Wien Bridge Oscillator Networks Enable Autonomous Learning of Attractor States

Neuromorphic computing seeks to mimic the brain’s efficiency, and a key challenge lies in creating hardware that learns continuously without distinct training and inference stages. Riley Acker, Aman Desai, and Garrett Kenyon, alongside Frank Barrows, all from Los Alamos National Laboratory, now demonstrate a novel approach using networks of coupled Wien bridge oscillators. Their research establishes how these oscillating circuits can learn and recall patterns through ongoing analog dynamics, effectively reshaping their internal energy landscape to reduce ‘surprise’ when presented with new inputs. This achievement supports coupled oscillator circuits as a promising hardware platform for energy-based computing with autonomous, continuous learning, potentially offering a more brain-like and energy-efficient computing paradigm.

Researchers have now demonstrated a novel approach using networks of coupled Wien bridge oscillators, establishing how these oscillating circuits can learn and recall patterns through ongoing analog dynamics. This achievement supports coupled oscillator circuits as a promising hardware platform for energy-based computing with autonomous, continuous learning, potentially offering a more brain-like and energy-efficient computing paradigm. The research explores the development and analysis of neuromorphic computing systems based on coupled oscillatory networks, aiming to move beyond traditional digital computing paradigms by exploiting the inherent parallelism, energy efficiency, and robustness of oscillatory networks.

The team specifically chose Wien-bridge oscillators as the building blocks for their networks, as these oscillators offer advantages in terms of tunability, stability, and ease of implementation in hardware. They implemented and tested various synaptic plasticity rules, including mechanisms inspired by spike-timing-dependent plasticity, allowing the network to learn associations and patterns from input data. A significant contribution is the development of a software framework based on JAX and Equinox for simulating and analyzing these oscillatory networks, allowing for efficient numerical simulations, automatic differentiation, and optimization of network parameters.,.

Oscillator Networks Enable Robust Associative Memory

Scientists have engineered an oscillatory primitive based on networks of coupled Wien bridge oscillators, creating a novel platform for associative memory. These oscillators, functioning as computational units, are interconnected with tunable resistive couplings, allowing for dynamic adjustment of signal flow between them. The team implemented a 2-4-2 architecture, featuring a hidden layer of oscillators positioned between input and output layers, enabling complex pattern recognition and recall. To establish learning and recall within the same system, researchers employed a local Hebbian learning rule, continuously adapting the resistive couplings based on the correlation of oscillator signals, bypassing traditional separate training and inference phases. The study pioneered the use of a Kuramoto-style phase model, incorporating an effective energy function to analyze the learned phase patterns and demonstrate their formation as attractor states, validated through both simulation and hardware implementation.,.

Oscillator Networks Enable Continuous Associative Memory

Scientists have developed a novel neuromorphic primitive based on networks of coupled Wien bridge oscillators, demonstrating a system capable of phase-based associative memory with autonomous, continuous learning. The core of this work lies in utilizing the phase relationships between oscillators to encode patterns, and a local Hebbian learning rule continuously adapts the coupling strengths between them. This allows the same physical dynamics to support both storage and retrieval of information, eliminating the need for separate training and inference phases. The team constructed a network of four Wien bridge oscillators, each producing a stable sinusoidal oscillation with a tunable frequency.

Resistive coupling between these oscillators allows for phase adjustments, effectively “pulling” or “pushing” phases together. This architecture mirrors the structure of a Boltzmann machine, creating a non-unique internal energy landscape suitable for complex pattern recognition. Experiments validate that learned phase patterns form attractor states, confirming the system’s ability to stabilize on specific configurations representing stored information. Further investigation involved a 2-4-2 multilayer architecture with a hidden layer of oscillators, demonstrating the ability to create more complex internal representations. This bipartite coupling structure allows multiple internal configurations to produce the same visible phase states, enhancing the network’s capacity and robustness. When inputs are switched, transient spikes in energy are recorded, followed by relaxation as the network reshapes its energy landscape to minimize surprise and adapt to new information, enabling continuous learning.,.

Associative Memory via Oscillator Network Dynamics

This research demonstrates that networks of coupled Wien bridge oscillators can function as a continuous-time oscillatory neuromorphic primitive for associative memory, offering a novel approach to hardware-based computation. By encoding patterns through phase relationships between oscillators and employing a local Hebbian learning rule, the system shapes its effective coupling matrix, enabling desired phase patterns to become stable attractors within the network’s dynamics. Importantly, learning and recall emerge from the same ongoing analog process, eliminating the need for separate training and inference phases and allowing for autonomous, continuous operation. The team observed that the network minimizes an effective energy over phase configurations, with transient energy spikes occurring when inputs change, followed by relaxation into a new attractor state, suggesting a mechanism for learning driven by ongoing dynamics. The system exhibits robustness to frequency dispersion and device mismatch, a critical advantage for real-world implementation, and the use of a hidden layer in a 2-4-2 architecture mirrors the functionality of a Boltzmann machine, allowing for rich internal representations.