Keywords: Deep Learning, Tempered Overfitting, Generalization
TL;DR: We prove that fully connected neural networks with quantized weights exhibit tempered overfitting when using both the smallest interpolating NN and a random interpolating NN.
Abstract: 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.
Primary Area: Learning theory
Submission Number: 20613
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