Frequency-Based Reservoir computing

Reservoir computing has emerged as an efficient machine learning framework for predicting time series generated by dynamical systems. In contrast to other machine and deep learning approaches, a reservoir computing trains only the output layer via linear regression, leaving the reservoir (recurrent layer) untrained. This simplification makes reservoir computers easier to train and more amenable to experimentation. However, because current reservoirs consist of networks of randomly connected nodes and require the optimization of numerous hyperparameters, a framework that precisely explains how reservoir computing operates and how it can be optimized remains missing. Here, we propose a frequency-based reservoir inspired by the brain's oscillatory dynamics and its hierarchy of timescales. The frequency-based reservoir can be interpreted as an ensemble of independent oscillatory units, each processing a portion of the input's frequency content. This allows us to understand the reservoir's internal behavior by modeling it as a single unit driven by an external input. Borrowing from the theory of a nonlinear oscillator forced by complex periodic inputs, we found that units of the frequency-based reservoir selectively amplify and store specific input frequencies, which are then used for prediction. The frequency-based reservoir performs as well as or better than equivalent random reservoirs. Furthermore, the frequency-based approach can be optimized to improve short-term prediction, a property that random reservoirs lack. Finally, we show that the frequency-based reservoir can also predict complex spatiotemporal dynamics. Our results show that reservoir computing can be designed using brain properties and theoretical insights borrowed from the physics of forced nonlinear oscillators.

Dynamic Hypergraph Representation Learning for Multivariate Time Series without Prior Knowledge

Hypergraphs have the capacity to capture higher-dimensional relationships among entities across various domains, making them a subject of growing interest within the research community for understanding the structure and dynamics of complex systems. However, a key challenge is the derivation of hypergraph representations from time series data in situations where the structure of the hypergraph is limited or absent. In this study, we propose a model that constructs a dynamic hypergraph representation for multivariate time series without relying on prior knowledge of the data. This is achieved by applying community detection to the time series and transforming the resulting communities, obtained through an attention mechanism, into a hypergraph using a clique-based technique. Hypergraph representations are derived from different time series datasets, and the resulting hypergraphs are then used by a Dynamic Hypergraph Attention Convolution Network (DHACN) for multivariate time series predictions. This research advances the field of hypergraph representation by introducing a novel approach that is better suited to uncover high-order relationships without prior knowledge.