Kolmogorov-Arnold Networks and Energy-Based Modeling in an RKHS General Framework and Application to the Malagasy Monetary Instability Model

We develop a unified framework combining Kolmogorov-Arnold Networks (KAN), reproducing kernel Hilbert spaces (RKHS), and an energy-based formulation for the modeling of complex systems. This framework makes it possible to represent nonlinear, multiscale, and potentially unstable dynamics using univariate functions parameterized by B-splines with grid extension, ensuring expressiveness, numerical stability, and interpretability. We show that this approach naturally applies to economic systems, in particular financial markets, institutional networks, and unstable monetary systems. The study includes a complete reformulation of the Malagasy monetary instability model, which becomes a natural special case of the KAN-RKHS-Energy framework. This reformulation captures extreme behaviors, regime transitions, and structural breaks characteristic of emerging economies, while providing an energy-based interpretation of monetary stability. This work thus establishes a bridge between functional theory, interpretable machine learning, and advanced economic modeling.