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

arXiv: https://arxiv.org/abs/2112.00848 · HTML: https://mlsanity.com/paper/2112.00848/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 13 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [Minimum Description Length Revisited](https://mlsanity.com/paper/1908.08484/) (2019)
- [Interpretable multiclass classification by MDL-based rule lists](https://mlsanity.com/paper/1905.00328/) (2019)
- [The Long and the Short of It: Summarising Event Sequences with Serial Episodes](https://mlsanity.com/paper/1902.02834/) (2019)

## Built on by (most cited first, 13 of 13)

- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [Large Language Models as General Pattern Machines](https://mlsanity.com/paper/2307.04721/) (2023)
- [The ConceptARC Benchmark: Evaluating Understanding and Generalization in the ARC Domain](https://mlsanity.com/paper/2305.07141/) (2023)
- [LLMs and the Abstraction and Reasoning Corpus: Successes, Failures, and the Importance of Object-based Representations](https://mlsanity.com/paper/2305.18354/) (2023)
- [On the Diversity of Synthetic Data and its Impact on Training Large Language Models](https://mlsanity.com/paper/2410.15226/) (2024)
- [Graphs, Constraints, and Search for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2210.09880/) (2022)
- [CodeIt: Self-Improving Language Models with Prioritized Hindsight Replay](https://mlsanity.com/paper/2402.04858/) (2024)
- [Large Language Model (LLM) as a System of Multiple Expert Agents: An Approach to solve the Abstraction and Reasoning Corpus (ARC) Challenge](https://mlsanity.com/paper/2310.05146/) (2023)
- [Tackling the Abstraction and Reasoning Corpus with Vision Transformers: the Importance of 2D Representation, Positions, and Objects](https://mlsanity.com/paper/2410.06405/) (2024)
- [A Neurodiversity-Inspired Solver for the Abstraction & Reasoning Corpus (ARC) Using Visual Imagery and Program Synthesis](https://mlsanity.com/paper/2302.09425/) (2023)
- [A Survey of LLM × DATA](https://mlsanity.com/paper/2505.18458/) (2025)
- [NSA: Neuro-symbolic ARC Challenge](https://mlsanity.com/paper/2501.04424/) (2025)
- [Modality-Driven Search with Holistic Trace Judging for ARC-AGI-2](https://mlsanity.com/paper/2606.31543/) (2026)

## Abstract (arXiv)

The Abstraction and Reasoning Corpus (ARC) was recently introduced by Franccois 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.