Learning Differentiable Programs with Admissible Neural Heuristics

TL;DR

This paper introduces a method for learning differentiable programs using neural heuristics that guide combinatorial search, resulting in interpretable classifiers with competitive accuracy.

Contribution

It presents a novel approach that relaxes program synthesis into a differentiable problem, enabling end-to-end training and improved search efficiency.

Findings

Outperforms state-of-the-art program learning methods

Discovers interpretable programmatic classifiers

Achieves competitive accuracy on sequence classification tasks

Abstract

We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program "architectures". We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. This relaxed program is differentiable and can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search. We instantiate our approach on top of the A-star algorithm and an iteratively deepened branch-and-bound search, and use these algorithms to learn programmatic classifiers in three sequence classification tasks. Our experiments show that the algorithms outperform state-of-the-art methods for program learning, and that they discover programmatic classifiers that yield natural interpretations and achieve competitive accuracy.