Heisenberg Limited Liquid Networks: Solver‑Free Neural Dynamics via Phase‑Space Uncertainty

We propose Heisenberg-Limited Liquid Networks (HLLN 2.1), a recurrent neural architecture that achieves continuous-time, liquid dynamics without numerical ODE solvers. By grounding state updates in a learnable uncertainty principle, the network modulates its own temporal integration rate in response to input surprise. HLLN 2.1 uses 75–80% fewer parameters than Gated Recurrent Units (GRUs) while matching or exceeding performance on chaotic time-series forecasting, regime-shift adaptation, and character-level language modelling. The architecture exposes an interpretable “Metabolic Friction” signal that correlates with environmental instability, providing built-in uncertainty quantification. All code is available at github.com/Kshitiz-Maurya/HLLN2.1.