neural-odes

This paper presents a memory–stability–expressivity trilemma for trainable dissipative oscillator networks, showing that damping governs all three and limits trainability, with experimental validation on a 20-oscillator network confirming the theoretical bounds.

The author compares Structural Equation Modeling, Neural ODEs, and AI Programs like DSPy as declarative frameworks for defining and optimizing computational graphs, arguing that structured flows are essential for trustworthy AI agents.

This paper introduces Dynamical Physics-Modeled Neural Networks (DynPMNNs), a continuous-time deep learning architecture where hidden layers are defined by ordinary differential equations. It presents a biologically inspired approach grounded in Reproducing Kernel Banach Spaces, demonstrating competitive performance on the California Housing dataset with fewer parameters than standard Neural ODEs.