# Fully analogue in-memory neural computing via quantum tunneling effect

arXiv: https://arxiv.org/abs/2510.23638 · HTML: https://mlsanity.com/paper/2510.23638/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functions](https://mlsanity.com/paper/2406.07456/) (2024)
- [Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensing](https://mlsanity.com/paper/2406.00600/) (2024)
- [Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomials](https://mlsanity.com/paper/2406.02583/) (2024)
- [Fast offset corrected in-memory training](https://mlsanity.com/paper/2303.04721/) (2023)
- [Hardware Acceleration of Kolmogorov-Arnold Network (KAN) for Lightweight Edge Inference](https://mlsanity.com/paper/2409.11418/) (2024)
- [Towards Exact Gradient-based Training on Analog In-memory Computing](https://mlsanity.com/paper/2406.12774/) (2024)
- [Efficient Nonlinear Function Approximation in Analog Resistive Crossbars for Recurrent Neural Networks](https://mlsanity.com/paper/2411.18271/) (2024)

## Built on by (most cited first, 2 of 2)

- [Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2601.15340/) (2026)
- [Physical Analogue Kolmogorov-Arnold Networks based on Reconfigurable Nonlinear-Processing Units](https://mlsanity.com/paper/2602.07518/) (2026)

## Abstract (arXiv)

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.