Generalized Kernel Inducing Points by Duality Gap for Dataset Distillation

Reducing the amount of training data while preserving model performance remains a fundamental challenge in machine learning. Dataset distillation seeks to generate synthetic instances that encapsulate the essential information of the original data [31]. This synthetic approach often proves more flexible and can potentially achieve greater data reduction than simply retaining subsets of actual instances. Such distilled datasets can also serve broader applications, for example by enabling efficient continual learning with reduced storage demands [14, 23, 3], and offering privacy safeguards through data corruption [2, 12]. Existing dataset distillation methods are essentially formulated as a bi-level optimization problem. This is because generating synthetic instances requires retraining the model with those instances as training data. Specifically, synthetic instances are created in the outer loop, and the model is trained in the inner loop, leading to high computational costs. A promising approach to avoid bi-level optimization is a method called Kernel Inducing Point (KIP) [18]. The KIP method avoids bi-level optimization by obtaining an analytical solution in its inner loop, effectively leveraging the fact that its loss function is a variant of squared loss.