Autonomous Learning of Attractors for Neuromorphic Computing with Wien Bridge Oscillator Networks

We present an oscillatory neuromorphic primitive implemented with networks of coupled Wien bridge oscillators and tunable resistive couplings. Phase relationships between oscillators encode patterns, and a local Hebbian learning rule continuously adapts the couplings, allowing learning and recall to emerge from the same ongoing analog dynamics rather than from separate training and inference phases. Using a Kuramoto-style phase model with an effective energy function, we show that learned phase patterns form attractor states and validate this behavior in simulation and hardware. We further realize a 2-4-2 architecture with a hidden layer of oscillators, whose bipartite visible-hidden coupling allows multiple internal configurations to produce the same visible phase states. When inputs are switched, transient spikes in energy followed by relaxation indicate how the network can reduce surprise by reshaping its energy landscape. These results support coupled oscillator circuits as a hardware platform for energy-based neuromorphic computing with autonomous, continuous learning.

💡 Research Summary

This paper presents a neuromorphic primitive built from networks of coupled Wien‑bridge oscillators whose phases encode information. Each oscillator generates a stable sinusoidal signal whose natural frequency is set by an RC bridge; coupling between oscillators is realized with tunable resistors (digital potentiometers) that can provide either positive (non‑inverting) or negative (inverting) interaction. The authors show that the collective dynamics of this hardware map directly onto a Kuramoto‑type phase model with an associated energy function that is mathematically equivalent to the Hopfield network energy. By fitting measured voltage waveforms to the Kuramoto model (using Hilbert‑transform phase extraction and gradient‑based parameter estimation), they demonstrate that the physical circuit indeed follows the predicted phase dynamics and minimizes the defined energy landscape.

Learning is achieved through a continuous, local Hebbian rule applied directly to the coupling strengths:

  (\dot K_{ij}= \eta \cos(\phi_i-\phi_j) - \lambda \eta K_{ij})

where (\eta) is a learning rate and (\lambda) implements Oja‑style weight decay. The rule depends only on the instantaneous phase difference between two oscillators, embodying the “neurons that fire together wire together” principle without any external clock or digital update step. During training, two oscillators are clamped to desired phases using a DDS generator, while the other two are nudged toward target phases with a small bias current. Alternating the clamped inputs between two binary patterns (