# LTC-SE: Expanding the Potential of Liquid Time-Constant Neural Networks for Scalable AI and Embedded Systems

arXiv: https://arxiv.org/abs/2304.08691 · HTML: https://mlsanity.com/paper/2304.08691/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 18 Apr 2023.

## Builds on (most cited first, 6 of 6)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)

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

- [Implementing engrams from a machine learning perspective: the relevance of a latent space](https://mlsanity.com/paper/2407.16616/) (2024)
- [Pulse-Driven Neural Architecture: Learnable Oscillatory Dynamics for Robust Continuous-Time Sequence Processing](https://mlsanity.com/paper/2603.00153/) (2026)

## Abstract (arXiv)

We present LTC-SE, an improved version of the Liquid Time-Constant (LTC) neural network algorithm originally proposed by Hasani et al. in 2021. This algorithm unifies the Leaky-Integrate-and-Fire (LIF) spiking neural network model with Continuous-Time Recurrent Neural Networks (CTRNNs), Neural Ordinary Differential Equations (NODEs), and bespoke Gated Recurrent Units (GRUs). The enhancements in LTC-SE focus on augmenting flexibility, compatibility, and code organization, targeting the unique constraints of embedded systems with limited computational resources and strict performance requirements. The updated code serves as a consolidated class library compatible with TensorFlow 2.x, offering comprehensive configuration options for LTCCell, CTRNN, NODE, and CTGRU classes. We evaluate LTC-SE against its predecessors, showcasing the advantages of our optimizations in user experience, Keras function compatibility, and code clarity. These refinements expand the applicability of liquid neural networks in diverse machine learning tasks, such as robotics, causality analysis, and time-series prediction, and build on the foundational work of Hasani et al.