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Training neural networks on a large dataset requires substantialcomputational costs. Dataset reduction selects or synthesizes data instancesbased on the large dataset, while minimizing the degradation in generalizationperformance from the full dataset. Existing methods utilize the neural networkduring the dataset reduction procedure, so the model parameter becomesimportant factor in preserving the performance after reduction. By dependingupon the importance of parameters, this paper introduces a new reductionobjective, coined LCMat, which Matches the Loss Curvatures of the originaldataset and reduced dataset over the model parameter space, more than theparameter point. This new objective induces a better adaptation of the reduceddataset on the perturbed parameter region than the exact point matching.Particularly, we identify the worst case of the loss curvature gap from thelocal parameter region, and we derive the implementable upper bound of suchworst-case with theoretical analyses. Our experiments on both coreset selectionand condensation benchmarks illustrate that LCMat shows better generalizationperformances than existing baselines.

Loss-Curvature Matching for Dataset Selection and Condensation