Learning Nonlinear Heterogeneity in Physical Kolmogorov-Arnold Networks

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 ~250 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.

Machine learning using magnetic stochastic synapses

The impressive performance of artificial neural networks has come at the cost of high energy usage and CO$_2$ emissions. Unconventional computing architectures, with magnetic systems as a candidate, have potential as alternative energy-efficient hardware, but, still face challenges, such as stochastic behaviour, in implementation. Here, we present a methodology for exploiting the traditionally detrimental stochastic effects in magnetic domain-wall motion in nanowires. We demonstrate functional binary stochastic synapses alongside a gradient learning rule that allows their training with applicability to a range of stochastic systems. The rule, utilising the mean and variance of the neuronal output distribution, finds a trade-off between synaptic stochasticity and energy efficiency depending on the number of measurements of each synapse. For single measurements, the rule results in binary synapses with minimal stochasticity, sacrificing potential performance for robustness. For multiple measurements, synaptic distributions are broad, approximating better-performing continuous synapses. This observation allows us to choose design principles depending on the desired performance and the device's operational speed and energy cost. We verify performance on physical hardware, showing it is comparable to a standard neural network.