# Linking connectivity, dynamics and computations in low-rank recurrent neural networks

arXiv: https://arxiv.org/abs/1711.09672 · HTML: https://mlsanity.com/paper/1711.09672/

## Key facts

- Cited by 51 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2017.

## Built on by (most cited first, 30 of 51)

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- [Bayesian reconstruction of memories stored in neural networks from their connectivity](https://mlsanity.com/paper/2105.07416/) (2021)
- [Trainability, Expressivity and Interpretability in Gated Neural ODEs](https://mlsanity.com/paper/2307.06398/) (2023)
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- [Characterising representation dynamics in recurrent neural networks for object recognition](https://mlsanity.com/paper/2308.12435/) (2023)
- [Leveraging Low-Rank and Sparse Recurrent Connectivity for Robust Closed-Loop Control](https://mlsanity.com/paper/2310.03915/) (2023)
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- [Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA](https://mlsanity.com/paper/2501.12582/) (2025)
- [Learning Dynamics of RNNs in Closed-Loop Environments](https://mlsanity.com/paper/2505.13567/) (2025)
- [Diagnosing Generalization Failures from Representational Geometry Markers](https://mlsanity.com/paper/2603.01879/) (2026)
- [The Global Empirical NTK: Self-Referential Bias and Dimensionality of Gradient Descent Learning](https://mlsanity.com/paper/2605.08746/) (2026)
- [Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning](https://mlsanity.com/paper/2606.13260/) (2026)
- [Learning Task-Sufficient World Models by Synergizing Agentic Exploration and Structured Modeling](https://mlsanity.com/paper/2607.04409/) (2026)
- [Slow manifolds in recurrent networks encode working memory efficiently and robustly](https://mlsanity.com/paper/2101.03163/) (2021)
- [A brain basis of dynamical intelligence for AI and computational neuroscience](https://mlsanity.com/paper/2105.07284/) (2021)
- [The impact of memory on learning sequence-to-sequence tasks](https://mlsanity.com/paper/2205.14683/) (2022)
- [Spiking mode-based neural networks](https://mlsanity.com/paper/2310.14621/) (2023)
- [Astrocytes as a mechanism for meta-plasticity and contextually-guided network function](https://mlsanity.com/paper/2311.03508/) (2023)
- [A ghost mechanism: An analytical model of abrupt learning in recurrent networks](https://mlsanity.com/paper/2501.02378/) (2025)
- [Category learning in deep neural networks: Information content and geometry of internal representations](https://mlsanity.com/paper/2510.19021/) (2025)
- [A Factorized Low-Rank RNN Framework for Uncovering Independent Neural Latent Dynamics and Connectivity](https://mlsanity.com/paper/2511.13899/) (2025)
- [RNNs perform task computations by dynamically warping neural representations](https://mlsanity.com/paper/2512.04310/) (2025)
- [Learning reveals invisible structure in low-rank RNNs](https://mlsanity.com/paper/2605.04115/) (2026)

## Abstract (arXiv)

Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how low-dimensional computations on mixed, distributed representations emerge from the structure of the recurrent connectivity and inputs to cortical networks is a major challenge. Here, we study a class of recurrent network models in which the connectivity is a sum of a random part and a minimal, low-dimensional structure. We show that, in such networks, the dynamics are low dimensional and can be directly inferred from connectivity using a geometrical approach. We exploit this understanding to determine minimal connectivity required to implement specific computations, and find that the dynamical range and computational capacity quickly increase with the dimensionality of the connectivity structure. This framework produces testable experimental predictions for the relationship between connectivity, low-dimensional dynamics and computational features of recorded neurons.