# Program Synthesis using Inductive Logic Programming for the Abstraction and Reasoning Corpus

arXiv: https://arxiv.org/abs/2405.06399 · HTML: https://mlsanity.com/paper/2405.06399/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 46 references that are in the map.
- First posted on arXiv 10 May 2024.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 22 of 22)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [Evaluating Large Language Models: A Comprehensive Survey](https://mlsanity.com/paper/2310.19736/) (2023)
- [Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solve](https://mlsanity.com/paper/2309.13638/) (2023)
- [OoD-Bench: Quantifying and Understanding Two Dimensions of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.03721/) (2021)
- [LLMs and the Abstraction and Reasoning Corpus: Successes, Failures, and the Importance of Object-based Representations](https://mlsanity.com/paper/2305.18354/) (2023)
- [Comparing Humans, GPT-4, and GPT-4V On Abstraction and Reasoning Tasks](https://mlsanity.com/paper/2311.09247/) (2023)
- [Inductive logic programming at 30](https://mlsanity.com/paper/2102.10556/) (2021)
- [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)
- [Graphs, Constraints, and Search for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2210.09880/) (2022)
- [Reasoning Abilities of Large Language Models: In-Depth Analysis on the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2403.11793/) (2024)
- [Neural-guided, Bidirectional Program Search for Abstraction and Reasoning](https://mlsanity.com/paper/2110.11536/) (2021)
- [CodeIt: Self-Improving Language Models with Prioritized Hindsight Replay](https://mlsanity.com/paper/2402.04858/) (2024)
- [Fifty Years of Prolog and Beyond](https://mlsanity.com/paper/2201.10816/) (2022)
- [Assessing GPT4-V on Structured Reasoning Tasks](https://mlsanity.com/paper/2312.11524/) (2023)
- [Neural networks for abstraction and reasoning: Towards broad generalization in machines](https://mlsanity.com/paper/2402.03507/) (2024)
- [Generalized Planning for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2401.07426/) (2024)
- [A Divide-Align-Conquer Strategy for Program Synthesis](https://mlsanity.com/paper/2301.03094/) (2023)

## Built on by (most cited first, 4 of 4)

- [Engineering Systems for Data Analysis Using Interactive Structured Inductive Programming](https://mlsanity.com/paper/2503.14488/) (2025)
- [Vector Symbolic Algebras for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2511.08747/) (2025)
- [System 2 Reasoning for Human-AI Alignment: Generality and Adaptivity via ARC-AGI](https://mlsanity.com/paper/2410.07866/) (2024)
- [Exactness at Inference: A Representational Criterion for Out-of-Distribution Generalization](https://mlsanity.com/paper/2609.24942/) (2026)

## Abstract (arXiv)

The Abstraction and Reasoning Corpus (ARC) is a general artificial intelligence benchmark that is currently unsolvable by any Machine Learning method, including Large Language Models (LLMs). It demands strong generalization and reasoning capabilities which are known to be weaknesses of Neural Network based systems. In this work, we propose a Program Synthesis system that uses Inductive Logic Programming (ILP), a branch of Symbolic AI, to solve ARC. We have manually defined a simple Domain Specific Language (DSL) that corresponds to a small set of object-centric abstractions relevant to ARC. This is the Background Knowledge used by ILP to create Logic Programs that provide reasoning capabilities to our system. The full system is capable of generalize to unseen tasks, since ILP can create Logic Program(s) from few examples, in the case of ARC: pairs of Input-Output grids examples for each task. These Logic Programs are able to generate Objects present in the Output grid and the combination of these can form a complete program that transforms an Input grid into an Output grid. We randomly chose some tasks from ARC that dont require more than the small number of the Object primitives we implemented and show that given only these, our system can solve tasks that require each, such different reasoning.