# Recursive Algorithmic Reasoning

arXiv: https://arxiv.org/abs/2307.00337 · HTML: https://mlsanity.com/paper/2307.00337/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 22 references that are in the map.
- First posted on arXiv 1 Jul 2023.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Neural Networks and the Chomsky Hierarchy](https://mlsanity.com/paper/2207.02098/) (2022)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [The CLRS Algorithmic Reasoning Benchmark](https://mlsanity.com/paper/2205.15659/) (2022)
- [Neural Programmer-Interpreters](https://mlsanity.com/paper/1511.06279/) (2015)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [Inferring Algorithmic Patterns with Stack-Augmented Recurrent Nets](https://mlsanity.com/paper/1503.01007/) (2015)
- [A Clockwork RNN](https://mlsanity.com/paper/1402.3511/) (2014)
- [A Generalist Neural Algorithmic Learner](https://mlsanity.com/paper/2209.11142/) (2022)
- [Making Neural Programming Architectures Generalize via Recursion](https://mlsanity.com/paper/1704.06611/) (2017)
- [Neural Algorithmic Reasoning with Causal Regularisation](https://mlsanity.com/paper/2302.10258/) (2023)
- [How to transfer algorithmic reasoning knowledge to learn new algorithms?](https://mlsanity.com/paper/2110.14056/) (2021)
- [Learning with Algorithmic Supervision via Continuous Relaxations](https://mlsanity.com/paper/2110.05651/) (2021)
- [Dual Algorithmic Reasoning](https://mlsanity.com/paper/2302.04496/) (2023)
- [Strong Generalization and Efficiency in Neural Programs](https://mlsanity.com/paper/2007.03629/) (2020)

## Built on by (most cited first, 9 of 9)

- [The CLRS-Text Algorithmic Reasoning Language Benchmark](https://mlsanity.com/paper/2406.04229/) (2024)
- [Discrete Neural Algorithmic Reasoning](https://mlsanity.com/paper/2402.11628/) (2024)
- [Primal-Dual Neural Algorithmic Reasoning](https://mlsanity.com/paper/2505.24067/) (2025)
- [Benchmarking ChatGPT on Algorithmic Reasoning](https://mlsanity.com/paper/2404.03441/) (2024)
- [Open-Book Neural Algorithmic Reasoning](https://mlsanity.com/paper/2501.00072/) (2024)
- [The Logical Expressiveness of Topological Neural Networks](https://mlsanity.com/paper/2604.19212/) (2026)
- [A Context-Enhanced Framework for Sequential Graph Reasoning](https://mlsanity.com/paper/2412.09056/) (2024)
- [Positional Encoding meets Persistent Homology on Graphs](https://mlsanity.com/paper/2506.05814/) (2025)
- [KNARsack: Teaching Neural Algorithmic Reasoners to Solve Pseudo-Polynomial Problems](https://mlsanity.com/paper/2509.15239/) (2025)

## Abstract (arXiv)

Learning models that execute algorithms can enable us to address a key problem in deep learning: generalizing to out-of-distribution data. However, neural networks are currently unable to execute recursive algorithms because they do not have arbitrarily large memory to store and recall state. To address this, we (1) propose a way to augment graph neural networks (GNNs) with a stack, and (2) develop an approach for capturing intermediate algorithm trajectories that improves algorithmic alignment with recursive algorithms over previous methods. The stack allows the network to learn to store and recall a portion of the state of the network at a particular time, analogous to the action of a call stack in a recursive algorithm. This augmentation permits the network to reason recursively. We empirically demonstrate that our proposals significantly improve generalization to larger input graphs over prior work on depth-first search (DFS).