# Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2601.15340 · HTML: https://mlsanity.com/paper/2601.15340/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 54 references that are in the map.
- First posted on arXiv 20 Jan 2026.

## Builds on (most cited first, 19 of 19)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [The Hardware Lottery](https://mlsanity.com/paper/2009.06489/) (2020)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [Kolmogorov-Arnold Networks (KANs) for Time Series Analysis](https://mlsanity.com/paper/2405.08790/) (2024)
- [Convolutional Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2406.13155/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [Self-Contrastive Forward-Forward Algorithm](https://mlsanity.com/paper/2409.11593/) (2024)
- [Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations](https://mlsanity.com/paper/2108.02318/) (2021)
- [A perspective on physical reservoir computing with nanomagnetic devices](https://mlsanity.com/paper/2212.04851/) (2022)
- [Initialization Schemes for Kolmogorov-Arnold Networks: An Empirical Study](https://mlsanity.com/paper/2509.03417/) (2025)
- [Dopant Network Processing Units: Towards Efficient Neural-network Emulators with High-capacity Nanoelectronic Nodes](https://mlsanity.com/paper/2007.12371/) (2020)
- [Noise-Aware Training of Neuromorphic Dynamic Device Networks](https://mlsanity.com/paper/2401.07387/) (2024)
- [In-Materia Speech Recognition](https://mlsanity.com/paper/2410.10434/) (2024)
- [Programmable k-local Ising interactions and shallow optical Kolmogorov--Arnold networks through repeated data encounters](https://mlsanity.com/paper/2508.17440/) (2025)
- [Fully analogue in-memory neural computing via quantum tunneling effect](https://mlsanity.com/paper/2510.23638/) (2025)
- [Spatial Analysis of Physical Reservoir Computers](https://mlsanity.com/paper/2108.01512/) (2021)
- [Spectral Methods in Complex Systems](https://mlsanity.com/paper/2509.05793/) (2025)

## Built on by (most cited first, 1 of 1)

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

## Abstract (arXiv)

Physical neural networks typically train linear synaptic weights while treating device nonlinearities as fixed. We show the opposite - by training the synaptic nonlinearity itself, as in Kolmogorov-Arnold Network (KAN) architectures, we yield markedly higher task performance per physical resource and improved performance-parameter scaling than conventional linear weight-based networks, demonstrating ability of KAN topologies to exploit reconfigurable nonlinear physical dynamics. We experimentally realise physical KANs in silicon-on-insulator devices we term 'Synaptic Nonlinear Elements' (SYNEs), operating at room temperature, microampere currents, 2 MHz speeds and ~750 fJ per nonlinear operation, with no observed degradation over 10^13 measurements and months-long timescales. We demonstrate nonlinear function regression, classification, and prediction of Li-Ion battery dynamics from noisy real-world multi-sensor data. Physical KANs outperform equivalently-parameterised software multilayer perceptron networks across all tasks, with up to two orders of magnitude fewer parameters, and two orders of magnitude fewer devices than linear weight based physical networks. These results establish learned physical nonlinearity as a hardware-native computational primitive for compact and efficient learning systems, and SYNE devices as effective substrates for heterogenous nonlinear computing.