# Graphs, Constraints, and Search for the Abstraction and Reasoning Corpus

arXiv: https://arxiv.org/abs/2210.09880 · HTML: https://mlsanity.com/paper/2210.09880/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 28 references that are in the map.
- First posted on arXiv 18 Oct 2022.

## Builds on (most cited first, 6 of 6)

- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [Communicating Natural Programs to Humans and Machines](https://mlsanity.com/paper/2106.07824/) (2021)
- [Fast and flexible: Human program induction in abstract reasoning tasks](https://mlsanity.com/paper/2103.05823/) (2021)
- [Neural-guided, Bidirectional Program Search for Abstraction and Reasoning](https://mlsanity.com/paper/2110.11536/) (2021)
- [First Steps of an Approach to the ARC Challenge based on Descriptive Grid Models and the Minimum Description Length Principle](https://mlsanity.com/paper/2112.00848/) (2021)
- [Neural Abstract Reasoner](https://mlsanity.com/paper/2011.09860/) (2020)

## Built on by (most cited first, 30 of 32)

- [Large Language Models as General Pattern Machines](https://mlsanity.com/paper/2307.04721/) (2023)
- [Hypothesis Search: Inductive Reasoning with Language Models](https://mlsanity.com/paper/2309.05660/) (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)
- [Reasoning Abilities of Large Language Models: In-Depth Analysis on the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2403.11793/) (2024)
- [Abstract Visual Reasoning Enabled by Language](https://mlsanity.com/paper/2303.04091/) (2023)
- [HYSYNTH: Context-Free LLM Approximation for Guiding Program Synthesis](https://mlsanity.com/paper/2405.15880/) (2024)
- [Neural networks for abstraction and reasoning: Towards broad generalization in machines](https://mlsanity.com/paper/2402.03507/) (2024)
- [Unraveling the ARC Puzzle: Mimicking Human Solutions with Object-Centric Decision Transformer](https://mlsanity.com/paper/2306.08204/) (2023)
- [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)
- [Generalized Planning for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2401.07426/) (2024)
- [Tackling the Abstraction and Reasoning Corpus with Vision Transformers: the Importance of 2D Representation, Positions, and Objects](https://mlsanity.com/paper/2410.06405/) (2024)
- [Solving ARC visual analogies with neural embeddings and vector arithmetic: A generalized method](https://mlsanity.com/paper/2311.08083/) (2023)
- [ConceptSearch: Towards Efficient Program Search Using LLMs for Abstraction and Reasoning Corpus (ARC)](https://mlsanity.com/paper/2412.07322/) (2024)
- [Tackling the Abstraction and Reasoning Corpus (ARC) with Object-centric Models and the MDL Principle](https://mlsanity.com/paper/2311.00545/) (2023)
- [ARCLE: The Abstraction and Reasoning Corpus Learning Environment for Reinforcement Learning](https://mlsanity.com/paper/2407.20806/) (2024)
- [Creativity in AI: Progresses and Challenges](https://mlsanity.com/paper/2410.17218/) (2024)
- [Relational decomposition for program synthesis](https://mlsanity.com/paper/2408.12212/) (2024)
- [Speak It Out: Solving Symbol-Related Problems with Symbol-to-Language Conversion for Language Models](https://mlsanity.com/paper/2401.11725/) (2024)
- [Program Synthesis using Inductive Logic Programming for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2405.06399/) (2024)
- [Language Models, Graph Searching, and Supervision Adulteration: When More Supervision is Less and How to Make More More](https://mlsanity.com/paper/2503.10542/) (2025)
- [One Step Forward and K Steps Back: Better Reasoning with Denoising Recursion Models](https://mlsanity.com/paper/2604.18839/) (2026)
- [Abductive Symbolic Solver on Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2411.18158/) (2024)
- [NSA: Neuro-symbolic ARC Challenge](https://mlsanity.com/paper/2501.04424/) (2025)
- [From Reasoning to Generalization: Knowledge-Augmented LLMs for ARC Benchmark](https://mlsanity.com/paper/2505.17482/) (2025)
- [Intelligence Analysis of Language Models](https://mlsanity.com/paper/2407.18968/) (2024)
- [Vector Symbolic Algebras for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2511.08747/) (2025)
- [TraceViT: Grounded Trace Supervision for Visual Abstract Reasoning](https://mlsanity.com/paper/2607.29586/) (2026)
- [System 2 Reasoning for Human-AI Alignment: Generality and Adaptivity via ARC-AGI](https://mlsanity.com/paper/2410.07866/) (2024)
- [From Global to Factor-Wise Expert Composition in Discrete Diffusion Models](https://mlsanity.com/paper/2607.11758/) (2026)

## Abstract (arXiv)

The Abstraction and Reasoning Corpus (ARC) aims at benchmarking the performance of general artificial intelligence algorithms. The ARC's focus on broad generalization and few-shot learning has made it difficult to solve using pure machine learning. A more promising approach has been to perform program synthesis within an appropriately designed Domain Specific Language (DSL). However, these too have seen limited success. We propose Abstract Reasoning with Graph Abstractions (ARGA), a new object-centric framework that first represents images using graphs and then performs a search for a correct program in a DSL that is based on the abstracted graph space. The complexity of this combinatorial search is tamed through the use of constraint acquisition, state hashing, and Tabu search. An extensive set of experiments demonstrates the promise of ARGA in tackling some of the complicated object-centric tasks of the ARC rather efficiently, producing programs that are correct and easy to understand.