MADIL: An MDL-based Framework for Efficient Program Synthesis in the ARC Benchmark
Sébastien Ferré
TL;DR
MADIL introduces an MDL-guided framework for inductive program synthesis tailored to ARC, emphasizing pattern-based decomposition of inputs and outputs to form compressive task models. By formalizing values, patterns, expressions, descriptions, and task models, MADIL derives a description-length objective that drives a deep-but-narrow search over model space, enabling efficient discovery of solutions on CPU. While its raw accuracy on ARC tasks trails state-of-the-art LLM-based methods, MADIL offers strong interpretability, explicit compression-driven reasoning, and notable efficiency, solving a meaningful subset of tasks with relatively modest compute. The work further extends MADIL with collections of parts, dependent patterns, and Monte Carlo Tree Search, analyzes failures and limits, and outlines avenues to broaden primitives and global reasoning for improved ARC generalization and beyond.
Abstract
Artificial Intelligence (AI) has achieved remarkable success in specialized tasks but struggles with efficient skill acquisition and generalization. The Abstraction and Reasoning Corpus (ARC) benchmark evaluates intelligence based on minimal training requirements. While Large Language Models (LLMs) have recently improved ARC performance, they rely on extensive pre-training and high computational costs. We introduce MADIL (MDL-based AI), a novel approach leveraging the Minimum Description Length (MDL) principle for efficient inductive learning. MADIL performs pattern-based decomposition, enabling structured generalization. While its performance (7% at ArcPrize 2024) remains below LLM-based methods, it offers greater efficiency and interpretability. This paper details MADIL's methodology, its application to ARC, and experimental evaluations.