# Influence Functions

For machine unlearning under privacy rules, IDSISA adds influence-guided shard assignment and cross-shard distillation to SISA's shard-retraining framework. Influence scores are computed once before training and co-locate samples likely to be deleted together, so a deletion request touches fewer shards than under random partitioning; retrained shards also learn from unaffected shards' soft outputs to recover utility lost to isolation. On ResNet-18/CIFAR-10, BiLSTM/IMDB, TCN/IMDB and a fully connected Fashion-MNIST network, the deletion guarantee still comes from retraining itself, and distillation is only a separately quantified utility-recovery step.

For machine unlearning under privacy rules, IDSISA adds influence-guided shard assignment and cross-shard distillation to SISA's shard-retraining framework. Influence scores are computed once before training and co-locate samples likely to be deleted together, so a deletion request touches fewer shards than under random partitioning; retrained shards also learn from unaffected shards' soft outputs to recover utility lost to isolation. On ResNet-18/CIFAR-10, BiLSTM/IMDB, TCN/IMDB and a fully connected Fashion-MNIST network, the deletion guarantee still comes from retraining itself, and distillation is only a separately quantified utility-recovery step.

When a traffic forecasting model enforces junction flow conservation at its output, a training sample's influence on predictions no longer travels only through the loss but also through the constraint projection. Classical influence functions assume unconstrained learning and cannot separate perturbations the physics keeps from those the projection removes. This work computes influence inside the feasible set, ranks station sensitivity on hourly PeMS District 3 data covering 318 freeway links, and shows that withholding the ten highest-ranked stations raises the constrained model's MAE by 44.2%.

When a traffic forecasting model enforces junction flow conservation at its output, a training sample's influence on predictions no longer travels only through the loss but also through the constraint projection. Classical influence functions assume unconstrained learning and cannot separate perturbations the physics keeps from those the projection removes. This work computes influence inside the feasible set, ranks station sensitivity on hourly PeMS District 3 data covering 318 freeway links, and shows that withholding the ten highest-ranked stations raises the constrained model's MAE by 44.2%.