# Leveraging Low-Rank and Sparse Recurrent Connectivity for Robust Closed-Loop Control

arXiv: https://arxiv.org/abs/2310.03915 · HTML: https://mlsanity.com/paper/2310.03915/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 57 references that are in the map.
- First posted on arXiv 5 Oct 2023.

## Builds on (most cited first, 30 of 35)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Temporal Convolutional Networks for Action Segmentation and Detection](https://mlsanity.com/paper/1611.05267/) (2016)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [Causal Confusion in Imitation Learning](https://mlsanity.com/paper/1905.11979/) (2019)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [Distributed Prioritized Experience Replay](https://mlsanity.com/paper/1803.00933/) (2018)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [One-Shot Visual Imitation Learning via Meta-Learning](https://mlsanity.com/paper/1709.04905/) (2017)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Adversarial Examples Are a Natural Consequence of Test Error in Noise](https://mlsanity.com/paper/1901.10513/) (2019)
- [AntisymmetricRNN: A Dynamical System View on Recurrent Neural Networks](https://mlsanity.com/paper/1902.09689/) (2019)
- [Training Agents using Upside-Down Reinforcement Learning](https://mlsanity.com/paper/1912.02877/) (2019)
- [A Signal Propagation Perspective for Pruning Neural Networks at Initialization](https://mlsanity.com/paper/1906.06307/) (2019)
- [Lipschitz Recurrent Neural Networks](https://mlsanity.com/paper/2006.12070/) (2020)
- [Orthogonal Recurrent Neural Networks with Scaled Cayley Transform](https://mlsanity.com/paper/1707.09520/) (2017)
- [Sparse DNNs with Improved Adversarial Robustness](https://mlsanity.com/paper/1810.09619/) (2018)
- [Task-Embedded Control Networks for Few-Shot Imitation Learning](https://mlsanity.com/paper/1810.03237/) (2018)
- [RLlib: Abstractions for Distributed Reinforcement Learning](https://mlsanity.com/paper/1712.09381/) (2017)
- [Linking connectivity, dynamics and computations in low-rank recurrent neural networks](https://mlsanity.com/paper/1711.09672/) (2017)
- [Limitations of the Lipschitz constant as a defense against adversarial examples](https://mlsanity.com/paper/1807.09705/) (2018)
- [Sparsity Winning Twice: Better Robust Generalization from More Efficient Training](https://mlsanity.com/paper/2202.09844/) (2022)

## Built on by (most cited first, 2 of 2)

- [Preconditioned DeltaNet: Curvature-aware Sequence Modeling for Linear Recurrences](https://mlsanity.com/paper/2604.21100/) (2026)
- [Deep RL Needs Deep Behavior Analysis: Exploring Implicit Planning by Model-Free Agents in Open-Ended Environments](https://mlsanity.com/paper/2506.06981/) (2025)

## Abstract (arXiv)

Developing autonomous agents that can interact with changing environments is an open challenge in machine learning. Robustness is particularly important in these settings as agents are often fit offline on expert demonstrations but deployed online where they must generalize to the closed feedback loop within the environment. In this work, we explore the application of recurrent neural networks to tasks of this nature and understand how a parameterization of their recurrent connectivity influences robustness in closed-loop settings. Specifically, we represent the recurrent connectivity as a function of rank and sparsity and show both theoretically and empirically that modulating these two variables has desirable effects on network dynamics. The proposed low-rank, sparse connectivity induces an interpretable prior on the network that proves to be most amenable for a class of models known as closed-form continuous-time neural networks (CfCs). We find that CfCs with fewer parameters can outperform their full-rank, fully-connected counterparts in the online setting under distribution shift. This yields memory-efficient and robust agents while opening a new perspective on how we can modulate network dynamics through connectivity.