Paper ID: 2410.19092

Provable Tempered Overfitting of Minimal Nets and Typical Nets

Itamar Harel, William M. Hoza, Gal Vardi, Itay Evron, Nathan Srebro, Daniel Soudry

We study the overfitting behavior of fully connected deep Neural Networks (NNs) with binary weights fitted to perfectly classify a noisy training set. We consider interpolation using both the smallest NN (having the minimal number of weights) and a random interpolating NN. For both learning rules, we prove overfitting is tempered. Our analysis rests on a new bound on the size of a threshold circuit consistent with a partial function. To the best of our knowledge, ours are the first theoretical results on benign or tempered overfitting that: (1) apply to deep NNs, and (2) do not require a very high or very low input dimension.

Submitted: Oct 24, 2024