# Liquid Resistance Liquid Capacitance Networks

arXiv: https://arxiv.org/abs/2403.08791 · HTML: https://mlsanity.com/paper/2403.08791/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2024.

## Built on by (most cited first, 7 of 7)

- [Parallelization of Non-linear State-Space Models: Scaling Up Liquid-Resistance Liquid-Capacitance Networks for Efficient Sequence Modeling](https://mlsanity.com/paper/2505.21717/) (2025)
- [Accuracy, Memory Efficiency and Generalization: A Comparative Study on Liquid Neural Networks and Recurrent Neural Networks](https://mlsanity.com/paper/2510.07578/) (2025)
- [Depth Matters: Multimodal RGB-D Perception for Robust Autonomous Agents](https://mlsanity.com/paper/2503.16711/) (2025)
- [Adaptive Control in Autonomous Driving via Real-Time Recurrent RL](https://mlsanity.com/paper/2602.02236/) (2026)
- [Synaptic Activation and Dual Liquid Dynamics for Interpretable Bio-Inspired Models](https://mlsanity.com/paper/2602.13017/) (2026)
- [Continuous-Time Machine Learning: A Unified Mathematical Perspective](https://mlsanity.com/paper/2609.16710/) (2026)
- [Riccati State Space Models: Non-iterative Parallelization for Nonlinear Sequence Modeling](https://mlsanity.com/paper/2609.35441/) (2026)

## Abstract (arXiv)

We introduce liquid-resistance liquid-capacitance neural networks (LRCs), a neural-ODE model which considerably improve the generalization, accuracy, and biological plausibility of electrical equivalent circuits (EECs), liquid time-constant networks (LTCs), and saturated liquid time-constant networks (STCs), respectively. We also introduce LRC units (LRCUs), as a very efficient and accurate gated RNN-model, which results from solving LRCs with an explicit Euler scheme using just one unfolding. We empirically show and formally prove that the liquid capacitance of LRCs considerably dampens the oscillations of LTCs and STCs, while at the same time dramatically increasing accuracy even for cheap solvers. We experimentally demonstrate that LRCs are a highly competitive alternative to popular neural ODEs and gated RNNs in terms of accuracy, efficiency, and interpretability, on classic time-series benchmarks and a complex autonomous-driving lane-keeping task.