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\nFran\\c{c}ois Chollet as a tool to measure broad intelligence in both humans and\nmachines. It is very challenging, and the best approach in a Kaggle competition\ncould only solve 20% of the tasks, relying on brute-force search for chains of\nhand-crafted transformations. In this paper, we present the first steps\nexploring an approach based on descriptive grid models and the Minimum\nDescription Length (MDL) principle. The grid models describe the contents of a\ngrid, and support both parsing grids and generating grids. The MDL principle is\nused to guide the search for good models, i.e. models that compress the grids\nthe most. We report on our progress over a year, improving on the general\napproach and the models. Out of the 400 training tasks, our performance\nincreased from 5 to 29 solved tasks, only using 30s computation time per task.\nOur approach not only predicts the output grids, but also outputs an\nintelligible model and explanations for how the model was incrementally built.\n