Abstract
A number of machine learning models have been proposed with the goal of achieving systematic generalization: the ability to reason about new situations by combining aspects of previous experiences. These models leverage compositional architectures which aim to learn specialized modules dedicated to structures in a task that can be composed to solve novel problems with similar structures. While the compositionality of these architectures is guaranteed by design, the modules specializing is not. Here we theoretically study the ability of network modules to specialize to useful structures in a dataset and achieve systematic generalization. To this end we introduce a minimal space of datasets motivated by practical systematic generalization benchmarks. From this space of datasets we present a mathematical definition of systematicity and study the learning dynamics of linear neural modules when solving components of the task. Our results shed light on the difficulty of module specialization, what is required for modules to successfully specialize, and the necessity of modular architectures to achieve systematicity. Finally, we confirm that the theoretical results in our tractable setting generalize to more complex datasets and non-linear architectures.
Devon Jarvis
Associate Lecturer
I am a PhD candidate and Associate Lecturer at Wits interested in studying systematic generalization and the emergence of modularity in the brain and machines.
Richard Klein
PRIME Lab Director
I am an Associate Professor in the School of Computer Science and Applied Mathematics at the University of the Witwatersrand in Johannesburg, and a co-PI of the PRIME lab.
Benjamin Rosman
Lab Director
I am a Professor in the School of Computer Science and Applied Mathematics at the University of the Witwatersrand in Johannesburg. I work in robotics, artificial intelligence, decision theory and machine learning.