Program Synthesis using Inductive Logic Programming for the Abstraction and Reasoning Corpus

TL;DR

This paper introduces a symbolic program synthesis approach using Inductive Logic Programming to solve the challenging Abstraction and Reasoning Corpus benchmark, demonstrating strong generalization from few examples.

Contribution

It presents a novel ILP-based system with a custom DSL that can generalize to unseen ARC tasks by generating logic programs from minimal input-output examples.

Findings

Successfully solves ARC tasks requiring object reasoning

Generalizes to unseen tasks with minimal examples

Uses a symbolic approach to overcome neural network limitations

Abstract

The Abstraction and Reasoning Corpus (ARC) is a general artificial intelligence benchmark that is currently unsolvable by any Machine Learning method, including Large Language Models (LLMs). It demands strong generalization and reasoning capabilities which are known to be weaknesses of Neural Network based systems. In this work, we propose a Program Synthesis system that uses Inductive Logic Programming (ILP), a branch of Symbolic AI, to solve ARC. We have manually defined a simple Domain Specific Language (DSL) that corresponds to a small set of object-centric abstractions relevant to ARC. This is the Background Knowledge used by ILP to create Logic Programs that provide reasoning capabilities to our system. The full system is capable of generalize to unseen tasks, since ILP can create Logic Program(s) from few examples, in the case of ARC: pairs of Input-Output grids examples for each task. These Logic Programs are able to generate Objects present in the Output grid and the combination of these can form a complete program that transforms an Input grid into an Output grid. We randomly chose some tasks from ARC that dont require more than the small number of the Object primitives we implemented and show that given only these, our system can solve tasks that require each, such different reasoning.