mlsanityData to 7 Oct 2026

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

arXiv 1711.09672 ↗First posted 27 Nov 2017q-bio.NCcited by 51

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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.

Key facts. Cited by 51 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Nov 2017.

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Citing papers per year: 2021: 4; 2022: 2; 2023: 10; 2024: 7; 2025: 10; 2026: 18.

51 papers.

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  1. 2023How connectivity structure shapes rich and lazy learning in neural circuitscited by 15
  2. 2024Inferring stochastic low-rank recurrent neural networks from neural datacited by 15
  3. 2023Interpretable statistical representations of neural population dynamics and geometrycited by 12
  4. 2023Low Tensor Rank Learning of Neural Dynamicscited by 12
  5. 2022Input correlations impede suppression of chaos and learning in balanced rate networkscited by 3
  6. 2024DFORM: Diffeomorphic vector field alignment for assessing dynamics across learned modelscited by 3
  7. 2024Neural timescales from a computational perspectivecited by 3
  8. 2021Ensemble perspective for understanding temporal credit assignmentcited by 2
  9. 2021Bayesian reconstruction of memories stored in neural networks from their connectivitycited by 2
  10. 2023Trainability, Expressivity and Interpretability in Gated Neural ODEscited by 2
  11. 2023Fading memory as inductive bias in residual recurrent networkscited by 2
  12. 2023Characterising representation dynamics in recurrent neural networks for object recognitioncited by 2
38 more
  1. 2023Leveraging Low-Rank and Sparse Recurrent Connectivity for Robust Closed-Loop Controlcited by 2
  2. 2024Deep Continuous Networkscited by 2
  3. 2025Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCAcited by 2
  4. 2025Learning Dynamics of RNNs in Closed-Loop Environmentscited by 2
  5. 2026Diagnosing Generalization Failures from Representational Geometry Markerscited by 2
  6. 2026The Global Empirical NTK: Self-Referential Bias and Dimensionality of Gradient Descent Learningcited by 2
  7. 2026Learning Task-Sufficient World Models by Synergizing Agentic Exploration and Structured Modelingcited by 2
  8. 2021Slow manifolds in recurrent networks encode working memory efficiently and robustlycited by 1
  9. 2021A brain basis of dynamical intelligence for AI and computational neurosciencecited by 1
  10. 2022The impact of memory on learning sequence-to-sequence taskscited by 1
  11. 2023Spiking mode-based neural networkscited by 1
  12. 2023Astrocytes as a mechanism for meta-plasticity and contextually-guided network functioncited by 1
  13. 2025A ghost mechanism: An analytical model of abrupt learning in recurrent networkscited by 1
  14. 2025Category learning in deep neural networks: Information content and geometry of internal representationscited by 1
  15. 2025A Factorized Low-Rank RNN Framework for Uncovering Independent Neural Latent Dynamics and Connectivitycited by 1
  16. 2025RNNs perform task computations by dynamically warping neural representationscited by 1
  17. 2026Learning reveals invisible structure in low-rank RNNscited by 1
  18. 2026Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learningcited by 1
  19. 2023Decoding Neuronal Networks: A Reservoir Computing Approach for Predicting Connectivity and Functionalitycited by 0
  20. 2024Synergistic pathways of modulation enable robust task packing within neural dynamicscited by 0
  21. 2024Measuring and Controlling Solution Degeneracy across Task-Trained Recurrent Neural Networkscited by 0
  22. 2024Storing overlapping associative memories on latent manifolds in low-rank spiking networkscited by 0
  23. 2025Dynamic Manifold Hopfield Networks for Context-Dependent Associative Memorycited by 0
  24. 2025High-resolution spatial memory requires grid-cell-like neural codescited by 0
  25. 2025Dynamical stability for dense patterns in attractor neural networkscited by 0
  26. 2025Mechanistic Interpretability of RNNs emulating Hidden Markov Modelscited by 0
  27. 2026Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networkscited by 0
  28. 2026JEDI: Jointly Embedded Inference of Neural Dynamicscited by 0
  29. 2026Identifying Connectivity Distributions from Neural Dynamics Using Flowscited by 0
  30. 2026Center-Manifold Reduction of Learning at Bifurcations: Interference and Rich Learning in Recurrent Neural Networkscited by 0
  31. 2026Back to Parsimonious Latents: Learning Task-Centric World Models from Visual Foundationscited by 0
  32. 2026Dynamics and Representation Structure of Local Approximations to Gradient-Based Learning in Linear Recurrent Neural Networkscited by 0
  33. 2026Finite-Lag Operator Geometry of Recurrent Representationscited by 0
  34. 2026Motif-Mamba: network motif improved mamba for long-range sequence modelingcited by 0
  35. 2026Divisive Normalization Shapes Low-Rank Slow Manifolds for Continuous Working Memorycited by 0
  36. 2026Certified Inference and Training for Deep Equilibrium Networks: A Continuation Framework with Polynomial Complexity Guaranteescited by 0
  37. 2026Learning-Induced Dynamical Transition in Recurrent Neural Networkscited by 0
  38. 2026A neural network that maintains and retrieves memories based on contextcited by 0

50 most cited of 51 All 51 (JSON)