Programming with a Differentiable Forth Interpreter

TL;DR

This paper introduces a differentiable Forth interpreter that allows neural networks to incorporate prior procedural knowledge, enabling learning of complex behaviors and improving reasoning tasks involving natural language understanding.

Contribution

It presents a novel end-to-end differentiable Forth interpreter that integrates program sketches with trainable behavior, facilitating gradient-based learning of procedural knowledge.

Findings

Effectively leverages prior program structure for learning complex behaviors

Achieves state-of-the-art accuracy in reasoning about natural language stories

Enables integration of program execution into neural computation graphs

Abstract

Given that in practice training data is scarce for all but a small set of problems, a core question is how to incorporate prior knowledge into a model. In this paper, we consider the case of prior procedural knowledge for neural networks, such as knowing how a program should traverse a sequence, but not what local actions should be performed at each step. To this end, we present an end-to-end differentiable interpreter for the programming language Forth which enables programmers to write program sketches with slots that can be filled with behaviour trained from program input-output data. We can optimise this behaviour directly through gradient descent techniques on user-specified objectives, and also integrate the program into any larger neural computation graph. We show empirically that our interpreter is able to effectively leverage different levels of prior program structure and learn complex behaviours such as sequence sorting and addition. When connected to outputs of an LSTM and trained jointly, our interpreter achieves state-of-the-art accuracy for end-to-end reasoning about quantities expressed in natural language stories.