# Low-power analogue neural networks with trainable nonlinear connections for continuous control

arXiv: https://arxiv.org/abs/2606.23742 · HTML: https://mlsanity.com/paper/2606.23742/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 21 Jun 2026.

## Builds on (most cited first, 11 of 11)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [A perspective on physical reservoir computing with nanomagnetic devices](https://mlsanity.com/paper/2212.04851/) (2022)
- [Trainable and Dynamic Computing: Error Backpropagation through Physical Media](https://mlsanity.com/paper/1407.6637/) (2014)
- [Relative intrinsic dimensionality is intrinsic to learning](https://mlsanity.com/paper/2311.07579/) (2023)
- [Noise-Aware Training of Neuromorphic Dynamic Device Networks](https://mlsanity.com/paper/2401.07387/) (2024)
- [Small-scale photonic Kolmogorov-Arnold networks using standard telecom nonlinear modules](https://mlsanity.com/paper/2604.08432/) (2026)

## Abstract (arXiv)

Physical neural networks promise low-power machine learning by computing directly with analogue device physics, but most architectures force nonlinear device responses to act as scalar weights. Inspired by Kolmogorov-Arnold networks, we place trainable nonlinear functions on the connections, making each physical connection a learnable computational element. Realising these functions as analogue band-pass filters on field-programmable analogue arrays, we find that the benefit is task-dependent and follows from the smoothness of the physical basis: the networks represent smooth, continuously valued targets, including robotic kinematics, continuous control, and photovoltaic maximum-power-point tracking, with far fewer nodes and connections than multilayer perceptrons, but offer no parameter-efficiency advantage on classification-like decision boundaries. Trained networks transfer to hardware across approximately 35,000 connections with quantified fidelity, and a dedicated CMOS implementation is projected to operate at approximately 30 microwatts. A memristive realisation reproduces the same behaviour in simulation, indicating that the advantage comes from placing trainable nonlinearity on connections, rather than from a particular device.