# Attractor and integrator networks in the brain

arXiv: https://arxiv.org/abs/2112.03978 · HTML: https://mlsanity.com/paper/2112.03978/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2021.

## Built on by (most cited first, 30 of 61)

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- [Trainability, Expressivity and Interpretability in Gated Neural ODEs](https://mlsanity.com/paper/2307.06398/) (2023)
- [Discrete, compositional, and symbolic representations through attractor dynamics](https://mlsanity.com/paper/2310.01807/) (2023)
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- [Learning Dynamics of RNNs in Closed-Loop Environments](https://mlsanity.com/paper/2505.13567/) (2025)
- [Sufficient conditions for offline reactivation in recurrent neural networks](https://mlsanity.com/paper/2505.17003/) (2025)
- [Self-orthogonalizing attractor neural networks emerging from the free energy principle](https://mlsanity.com/paper/2505.22749/) (2025)
- [Emergence of Adaptive Circadian Rhythms in Deep Reinforcement Learning](https://mlsanity.com/paper/2307.12143/) (2023)
- [Astrocytes as a mechanism for meta-plasticity and contextually-guided network function](https://mlsanity.com/paper/2311.03508/) (2023)
- [Learning Sequence Attractors in Recurrent Networks with Hidden Neurons](https://mlsanity.com/paper/2404.02729/) (2024)

## Abstract (arXiv)

In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms by which simple and forgetful units can organize to collectively generate dynamics on the long time-scales required for such computations. We discuss the myriad potential uses of attractor dynamics for computation in the brain, and showcase notable examples of brain systems in which inherently low-dimensional continuous attractor dynamics have been concretely and rigorously identified. Thus, it is now possible to conclusively state that the brain constructs and uses such systems for computation. Finally, we look ahead by highlighting recent theoretical advances in understanding how the fundamental tradeoffs between robustness and capacity and between structure and flexibility can be overcome by reusing and recombining the same set of modular attractors for multiple functions, so they together produce representations that are structurally constrained and robust but exhibit high capacity and are flexible.