Fully analogue in-memory neural computing via quantum tunneling effect

TL;DR

KANalogue is introduced, a fully analogue realization of Kolmogorov-Arnold Networks (KANs) that instantiates univariate basis functions directly using negative-differential-resistance (NDR) devices, and establishes a device-grounded route toward scalable, energy-efficient, fully analogue neural networks.

Abstract

Fully analogue neural computation requires hardware that can implement both linear and nonlinear transformations without digital assistance. While analogue in-memory computing efficiently realizes matrix-vector multiplication, the absence of learnable analogue nonlinearities remains a central bottleneck. Here we introduce KANalogue, a fully analogue realization of Kolmogorov-Arnold Networks (KANs) that instantiates univariate basis functions directly using negative-differential-resistance (NDR) devices. By mapping the intrinsic current-voltage characteristics of NDR devices to learnable coordinate-wise nonlinear functions, KANalogue embeds function approximation into device physics while preserving a fully analogue signal path. Using cold-metal tunnel diodes as a representative platform, we construct diverse nonlinear bases and combine them through crossbar-based analogue summation. Experiments on MNIST, FashionMNIST, and CIFAR-10 demonstrate that KANalogue achieves competitive accuracy with substantially fewer parameters and higher crossbar node efficiency than analogue MLPs, while approaching the performance of digital KANs under strict hardware constraints. The framework is not limited to a specific device technology and naturally generalizes to a broad class of NDR devices. These results establish a device-grounded route toward scalable, energy-efficient, fully analogue neural networks.

Figures (15)

• Figure 1: Comparison between prior analogue neural architectures and the proposed KANalogue framework.a, Prior works: Conventional analogue accelerators implement only the linear operations of neural networks in crossbar arrays, while nonlinear activations remain fixed and must be computed digitally after analogue-to-digital conversion. This hybrid pipeline limits efficiency and prevents fully analogue neural computation. b, This work: KANalogue adopts the KAN architecture, in which learnable univariate functions reside on edges and additive mixing occurs at nodes. This structure naturally maps to hardware: both linear summation and nonlinear basis evaluations are implemented directly in the crossbar array, eliminating the digital nonlinear-processing stage. c, Device-level realization: Learnable activation functions are instantiated using cold-metal tunnel diodes (CMTDs). Distinct device geometries yield diverse nonlinear I--V characteristics, which serve as tunable basis functions $T_{k,j,i}(x)$. Weighted combinations by cross-sectional area adjusting of these device-derived basis functions form the analogue edge mappings $\phi_{k,i}$. This device-to-function correspondence enables a fully analogue computational path grounded in physical nonlinearities.
• Figure 2: KANalogue framework.a, KART expresses any continuous multivariate function as a finite superposition of univariate functions. This structure can be viewed as a two-layer network in which univariate mappings reside on the edges and additive mixing occurs at the nodes. b, KANs generalize this construction into a deep architecture by stacking multiple such layers, with each edge carrying a learnable univariate function. c, In original KANs, each univariate function is parameterized by a B-spline expansion with trainable coefficients. d, KANalogue transfers these basis functions into hardware by replacing digital B-splines with nonlinear I--V characteristics of NDR devices. e, Analogue crossbar realization of a KANalogue layer. Each edge combines multiple NDR devices and each node perform current summation governed by Kirchhoff's current law. f, Schematic illustration of a $2\times 2$ physical crossbar, showing how device geometry encodes effective conductance. g, Matrix-form representation of a KANalogue layer. Nonlinear device responses form learnable basis functions on each edge, while transimpedance amplification (TIAs) converts summed currents into output voltages.
• Figure 3: CMTD structures and their fitted nonlinear I--V characteristics.a, Armchair-oriented NbSi2N4/HfSi2N4 heterostructure with a 21 tunnel barrier. b, Zigzag-oriented heterostructure with the same 21 barrier length. c, Zigzag-oriented device with a shorter 15 barrier, highlighting the effect of barrier thickness on tunneling behaviour. d, Hybrid zigzag–armchair–zigzag configuration with a 15 barrier region. e-h, Corresponding I--V characteristics obtained from DFT--NEGF simulations (dots) and their smoothing-spline fits (solid curves), which serve as analogue nonlinear basis functions in KANalogue. The variations across geometry and orientation illustrate the device-level tunability of the nonlinear transformations.
• Figure 4: Overall pipeline for KANalogue. Inputs are hard-clipped into the device operating range, transformed by NDR-based univariate functions and crossbar mixing, normalized during training (with BatchNorm parameters fused into weights after training), hard-clipped again if needed, and passed through subsequent analogue KAN layers before final readout. All operations—including nonlinear transformation, summation, clipping, and fused normalization—can be implemented in continuous analogue circuitry. Effect of device-derived basis-function diversity.a-c, Classification accuracy obtained with different combinations of CMTD-based nonlinear basis functions under a fixed network architecture. Increasing the basis dimension improves peak accuracy and reduces performance variability across basis choices, particularly on more challenging datasets. d-f, Accuracy as a function of basis dimension under two experimental settings—fixed architecture and matched total parameter budget. Under parameter matching, higher basis dimensions require fewer crossbar nodes but retain comparable accuracy, indicating that performance gains arise from complementary nonlinear representations rather than increased parameter count. The shorthand labels A-21, Z-21, Z15, and ZAZ-15 correspond to the CMTD device geometries shown in Fig. \ref{['fig:cmtd']}.
• Figure 5: Crossbar node efficiency and robustness under coefficient disturbance.a, Comparison of classification accuracy for MLP, KAN, and KANalogue across datasets under increasing model capacity, measured by the total number of nodes. b, Each curve reports the worst-case classification accuracy over $10^4$ independent coefficient perturbation realizations, while the shaded bands indicate the corresponding maximum and minimum accuracies.