# Learning to Combine Per-Example Solutions for Neural Program Synthesis

arXiv: https://arxiv.org/abs/2106.07175 · HTML: https://mlsanity.com/paper/2106.07175/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 14 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [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)
- [Neuro-Symbolic Program Synthesis](https://mlsanity.com/paper/1611.01855/) (2016)
- [Leveraging Grammar and Reinforcement Learning for Neural Program Synthesis](https://mlsanity.com/paper/1805.04276/) (2018)
- [Learning to Infer Program Sketches](https://mlsanity.com/paper/1902.06349/) (2019)
- [Neural-Guided Deductive Search for Real-Time Program Synthesis from Examples](https://mlsanity.com/paper/1804.01186/) (2018)
- [Synthesize, Execute and Debug: Learning to Repair for Neural Program Synthesis](https://mlsanity.com/paper/2007.08095/) (2020)
- [BUSTLE: Bottom-Up Program Synthesis Through Learning-Guided Exploration](https://mlsanity.com/paper/2007.14381/) (2020)
- [Automatic Program Synthesis of Long Programs with a Learned Garbage Collector](https://mlsanity.com/paper/1809.04682/) (2018)
- [Neural Program Meta-Induction](https://mlsanity.com/paper/1710.04157/) (2017)
- [Just-in-Time Learning for Bottom-Up Enumerative Synthesis](https://mlsanity.com/paper/2010.08663/) (2020)
- [Learning to Represent Programs with Property Signatures](https://mlsanity.com/paper/2002.09030/) (2020)
- [FrAngel: Component-Based Synthesis with Control Structures](https://mlsanity.com/paper/1811.05175/) (2018)
- [Synthesis through Unification](https://mlsanity.com/paper/1505.05868/) (2015)

## Built on by (most cited first, 8 of 8)

- [ExeDec: Execution Decomposition for Compositional Generalization in Neural Program Synthesis](https://mlsanity.com/paper/2307.13883/) (2023)
- [Static Prediction of Runtime Errors by Learning to Execute Programs with External Resource Descriptions](https://mlsanity.com/paper/2203.03771/) (2022)
- [Compositional Generalization and Decomposition in Neural Program Synthesis](https://mlsanity.com/paper/2204.03758/) (2022)
- [LambdaBeam: Neural Program Search with Higher-Order Functions and Lambdas](https://mlsanity.com/paper/2306.02049/) (2023)
- [AbstractBeam: Enhancing Bottom-Up Program Synthesis using Library Learning](https://mlsanity.com/paper/2405.17514/) (2024)
- [Shedding Light in Task Decomposition in Program Synthesis: The Driving Force of the Synthesizer Model](https://mlsanity.com/paper/2503.08738/) (2025)
- [Neuro-Symbolic Regex Synthesis Framework via Neural Example Splitting](https://mlsanity.com/paper/2205.11258/) (2022)
- [Searching for Better Database Queries in the Outputs of Semantic Parsers](https://mlsanity.com/paper/2210.07201/) (2022)

## Abstract (arXiv)

The goal of program synthesis from examples is to find a computer program that is consistent with a given set of input-output examples. Most learning-based approaches try to find a program that satisfies all examples at once. Our work, by contrast, considers an approach that breaks the problem into two stages: (a) find programs that satisfy only one example, and (b) leverage these per-example solutions to yield a program that satisfies all examples. We introduce the Cross Aggregator neural network module based on a multi-head attention mechanism that learns to combine the cues present in these per-example solutions to synthesize a global solution. Evaluation across programs of different lengths and under two different experimental settings reveal that when given the same time budget, our technique significantly improves the success rate over PCCoder [Zohar et. al 2018] and other ablation baselines. The code, data and trained models for our work can be found at https://github.com/shrivastavadisha/N-PEPS.