Bridging Function Approximation and Device Physics via Negative Differential Resistance Networks

Abstract: Achieving fully analog neural computation requires hardware that can natively implement both linear and nonlinear operations with high efficiency. While analogue matrix-vector multiplication has advanced via compute-in-memory architectures, nonlinear activation functions remain a bottleneck, often requiring digital or hybrid solutions. Inspired by the Kolmogorov-Arnold framework, we propose KANalogue, a fully analogue implementation of Kolmogorov-Arnold Networks (KANs) using negative differential resistance devices as physical realizations of learnable univariate basis functions. By leveraging the intrinsic negative differential resistance characteristics of tunnel diodes fabricated from NbSi2N4/HfSi2N4 heterostructures, we construct coordinate-wise nonlinearities with distinct curvature and support profiles. We extract I-V data from fabricated armchair and zigzag devices, fit high-order polynomials to emulate diode behavior in software, and train KANs on vision benchmarks using these learned basis functions. Our results demonstrate that KANalogue can approximate complex functions with minimal parameters while maintaining classification accuracy competitive with digital baselines. This work bridges device-level physics and function approximation theory, charting a path toward scalable, energy-efficient analogue machine learning systems.