  Dataset distillation (DD) aims to synthesize a small dataset whose test
performance is comparable to a full dataset using the same model.
State-of-the-art (SoTA) methods optimize synthetic datasets primarily by
matching heuristic indicators extracted from two networks: one from real data
and one from synthetic data (see Fig.1, Left), such as gradients and training
trajectories. DD is essentially a compression problem that emphasizes
maximizing the preservation of information contained in the data. We argue that
well-defined metrics which measure the amount of shared information between
variables in information theory are necessary for success measurement but are
never considered by previous works. Thus, we introduce mutual information (MI)
as the metric to quantify the shared information between the synthetic and the
real datasets, and devise MIM4DD numerically maximizing the MI via a newly
designed optimizable objective within a contrastive learning framework to
update the synthetic dataset. Specifically, we designate the samples in
different datasets that share the same labels as positive pairs and vice versa
negative pairs. Then we respectively pull and push those samples in positive
and negative pairs into contrastive space via minimizing NCE loss. As a result,
the targeted MI can be transformed into a lower bound represented by feature
maps of samples, which is numerically feasible. Experiment results show that
MIM4DD can be implemented as an add-on module to existing SoTA DD methods.
