Chaotic Oscillator Networks for Classification Tasks

Abstract

Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator ensembles have led to the development of efficient signal processing frameworks that surpass traditional approaches. However, scaling such systems remains challenging due to the significant increase of computational resources and issues with training convergence. This study advances the state of the art by addressing the problem of data processing with ensembles of nonlinear oscillators that can be scaled up. In our approach, the processing is achieved as an anticipated local resonance or echo in a group of coupled chaotic oscillators, driven by external data input. Local resonance is enabled by tuning the coupling terms between the oscillators, which are approximated using the traditional artificial neural network and adapted to match the input feature distributions. Training the framework entails training this neural network to capture the dynamics of the entire oscillator system. The framework is evaluated using synthetic data and demonstrates an accuracy in machine learning classification task, while patterns recognition and dynamic system identification are also presented here as an extension of the functionality that involves additional modifications. Additionally, the universality of this approach is demonstrated by tests with different connections configurations between the oscillators and their types. The main advantage of the proposed framework is that it avoids hand-crafting explicit coupling terms, which requires expert knowledge and does not scale for large problems. Leveraging standard machine learning components simplifies both training and deployment of oscillator networks, enabling gradient-based optimization.