First Steps of an Approach to the ARC Challenge based on Descriptive Grid Models and the Minimum Description Length Principle

TL;DR

This paper explores an approach to the ARC challenge using descriptive grid models guided by the Minimum Description Length principle, achieving improved task-solving performance and providing interpretable models.

Contribution

It introduces a novel method combining grid models and MDL for ARC, demonstrating progress in solving more tasks with explainable models.

Findings

Solved 29 out of 400 training tasks

Improved from 5 to 29 tasks solved over a year

Models are interpretable and explain their construction process

Abstract

The Abstraction and Reasoning Corpus (ARC) was recently introduced by Fran\c{c}ois Chollet as a tool to measure broad intelligence in both humans and machines. It is very challenging, and the best approach in a Kaggle competition could only solve 20% of the tasks, relying on brute-force search for chains of hand-crafted transformations. In this paper, we present the first steps exploring an approach based on descriptive grid models and the Minimum Description Length (MDL) principle. The grid models describe the contents of a grid, and support both parsing grids and generating grids. The MDL principle is used to guide the search for good models, i.e. models that compress the grids the most. We report on our progress over a year, improving on the general approach and the models. Out of the 400 training tasks, our performance increased from 5 to 29 solved tasks, only using 30s computation time per task. Our approach not only predicts the output grids, but also outputs an intelligible model and explanations for how the model was incrementally built.