Dmitry Shchapin

The spatiotemporal dynamics of coupled nonlinear oscillators provide a natural substrate for the high-dimensional feature transformations required for complex pattern classification. We investigate this principle using an electronically implemented chain of FitzHugh – Nagumo neurons operating in the excitable regime. Static two-dimensional inputs are encoded by boundary pulse-train frequencies applied at the terminal nodes, driving the chain into reproducible, input-dependent voltage patterns distributed across space and time. We formalize this device as a physical kernel: a deterministic mapping from a low-dimensional input space to an explicit feature space derived from measured dynamics. To characterize the resulting kernel beyond accuracy alone, we introduce kernel tomography diagnostics based on the spectrum of the centered Gram matrix, including effective dimension and centered kernel alignment, and we benchmark against standard software classifiers defined directly on the input coordinates. Using controlled synthetic tasks with increasingly complex decision boundaries, we show that the physical-kernel representation supports strong performance with simple convex readouts and benefits from a hierarchical design that combines local spectral features with coupling-aware observables such as internodal coherence. Furthermore, a lightweight readout incorporating quadratic feature interactions significantly improves performance by capturing mode interactions while retaining convex training. Finally, we demonstrate cross-task reuse of a single precomputed response map by applying nearest-grid lookup to a real vowel formant dataset, achieving nontrivial separability without any hardware retuning. Overall, the proposed framework provides mechanistic insight into how forced excitable chains induce task-relevant feature geometry and offers principled guidance for designing and evaluating neuromorphic hardware as physical kernels for static classification.