Characterising the Inductive Biases of Neural Networks on Boolean Data

Chris Mingard, Lukas Seier, Niclas Alexander Göring, Andrei-Vlad Badelita, Charles London, Ard A. Louis

Keywords: discrete neural networks, Boolean functions, generalisation

Abstract: Deep neural networks are renowned for their ability to generalise well across diverse tasks, even when heavily overparameterized. Existing works offer only partial explanations (for example, the NTK-based task-model alignment explanation neglects feature learning). Here, we provide an end-to-end, analytically tractable case study that links a network’s inductive prior, its training dynamics including feature learning, and its eventual generalisation. Specifically, we exploit the one-to-one correspondence between depth-2 discrete fully connected networks and disjunctive normal form (DNF) formulas by training on Boolean functions. Under a Monte Carlo learning algorithm, our model exhibits predictable training dynamics and the emergence of interpretable features. This framework allows us to trace, in detail, how inductive bias and feature formation drive generalisation.

Primary Area: learning theory

Submission Number: 1097