Neural Integration of Continuous Dynamics
This work addresses a specific technical bottleneck in neural dynamical systems for researchers in computational neuroscience or machine learning, but it appears incremental as it adapts existing numerical methods to a neural context.
The authors tackled the problem of simulating continuous-time neural dynamical systems by proposing a compact neural circuit that implements common numerical integrators, achieving fully neural temporal output and demonstrating equivalence with numerical integration for polynomial dynamical systems.
Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we present a compact neural circuit for two common numerical integrators: the explicit fixed-step Runge-Kutta method of any order and the semi-implicit/predictor-corrector Adams-Bashforth-Moulton method. Modeled as constant-sized recurrent networks embedding a continuous neural differential equation, they achieve fully neural temporal output. Using the polynomial class of dynamical systems, we demonstrate the equivalence of neural and numerical integration.