UC Irvine

A deployed machine learning system must be affordable to train, must treat demographic groups equitably, and must be able to forget data on request. These demands are studied by separate literatures, evaluated by disjoint metrics, and addressed by methods that share almost no machinery. This dissertation argues that the separation is an artifact of how the problems have been posed. Efficiency, group fairness, and the right to be forgotten are three demands on one object, the training dynamics of a learning system, meaning the gradients a model sees and the parameter updates it retains, and all three can be met by intervening on that object rather than by redesigning architectures. The claim is developed at three control points. At the data, a small synthetic dataset is optimized so that models trained on it follow the same optimization trajectory as models trained on a large one. For graph learning this jointly condenses the node count and the feature dimension, cutting storage by over 99% while retaining up to 98.5% of the original accuracy. Because gradient matching encodes whatever property the target trajectory possesses, redirecting it from accuracy to equity yields data on which ordinary training produces fair models that transfer across architectures, including to tree ensembles no differentiable regularizer can reach. At the objective, in-process fairness methods are shown to reduce to a single choice of distance between group-conditional distributions. Two failure modes yield three requirements on that measure, namely a tight bound on the quantity of interest, robustness to scale, and applicability to arbitrary distributions, which the Cauchy-Schwarz divergence satisfies and the standard alternatives do not. At the parameters, a negative result: machine unlearning destroys installed fairness. A fairly trained model meeting a routine deletion request sees its demographic parity gap rise nineteen-fold while accuracy falls five percent, undetected by standard evaluation. The cause is a demographically one-sided edit to the sum of per-batch updates; the remedy is a matched, reversed-attribute edit, restoring fairness without retraining and up to 318x faster. At foundation-model scale the same principle confines the edit to low-rank adapters trained on negative examples alone. One lever, applied at three points, serves three demands ordinarily pursued in isolation.