Liquid Time-Constant Networks (LTCs) are a class of continuous-time Recurrent Neural Networks (RNNs) — created by Ramin Hasani et al., where the hidden state's decay rate (time constant) is not fixed but varies adaptively based on the input, inspired by C. elegans biology.

What Is an LTC?

• Definition: Neural ODEs where the time-constant $ au$ is a function of the input $I(t)$.
• Equation: $dx/dt = -(x/ au(x, I)) + S(x, I)$.
• Behavior: The system can be "fast" (react quickly) or "slow" (remember long term) dynamically.

Why LTCs Matter

• Causality: They explicitly model cause-and-effect dynamics governed by differential equations.
• Robustness: Showed superior performance in driving tasks, generalizing to uneven terrain better than standard CNN-RNNs.
• Interpretability: Sparse LTCs can be pruned down to very few neurons (19 cells) that are human-readable (Neural Circuit Policies).

Liquid Time-Constant Networks are adaptive dynamical systems — robust, expressive models that bridge the gap between deep learning and control theory.