# Neuro-Symbolic Program Synthesis

arXiv: https://arxiv.org/abs/1611.01855 · HTML: https://mlsanity.com/paper/1611.01855/

## Key facts

- Cited by 84 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2016.

## Built on by (most cited first, 30 of 84)

- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [Large Language Models for Software Engineering: A Systematic Literature Review](https://mlsanity.com/paper/2308.10620/) (2023)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Learning Performance-Improving Code Edits](https://mlsanity.com/paper/2302.07867/) (2023)
- [Learning to Synthesize Programs as Interpretable and Generalizable Policies](https://mlsanity.com/paper/2108.13643/) (2021)
- [CodeChain: Towards Modular Code Generation Through Chain of Self-revisions with Representative Sub-modules](https://mlsanity.com/paper/2310.08992/) (2023)
- [Neuro-Symbolic Artificial Intelligence: Current Trends](https://mlsanity.com/paper/2105.05330/) (2021)
- [LILO: Learning Interpretable Libraries by Compressing and Documenting Code](https://mlsanity.com/paper/2310.19791/) (2023)
- [Leveraging Language to Learn Program Abstractions and Search Heuristics](https://mlsanity.com/paper/2106.11053/) (2021)
- [SpreadsheetCoder: Formula Prediction from Semi-structured Context](https://mlsanity.com/paper/2106.15339/) (2021)
- [Communicating Natural Programs to Humans and Machines](https://mlsanity.com/paper/2106.07824/) (2021)
- [Latent Execution for Neural Program Synthesis](https://mlsanity.com/paper/2107.00101/) (2021)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Natural Language Generation and Understanding of Big Code for AI-Assisted Programming: A Review](https://mlsanity.com/paper/2307.02503/) (2023)
- [Few-Shot Bayesian Imitation Learning with Logical Program Policies](https://mlsanity.com/paper/1904.06317/) (2019)
- [TikZero: Zero-Shot Text-Guided Graphics Program Synthesis](https://mlsanity.com/paper/2503.11509/) (2025)
- [Measuring and Improving BERT's Mathematical Abilities by Predicting the Order of Reasoning](https://mlsanity.com/paper/2106.03921/) (2021)
- [Learning to Complete Code with Sketches](https://mlsanity.com/paper/2106.10158/) (2021)
- [CodeIt: Self-Improving Language Models with Prioritized Hindsight Replay](https://mlsanity.com/paper/2402.04858/) (2024)
- [PyGlove: Symbolic Programming for Automated Machine Learning](https://mlsanity.com/paper/2101.08809/) (2021)
- [CrossBeam: Learning to Search in Bottom-Up Program Synthesis](https://mlsanity.com/paper/2203.10452/) (2022)
- [Pix2Code: Learning to Compose Neural Visual Concepts as Programs](https://mlsanity.com/paper/2402.08280/) (2024)
- [Neural Circuit Synthesis from Specification Patterns](https://mlsanity.com/paper/2107.11864/) (2021)
- [ExeDec: Execution Decomposition for Compositional Generalization in Neural Program Synthesis](https://mlsanity.com/paper/2307.13883/) (2023)
- [LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoning](https://mlsanity.com/paper/2309.13556/) (2023)
- [Neural Termination Analysis](https://mlsanity.com/paper/2102.03824/) (2021)
- [EZNAS: Evolving Zero Cost Proxies For Neural Architecture Scoring](https://mlsanity.com/paper/2209.07413/) (2022)
- [Codex Hacks HackerRank: Memorization Issues and a Framework for Code Synthesis Evaluation](https://mlsanity.com/paper/2212.02684/) (2022)
- [Neural Program Generation Modulo Static Analysis](https://mlsanity.com/paper/2111.01633/) (2021)

## Abstract (arXiv)

Recent years have seen the proposal of a number of neural architectures for the problem of Program Induction. Given a set of input-output examples, these architectures are able to learn mappings that generalize to new test inputs. While achieving impressive results, these approaches have a number of important limitations: (a) they are computationally expensive and hard to train, (b) a model has to be trained for each task (program) separately, and (c) it is hard to interpret or verify the correctness of the learnt mapping (as it is defined by a neural network). In this paper, we propose a novel technique, Neuro-Symbolic Program Synthesis, to overcome the above-mentioned problems. Once trained, our approach can automatically construct computer programs in a domain-specific language that are consistent with a set of input-output examples provided at test time. Our method is based on two novel neural modules. The first module, called the cross correlation I/O network, given a set of input-output examples, produces a continuous representation of the set of I/O examples. The second module, the Recursive-Reverse-Recursive Neural Network (R3NN), given the continuous representation of the examples, synthesizes a program by incrementally expanding partial programs. We demonstrate the effectiveness of our approach by applying it to the rich and complex domain of regular expression based string transformations. Experiments show that the R3NN model is not only able to construct programs from new input-output examples, but it is also able to construct new programs for tasks that it had never observed before during training.