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.

Figures (10)

• Figure 1: Tested network topologies with a) Albert-Barnabasi graph, b) Erdős--Rényi (random) graph, c) Watts-Strogatz (small-world graph) , d) full connectivity used for classification tests.
• Figure 2: Network feeding and training schemes: a) The examples from scikit-learn dataset pixel intensity is converted to the pulse-train b) The pulse-train is fed to the network of nonlinear oscillators with specific topology and nonlinear output is trained using the 3-layer neural network. The pattern in (b) corresponds to scikit-learn digits patterns. The coupling in (b) corresponds to $\Phi$ in Eq.(5); c) network training with reservoirs.
• Figure 3: The time evolution of the network of FHN oscillators. The network topology corresponds to the one from Figure \ref{['fig:fig1']}, d). The following oscillators parameters are used to obtain this dynamics: FitzHugh-Nagumo $a=0.5, \sigma= 0.06, e_0 = 0.0, j_0= g(t)$. The network includes 1797 nodes and 3227412 edges, here we are displaying only 8 oscillators during time evolution of 2048 steps.
• Figure 4: Confusion matrix for classification of scikit-learn dataset using Ridge Regression optimization.
• Figure 5: Confusion matrix for classification of the dry bean dataset