing approaches can be broadly categorized into three major groups: pruning by importance criteria [11, 42, 28, 27, 26, 46] , coverage or diversity-driven methods [48, 29, 33, 15] , and optimizationbased methods [38, 8, 23, 24, 21, 44] . Among these, the first group of studies is the most effective and popular. These studies assume that hard samples are critical and informative core-set samples, and thus, they design difficulty-based metrics to assess sample importance. Such metrics include prediction entropy [11] , forgetting [28] or memorization [46] score, gradient norm [27], E2LN (variance of prediction) [27], self-supervised prototype distance [42], diverse ensembles [26], and others.