An Empirical Study of Example Forgetting during Deep Neural Network Learning

What came before

Curriculum learning (Bengio et al. 2009) and self-paced learning (Kumar et al. 2010) define example "hardness" from the loss at one point in training; Chang et al. (2017) re-weight examples by the variance of their predictive distribution but do not analyze how often this occurs; Koh and Liang's influence functions and various importance-sampling schemes (Zhao and Zhang; Katharopoulos and Fleuret) score examples from gradient norms. None of these track whether an example, once correctly classified during training, is later misclassified again — the paper's own definition of "forgetting" — nor ask whether removing a data-derived subset preserves generalization.

The problem

It is unknown whether "catastrophic forgetting" (studied in continual learning as a consequence of a distribution shift between sequential tasks) also occurs for individual examples within a single, stationary classification task trained by ordinary SGD, and if so, whether that forgetting behavior reveals which training examples are redundant and safe to discard.

The idea

Track each training example's correct/incorrect classification state across all SGD updates where it appears in a minibatch; call a transition from correct to incorrect a "forgetting event." Some examples are forgotten repeatedly, others ("unforgettable") never are once first learned. Forgetting frequency is stable across seeds and architectures and correlates with an example's intrinsic difficulty (noisy labels, atypical features), so unforgettable examples are redundant and can be removed from training without hurting generalization, while highly forgotten examples behave like support vectors.

How it works

For each example $i$ and SGD step $t$, define $\text{acc}_i^t=\mathbb{1}[\hat{y}_i^t=y_i]$; a forgetting event occurs when $\text{acc}_i^t>\text{acc}_i^{t+1}$ (correct then incorrect) and a learning event when the reverse holds. Forgetting counts are accumulated only across the presentations of an example within its sampled minibatches (a lower bound on the true event count, Algorithm 1), avoiding the cost of scoring the whole dataset every step. An example is "unforgettable" if it is learned at some finite step and never misclassified again. The resulting per-example forgetting count is used to rank and prune the training set: examples are removed in increasing order of forgetting count (least-forgotten/most-redundant first) and a fresh model is retrained from scratch on each pruned subset. No teacher, generator, or bi-level optimization is involved; scoring requires one full training run of the same (or a smaller/cheaper) network on the full dataset. In the loop: only the network being scored (a 2-conv-layer net for MNIST/ permutedMNIST, a ResNet-18 with cutout for CIFAR-10/100, and separately a smaller CNN and a WideResNet used to test whether the ranking transfers across architectures).

Evidence

CIFAR-10, hard labels, ResNet-18 (Fig. 5, left): removing examples in increasing order of forgetting count allows 30% of the training set to be removed with performance comparable to the full-data model, and up to 35% removed with less than 0.2 percentage points of degradation, while removing a random 30% subset degrades accuracy much faster. Cross-dataset removal budgets (Fig. 6): up to 30% removable on CIFAR-10, 50% on permutedMNIST, 80% on MNIST, tracking each dataset's fraction of unforgettable examples (31.3% CIFAR-10, 75.3% permutedMNIST, 91.7% MNIST, all measured across 5 seeds). CIFAR-100 (Appendix 15): only 7.62% of examples are unforgettable and about 8% of the training set can be removed losslessly — far less headroom than CIFAR-10, tracking the harder, more fine-grained task. Stability: average pairwise Pearson correlation of per-example forgetting counts across 10 seeds is 89.2%, rising to 97.6% when comparing sums over two groups of 5 seeds; "chance" forgetting under randomized (shuffled) gradient updates occurs at most twice per example, versus the true distribution's much longer tail. Cross-architecture transfer (Fig. 7): an ordering computed from a much smaller 2-conv-layer network recovers ResNet-18's unforgettable examples with high precision/recall, and pruning a WideResNet's training set by 30% using a ResNet-18-derived ordering (2 GPU-hours to compute vs. 8 GPU-hours for the WideResNet itself, saving up to 6 hours) still yields near-optimal WideResNet accuracy. Noisy-label diagnostic (Fig. 3): with 20% of CIFAR-10 labels randomized, the most-forgotten examples are overwhelmingly the noisy ones, and no noisy example is unforgettable.

Limitations

Restricted to MNIST, permutedMNIST, CIFAR-10 and CIFAR-100 — no ImageNet-scale or modern architecture evaluation, and no comparison to any dataset-distillation method (predates the field's 2019-onward coreset/DD comparisons). Computing exact forgetting statistics requires one full training run per architecture, which the paper itself calls "computationally expensive," motivating its own cross-architecture-transfer experiment as a workaround rather than a solution. The ranking stabilizes only after roughly 50-75 epochs of the scoring run (Fig. 7 left), so early-stopping the scoring pass is not free. At the most aggressive pruning ratios, the most-forgotten examples themselves start to hurt generalization (Fig. 5, right, upturn at the tail), which the paper attributes to outliers/mislabeled data without a method to separate them from genuinely informative hard examples.