  This paper presents FreD, a novel parameterization method for dataset
distillation, which utilizes the frequency domain to distill a small-sized
synthetic dataset from a large-sized original dataset. Unlike conventional
approaches that focus on the spatial domain, FreD employs frequency-based
transforms to optimize the frequency representations of each data instance. By
leveraging the concentration of spatial domain information on specific
frequency components, FreD intelligently selects a subset of frequency
dimensions for optimization, leading to a significant reduction in the required
budget for synthesizing an instance. Through the selection of frequency
dimensions based on the explained variance, FreD demonstrates both theoretical
and empirical evidence of its ability to operate efficiently within a limited
budget, while better preserving the information of the original dataset
compared to conventional parameterization methods. Furthermore, based on the
orthogonal compatibility of FreD with existing methods, we confirm that FreD
consistently improves the performances of existing distillation methods over
the evaluation scenarios with different benchmark datasets. We release the code
at https://github.com/sdh0818/FreD.
