Tackling the Abstraction and Reasoning Corpus (ARC) with Object-centric Models and the MDL Principle

id:: 2311.00545
Authors:: Sébastien Ferré
Published:: 2023-11-01
arXiv:: https://arxiv.org/abs/2311.00545
PDF:: https://arxiv.org/pdf/2311.00545
DOI:: N/A
Journal Reference:: N/A
Primary Category:: cs.AI
Categories:: cs.AI
Comment:: N/A
github_url:: _

abstract

The Abstraction and Reasoning Corpus (ARC) is a challenging benchmark, introduced to foster AI research towards human-level intelligence. It is a collection of unique tasks about generating colored grids, specified by a few examples only. In contrast to the transformation-based programs of existing work, we introduce object-centric models that are in line with the natural programs produced by humans. Our models can not only perform predictions, but also provide joint descriptions for input/output pairs. The Minimum Description Length (MDL) principle is used to efficiently search the large model space. A diverse range of tasks are solved, and the learned models are similar to the natural programs. We demonstrate the generality of our approach by applying it to a different domain.

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Brief Overview

The paper tackles the Abstraction and Reasoning Corpus (ARC) challenge using object-centric models and the Minimum Description Length (MDL) principle. Unlike existing approaches that rely on program synthesis using transformations, this method focuses on models that mirror human problem-solving strategies, emphasizing object recognition and relationships. The MDL principle efficiently searches the large model space. The approach is also demonstrated on a different domain (spreadsheet column filling).

Key Points

Object-centric Models: The core innovation is the use of object-centric models, aligning with human approaches to problem-solving in ARC tasks. These models describe grids in terms of objects with properties like shape, color, and position.
Minimum Description Length (MDL) Principle: This principle is used to guide the efficient search of the model space by selecting the model that best compresses the data (training examples). It is employed at two levels: choosing the best parses of a grid and building progressively more accurate models.
Three Operational Modes: Task models can operate in three modes: predict (output given input), describe (joint description of input/output pair), and create (generate new input/output pairs).
Promising Results: The approach achieves promising results on the ARC benchmark, showing comparable performance to state-of-the-art methods while demonstrating greater efficiency and model clarity. It shows strong generalization capability.
Generalizability: The methodology demonstrates generalizability by successfully applying it to a different domain, namely the automatic filling of spreadsheet columns, showcasing its adaptability beyond the ARC task.

Notable Quotes

There are no particularly memorable quotes within the provided text, but the core idea is effectively summarized in the abstract and introduction. The MDL principle itself is stated as: “the model that best describes the data is the model that compresses them the more”.

Primary Themes

Human-Level AI: The work directly addresses the challenge of creating AI systems that exhibit human-like intelligence, specifically tackling the generalization and flexibility aspects of human cognitive abilities.
Efficient Learning: The study emphasizes efficient learning, highlighting the importance of minimizing prior knowledge and computational resources while achieving high performance on complex tasks.
Model Explainability: Object-centric models provide a more interpretable and understandable representation of the problem-solving process, making them more amenable to analysis and evaluation compared to purely procedural approaches.
Generalization and Transfer Learning: The successful application of the method to a separate domain highlights its potential for transfer learning and broad applicability beyond specialized benchmarks.