# The Deep Equilibrium Algorithmic Reasoner

arXiv: https://arxiv.org/abs/2402.06445 · HTML: https://mlsanity.com/paper/2402.06445/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 25 references that are in the map.
- First posted on arXiv 9 Feb 2024.

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

- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [A Survey on Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2303.10993/) (2023)
- [What Can Neural Networks Reason About?](https://mlsanity.com/paper/1905.13211/) (2019)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [The CLRS Algorithmic Reasoning Benchmark](https://mlsanity.com/paper/2205.15659/) (2022)
- [Implicit Graph Neural Networks](https://mlsanity.com/paper/2009.06211/) (2020)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [Stabilizing Equilibrium Models by Jacobian Regularization](https://mlsanity.com/paper/2106.14342/) (2021)
- [A Generalist Neural Algorithmic Learner](https://mlsanity.com/paper/2209.11142/) (2022)
- [Graph Neural Networks are Dynamic Programmers](https://mlsanity.com/paper/2203.15544/) (2022)
- [Pointer Graph Networks](https://mlsanity.com/paper/2006.06380/) (2020)
- [Relational inductive bias for physical construction in humans and machines](https://mlsanity.com/paper/1806.01203/) (2018)
- [Neural Algorithmic Reasoning with Causal Regularisation](https://mlsanity.com/paper/2302.10258/) (2023)
- [TorchDEQ: A Library for Deep Equilibrium Models](https://mlsanity.com/paper/2310.18605/) (2023)
- [Neural Algorithmic Reasoning Without Intermediate Supervision](https://mlsanity.com/paper/2306.13411/) (2023)
- [Latent Space Representations of Neural Algorithmic Reasoners](https://mlsanity.com/paper/2307.08874/) (2023)

## Built on by (most cited first, 1 of 1)

- [Primal-Dual Neural Algorithmic Reasoning](https://mlsanity.com/paper/2505.24067/) (2025)

## Abstract (arXiv)

Recent work on neural algorithmic reasoning has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. Doing so, however, has always used a recurrent architecture, where each iteration of the GNN aligns with an algorithm's iteration. Since an algorithm's solution is often an equilibrium, we conjecture and empirically validate that one can train a network to solve algorithmic problems by directly finding the equilibrium. Note that this does not require matching each GNN iteration with a step of the algorithm.