On the Inductive Bias of Neural Networks for Learning Read-once DNFs

Ido Bronstein, Alon Brutzkus, Amir Globerson

Research output: Contribution to journalConference articlepeer-review


Learning functions over Boolean variables is a fundamental problem in machine learning. But not much is known about learning such functions using neural networks. Here we focus on learning read-once disjunctive normal forms (DNFs) under the uniform distribution with a convex neural network and gradient methods. We first observe empirically that gradient methods converge to compact solutions with neurons that are aligned with the terms of the DNF. This is despite the fact that there are many zero training error networks that do not have this property. Thus, the learning process has a clear inductive bias towards such logical formulas. Following recent results which connect the inductive bias of gradient flow (GF) to Karush-Kuhn-Tucker (KKT) points of minimum norm problems, we study these KKT points in our setting. We prove that zero training error solutions that memorize training points are not KKT points and therefore GF cannot converge to them. On the other hand, we prove that globally optimal KKT points correspond exactly to networks that are aligned with the DNF terms. These results suggest a strong connection between the inductive bias of GF and solutions that align with the DNF. We conclude with extensive experiments which verify our findings.

Original languageEnglish
Pages (from-to)255-265
Number of pages11
JournalProceedings of Machine Learning Research
StatePublished - 2022
Event38th Conference on Uncertainty in Artificial Intelligence, UAI 2022 - Eindhoven, Netherlands
Duration: 1 Aug 20225 Aug 2022


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