# Neural-guided, Bidirectional Program Search for Abstraction and Reasoning

arXiv: https://arxiv.org/abs/2110.11536 · HTML: https://mlsanity.com/paper/2110.11536/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 22 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [DeepCoder: Learning to Write Programs](https://mlsanity.com/paper/1611.01989/) (2016)
- [RobustFill: Neural Program Learning under Noisy I/O](https://mlsanity.com/paper/1703.07469/) (2017)
- [Write, Execute, Assess: Program Synthesis with a REPL](https://mlsanity.com/paper/1906.04604/) (2019)
- [Learning to Infer Program Sketches](https://mlsanity.com/paper/1902.06349/) (2019)
- [HOUDINI: Lifelong Learning as Program Synthesis](https://mlsanity.com/paper/1804.00218/) (2018)
- [Making Neural Programming Architectures Generalize via Recursion](https://mlsanity.com/paper/1704.06611/) (2017)
- [Automatic Program Synthesis of Long Programs with a Learned Garbage Collector](https://mlsanity.com/paper/1809.04682/) (2018)

## Built on by (most cited first, 23 of 23)

- [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)
- [Combining Induction and Transduction for Abstract Reasoning](https://mlsanity.com/paper/2411.02272/) (2024)
- [Graphs, Constraints, and Search for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2210.09880/) (2022)
- [Double-Ended Synthesis Planning with Goal-Constrained Bidirectional Search](https://mlsanity.com/paper/2407.06334/) (2024)
- [CodeIt: Self-Improving Language Models with Prioritized Hindsight Replay](https://mlsanity.com/paper/2402.04858/) (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)
- [Tackling the Abstraction and Reasoning Corpus with Vision Transformers: the Importance of 2D Representation, Positions, and Objects](https://mlsanity.com/paper/2410.06405/) (2024)
- [ARC-GEN: A Mimetic Procedural Benchmark Generator for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2511.00162/) (2025)
- [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)
- [Program Synthesis using Inductive Logic Programming for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2405.06399/) (2024)
- [Enhancing Analogical Reasoning in the Abstraction and Reasoning Corpus via Model-Based RL](https://mlsanity.com/paper/2408.14855/) (2024)
- [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)
- [Intelligence Analysis of Language Models](https://mlsanity.com/paper/2407.18968/) (2024)
- [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)
- [JaxARC: A High-Performance JAX-based Environment for Abstraction and Reasoning Research](https://mlsanity.com/paper/2601.17564/) (2026)
- [From Global to Factor-Wise Expert Composition in Discrete Diffusion Models](https://mlsanity.com/paper/2607.11758/) (2026)
- [A Multi-Stage Rule-Chaining Framework for Compositional and Interpretable Cognitive Reasoning](https://mlsanity.com/paper/2609.10654/) (2026)
- [The Ups and Downs of Backprop Weights](https://mlsanity.com/paper/2609.22554/) (2026)

## Abstract (arXiv)

One of the challenges facing artificial intelligence research today is designing systems capable of utilizing systematic reasoning to generalize to new tasks. The Abstraction and Reasoning Corpus (ARC) measures such a capability through a set of visual reasoning tasks. In this paper we report incremental progress on ARC and lay the foundations for two approaches to abstraction and reasoning not based in brute-force search. We first apply an existing program synthesis system called DreamCoder to create symbolic abstractions out of tasks solved so far, and show how it enables solving of progressively more challenging ARC tasks. Second, we design a reasoning algorithm motivated by the way humans approach ARC. Our algorithm constructs a search graph and reasons over this graph structure to discover task solutions. More specifically, we extend existing execution-guided program synthesis approaches with deductive reasoning based on function inverse semantics to enable a neural-guided bidirectional search algorithm. We demonstrate the effectiveness of the algorithm on three domains: ARC, 24-Game tasks, and a 'double-and-add' arithmetic puzzle.