Does Compression Imply Generalization? A Minimum Description Length Perspective

The paper investigates whether compression explains why over‑parameterized neural networks generalize, using the minimum description length (MDL) principle. It introduces prequential regret, a computable metric from the training trajectory, and shows that in the nearly interpolating regime it upper‑bounds the description length of the trained parameters, leading to a high‑probability generalization bound in the PAC‑MDL setting. The study also connects MDL with the algorithm‑level information bottleneck by bounding encoder‑complexity correction with MDL parameter description length, and demonstrates that prequential regret correlates strongly (Pearson > 0.9) with generalization error on CIFAR‑10 and CIFAR‑100.

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