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

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.