We describe a thermodynamic-inspired computing paradigm based on oscillatory neural networks (ONNs). While ONNs have been widely studied as Ising machines for tackling complex combinatorial optimization problems, this work investigates their feasibility in solving linear algebra problems, specifically the inverse matrix. Grounded in thermodynamic principles, we analytically demonstrate that the linear approximation of the coupled Kuramoto oscillator model leads to the inverse matrix solution. Numerical simulations validate the theoretical framework, and we examine the parameter regimes that computation has the highest accuracy.

We propose a novel, brain-inspired deep neural network model known as the Deep Oscillatory Neural Network (DONN). Deep neural networks like the Recurrent Neural Networks indeed possess sequence processing capabilities but the internal states of the network are not designed to exhibit brain-like oscillatory activity. With this motivation, the DONN is designed to have oscillatory internal dynamics. Neurons of the DONN are either nonlinear neural oscillators or traditional neurons with sigmoidal or ReLU activation. The neural oscillator used in the model is the Hopf oscillator, with the dynamics described in the complex domain. Input can be presented to the neural oscillator in three possible modes. The sigmoid and ReLU neurons also use complex-valued extensions. All the weight stages are also complex-valued. Training follows the general principle of weight change by minimizing the output error and therefore has an overall resemblance to complex backpropagation. A generalization of DONN to convolutional networks known as the Oscillatory Convolutional Neural Network is also proposed. The two proposed oscillatory networks are applied to a variety of benchmark problems in signal and image/video processing. The performance of the proposed models is either comparable or superior to published results on the same data sets.

Researchers at the University of Gothenburg and Tohoku University jointly reported on an important experimental advance in this direction, demonstrating a novel voltage-controlled spintronic microwave oscillator capable of closely imitating the non-linear oscillatory neural networks of the human brain. The research team developed a voltage-controlled spintronic oscillator, whose properties can be strongly tuned, with negligible energy consumption. "This is an important breakthrough as these so-called spin Hall nano-oscillators (SHNOs) can act as interacting oscillator-based neurons but have so far lacked an energy-efficient tuning scheme -- an essential prerequisite to train the neural networks for cognitive neuromorphic tasks," proclaimed Shunsuke Fukami, co-author of the study. "The expansion of the developed technology can also drive the tuning of the synaptic interactions between each pair of spintronic neurons in a large complex oscillatory neural network." Earlier this year, the Johan Åkerman group at the University of Gothenburg demonstrated, for the first time, 2D mutually synchronized arrays accommodating 100 SHNOs while occupying an area of less than a square micron.

Physicists from Petrozavodsk State University have proposed a new method for oscillatory neural network to recognize simple images. Such networks with an adjustable synchronous state of individual neurons have, presumably, dynamics similar to neurons in the living brain. AN oscillatory neural network is a complex interlacing of interacting elements (oscillators) that are able to receive and transmit oscillations of a certain frequency. Receiving signals of various frequencies from preceding elements, the artificial neuron oscillator can synchronize its rhythm with these fluctuations. As a result, in the network, some of the elements are synchronized with each other (periodically and simultaneously activated), and other elements are not synchronized.