Algorithm Development in Neural Networks: Insights from the Streaming Parity Task

TL;DR

This paper investigates how recurrent neural networks develop algorithms capable of infinite generalization on the streaming parity task, revealing a phase transition and an implicit automaton construction that explains this phenomenon.

Contribution

It provides a theoretical framework for understanding how neural networks learn algorithms that enable infinite generalization from finite training data.

Findings

RNNs exhibit a phase transition to perfect infinite generalization.

An implicit automaton is constructed through representational merger.

The study offers a new perspective on neural network generalization mechanisms.

Abstract

Even when massively overparameterized, deep neural networks show a remarkable ability to generalize. Research on this phenomenon has focused on generalization within distribution, via smooth interpolation. Yet in some settings neural networks also learn to extrapolate to data far beyond the bounds of the original training set, sometimes even allowing for infinite generalization, implying that an algorithm capable of solving the task has been learned. Here we undertake a case study of the learning dynamics of recurrent neural networks (RNNs) trained on the streaming parity task in order to develop an effective theory of algorithm development. The streaming parity task is a simple but nonlinear task defined on sequences up to arbitrary length. We show that, with sufficient finite training experience, RNNs exhibit a phase transition to perfect infinite generalization. Using an effective theory for the representational dynamics, we find an implicit representational merger effect which can be interpreted as the construction of a finite automaton that reproduces the task. Overall, our results disclose one mechanism by which neural networks can generalize infinitely from finite training experience.