Structure Over Nonlinearity: Explicit Interaction Architectures for Dynamical Learning

A new preprint proposes a structural alternative to conventional black-box models for learning dynamical systems, arguing that interaction architecture can drive model expressivity more effectively than expressive nonlinear function approximation alone [1]. The work, submitted in 2026, introduces a class of explicit structured dynamical units inspired by wave-based computational principles [1]. Unlike classical wave digital formulations that often produce implicit fixed-point relations due to algebraic coupling, these units adopt a strictly causal, layered organization that eliminates algebraic loops [2]. This yields fully explicit models that can be evaluated sequentially without requiring implicit solvers [2]. Stacking the units produces layered dynamical architectures with emergent hierarchical behavior [1]. The researchers tested the approach on a nonlinear system identification task and found that depth improved both representation quality and generalization, even under limited parameter optimization [1]. The architectures produced informative internal representations under readout-only fitting, indicating that useful dynamical structure emerges from the organization of interactions before substantial parameter optimization occurs [1]. The findings align with broader trends in representation learning, where systems automatically discover the features needed for a task from raw data, replacing manual feature engineering [5]. In machine learning, deep neural networks with at least two hidden layers are known to learn sophisticated hierarchical representations [6], a principle the new architecture extends by embedding structure directly into the dynamical units rather than relying solely on learned nonlinearities [1]. A separate line of work, Structured Kolmogorov-Arnold Neural ODEs (SKANODEs), similarly emphasizes structured inductive biases for dynamical systems, unifying continuous-time neural modeling with end-to-end symbolic discovery of governing equations [4]. That framework uses adaptive, spline-based basis functions that are differentiable and expressive while retaining structure necessary for symbolic interpretability [4]. The wave-inspired architecture takes a different route, prioritizing causal interaction structure as the primary source of model expressivity [2]. Machine learning approaches to dynamical systems have traditionally relied on generic nonlinear function approximation, often demanding high model complexity to capture structured behaviors [1]. The authors argue that structure-first design provides a viable alternative, with interaction structure itself serving as a primary driver of model capability [2].