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Estimating the Generalization Error (GE) of Deep Neural Networks (DNNs) is animportant task that often relies on availability of held-out data. The abilityto better predict GE based on a single training set may yield overarching DNNdesign principles to reduce a reliance on trial-and-error, along with otherperformance assessment advantages. In search of a quantity relevant to GE, weinvestigate the Mutual Information (MI) between the input and final layerrepresentations, using the infinite-width DNN limit to bound MI. An existinginput compression-based GE bound is used to link MI and GE. To the best of ourknowledge, this represents the first empirical study of this bound. In ourattempt to empirically falsify the theoretical bound, we find that it is oftentight for best-performing models. Furthermore, it detects randomization oftraining labels in many cases, reflects test-time perturbation robustness, andworks well given only few training samples. These results are promising giventhat input compression is broadly applicable where MI can be estimated withconfidence.

Bounding generalization error with input compression: An empirical study with infinite-width networks