A Discrepancy-Based Perspective on Dataset Condensation

Given a dataset of finitely many elements $\mathcal{T} = \{\mathbf{x}_i\}_{i = 1}^N$, the goal of dataset condensation (DC) is to construct a synthetic dataset $\mathcal{S} = \{\tilde{\mathbf{x}}_j\}_{j = 1}^M$ which is significantly smaller ($M \ll N$) such that a model trained from scratch on $\mathcal{S}$ achieves comparable or even superior generalization performance to a model trained on $\mathcal{T}$. Recent advances in DC reveal a close connection to the problem of approximating the data distribution represented by $\mathcal{T}$ with a reduced set of points. In this work, we present a unified framework that encompasses existing DC methods and extend the task-specific notion of DC to a more general and formal definition using notions of discrepancy, which quantify the distance between probability distribution in different regimes. Our framework broadens the objective of DC beyond generalization, accommodating additional objectives such as robustness, privacy, and other desirable properties.