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原文摘要

Machine unlearning removes the influence of specific training examples to comply with privacy regulations. Full retraining gives strong guarantees but is computationally prohibitive at scale; approximate methods are efficient but lack formal guarantees. SISA (Sharded, Isolated, Sliced, and Aggregated training) achieves certified deletion through data sharding and independent retraining, but random partitioning scatters forget requests across most shards, and isolated retraining degrades utility. We introduce IDSISA (Influence-Distilled SISA), which uses influence functions to concentrate forget-prone samples into few shards and distillation from unaffected shards to recover utility lost to isolation. The deletion guarantee inherited from SISA's retraining step remains exact and requires no probabilistic qualification; the distillation-based utility recovery is a separately quantified, empirically bounded approximation ($ε_{\text{cert}} \leq 0.015$ in expectation). We further formalize certification under sequences of repeated deletion requests, where cross-shard distillation can create dependencies between shards; we prove that a closure-based cascading retraining procedure restores the deletion guarantee to the full aggregated model under any deletion sequence. Experiments on ResNet-18/CIFAR-10, ResNet-18/CIFAR-100, BiLSTM/IMDB, TCN/IMDB, and a fully connected network on Fashion-MNIST show $14-91\%$ better selective forgetting, up to $50\%$ better utility retention in relative terms (with consistent percentage-point gains on the other architectures, where a relative baseline is undefined), and unlearning-time changes ranging from $-6.7\%$ to $+6.4\%$ depending on architecture, relative to SISA.