Structure Over Nonlinearity: Explicit Interaction Architectures for Dynamical Learning
For researchers in dynamical system learning, this work offers a structure-first alternative to black-box models, potentially reducing model complexity and improving interpretability.
The paper proposes a new paradigm for learning dynamical systems where modeling capability comes from explicit interaction structures rather than nonlinear function approximation. Experiments on nonlinear system identification show that depth improves representation quality and generalization, with informative internal representations emerging even under readout-only fitting.
Most learning architectures for dynamical systems rely on generic nonlinear function approximation, often requiring high model complexity to capture structured behaviors. In this work, we propose an alternative paradigm in which modeling capability arises primarily from structure rather than from expressive nonlinearities. We introduce a class of explicit structured dynamical units based on wave-inspired interaction structures with internal state. Inspired by wave-based computational principles, the proposed units adopt a strictly causal organization that eliminates algebraic loops, yielding fully explicit models that can be evaluated without implicit solvers. Stacking such units produces layered dynamical architectures with emergent hierarchical behavior. Through experiments on a nonlinear system identification task, we show that depth improves both representation quality and generalization, even under limited parameter optimization. In particular, the proposed architectures produce informative internal representations even under readout-only fitting, indicating that useful dynamical structure emerges from the organization of interactions prior to substantial parameter optimization. These results suggest that structure-first design provides a viable and effective alternative to conventional black-box approaches for learning dynamical systems, highlighting the role of interaction structure as a primary source of model expressivity.