# Neural-Symbolic Recursive Machine for Systematic Generalization

arXiv: https://arxiv.org/abs/2210.01603 · HTML: https://mlsanity.com/paper/2210.01603/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 77 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [MineDojo: Building Open-Ended Embodied Agents with Internet-Scale Knowledge](https://mlsanity.com/paper/2206.08853/) (2022)
- [The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences From Natural Supervision](https://mlsanity.com/paper/1904.12584/) (2019)
- [SCAN: Learning to Classify Images without Labels](https://mlsanity.com/paper/2005.12320/) (2020)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Measuring Compositional Generalization: A Comprehensive Method on Realistic Data](https://mlsanity.com/paper/1912.09713/) (2019)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [COGS: A Compositional Generalization Challenge Based on Semantic Interpretation](https://mlsanity.com/paper/2010.05465/) (2020)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Good-Enough Compositional Data Augmentation](https://mlsanity.com/paper/1904.09545/) (2019)
- [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)
- [The Devil is in the Detail: Simple Tricks Improve Systematic Generalization of Transformers](https://mlsanity.com/paper/2108.12284/) (2021)
- [A Benchmark for Systematic Generalization in Grounded Language Understanding](https://mlsanity.com/paper/2003.05161/) (2020)
- [Compositional generalization through meta sequence-to-sequence learning](https://mlsanity.com/paper/1906.05381/) (2019)
- [Compositional Semantic Parsing with Large Language Models](https://mlsanity.com/paper/2209.15003/) (2022)
- [Compositional Generalization via Neural-Symbolic Stack Machines](https://mlsanity.com/paper/2008.06662/) (2020)
- [Span-based Semantic Parsing for Compositional Generalization](https://mlsanity.com/paper/2009.06040/) (2020)
- [Learning to Infer Graphics Programs from Hand-Drawn Images](https://mlsanity.com/paper/1707.09627/) (2017)
- [Learning Compositional Rules via Neural Program Synthesis](https://mlsanity.com/paper/2003.05562/) (2020)
- [Making Transformers Solve Compositional Tasks](https://mlsanity.com/paper/2108.04378/) (2021)
- [Learning to Recombine and Resample Data for Compositional Generalization](https://mlsanity.com/paper/2010.03706/) (2020)
- [CLOSURE: Assessing Systematic Generalization of CLEVR Models](https://mlsanity.com/paper/1912.05783/) (2019)
- [Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning](https://mlsanity.com/paper/2006.06649/) (2020)
- [Memory Augmented Policy Optimization for Program Synthesis and Semantic Parsing](https://mlsanity.com/paper/1807.02322/) (2018)
- [Compositional generalization in a deep seq2seq model by separating syntax and semantics](https://mlsanity.com/paper/1904.09708/) (2019)
- [GenDexGrasp: Generalizable Dexterous Grasping](https://mlsanity.com/paper/2210.00722/) (2022)
- [Compositional Generalization by Learning Analytical Expressions](https://mlsanity.com/paper/2006.10627/) (2020)

## Built on by (most cited first, 12 of 12)

- [Scaling Reasoning Efficiently via Relaxed On-Policy Distillation](https://mlsanity.com/paper/2603.11137/) (2026)
- [CLOVA: A Closed-Loop Visual Assistant with Tool Usage and Update](https://mlsanity.com/paper/2312.10908/) (2023)
- [SparseDFF: Sparse-View Feature Distillation for One-Shot Dexterous Manipulation](https://mlsanity.com/paper/2310.16838/) (2023)
- [MEWL: Few-shot multimodal word learning with referential uncertainty](https://mlsanity.com/paper/2306.00503/) (2023)
- [End-to-End Neuro-Symbolic Reinforcement Learning with Textual Explanations](https://mlsanity.com/paper/2403.12451/) (2024)
- [Active Reasoning in an Open-World Environment](https://mlsanity.com/paper/2311.02018/) (2023)
- [On the Complexity of Bayesian Generalization](https://mlsanity.com/paper/2211.11033/) (2022)
- [Learning to Compose Representations of Different Encoder Layers towards Improving Compositional Generalization](https://mlsanity.com/paper/2305.12169/) (2023)
- [Layer-wise Representation Fusion for Compositional Generalization](https://mlsanity.com/paper/2307.10799/) (2023)
- [Composing Linear Layers from Irreducibles](https://mlsanity.com/paper/2507.11688/) (2025)
- [A Neuroscience-Inspired Dual-Process Model of Compositional Generalization](https://mlsanity.com/paper/2507.18868/) (2025)
- [LOOP: A Plug-and-Play Neuro-Symbolic Framework for Enhancing Planning in Autonomous Systems](https://mlsanity.com/paper/2508.13371/) (2025)

## Abstract (arXiv)

Current learning models often struggle with human-like systematic generalization, particularly in learning compositional rules from limited data and extrapolating them to novel combinations. We introduce the Neural-Symbolic Recursive Machine (NSR), whose core is a Grounded Symbol System (GSS), allowing for the emergence of combinatorial syntax and semantics directly from training data. The NSR employs a modular design that integrates neural perception, syntactic parsing, and semantic reasoning. These components are synergistically trained through a novel deduction-abduction algorithm. Our findings demonstrate that NSR's design, imbued with the inductive biases of equivariance and compositionality, grants it the expressiveness to adeptly handle diverse sequence-to-sequence tasks and achieve unparalleled systematic generalization. We evaluate NSR's efficacy across four challenging benchmarks designed to probe systematic generalization capabilities: SCAN for semantic parsing, PCFG for string manipulation, HINT for arithmetic reasoning, and a compositional machine translation task. The results affirm NSR's superiority over contemporary neural and hybrid models in terms of generalization and transferability.