  Given a real-world dataset, data condensation (DC) aims to synthesize a small
synthetic dataset that captures the knowledge of a natural dataset while being
usable for training models with comparable accuracy. Recent works propose to
enhance DC with data parameterization, which condenses data into very compact
parameterized data containers instead of images. The intuition behind data
parameterization is to encode shared features of images to avoid additional
storage costs. In this paper, we recognize that images share common features in
a hierarchical way due to the inherent hierarchical structure of the
classification system, which is overlooked by current data parameterization
methods. To better align DC with this hierarchical nature and encourage more
efficient information sharing inside data containers, we propose a novel data
parameterization architecture, Hierarchical Memory Network (HMN). HMN stores
condensed data in a three-tier structure, representing the dataset-level,
class-level, and instance-level features. Another helpful property of the
hierarchical architecture is that HMN naturally ensures good independence among
images despite achieving information sharing. This enables instance-level
pruning for HMN to reduce redundant information, thereby further minimizing
redundancy and enhancing performance. We evaluate HMN on five public datasets
and show that our proposed method outperforms all baselines.
