Information Processing Capacity of a Single-Node Reservoir Computer: An Experimental Evaluation

A QR Code for the Brain: A dynamical systems framework for computing neurophysiological biomarkers

Neural circuits are often considered the bridge connecting genetic causes and behavior. Whereas prenatal neural circuits are believed to be derived from a combination of genetic and intrinsic activity, postnatal circuits are largely influenced by exogenous activity and experience. A dynamical neuroelectric field maintained by neural activity is proposed as the fundamental information processing substrate of cognitive function. Time series measurements of the neuroelectric field can be collected by scalp sensors and used to mathematically quantify the essential dynamical features of the neuroelectric field by constructing a digital twin of the dynamical system phase space. The multiscale nonlinear values that result can be organized into tensor data structures, from which latent features can be extracted using tensor factorization. These latent features can be mapped to behavioral constructs to derive digital biomarkers. This computational framework provides a robust method for incorporating neurodynamical measures into neuropsychiatric biomarker discovery.

Quantifying the diversity of multiple time series with an ordinal symbolic approach

The main motivation of this paper is to introduce the ordinal diversity, a symbolic tool able to quantify the degree of diversity of multiple time series. Analytical, numerical, and experimental analyses illustrate the utility of this measure to quantify how diverse, from an ordinal perspective, a set of many time series is. We have shown that ordinal diversity is able to characterize dynamical richness and dynamical transitions in stochastic processes and deterministic systems, including chaotic regimes. This ordinal tool also serves to identify optimal operating conditions in the machine learning approach of reservoir computing. These results allow us to envision potential applications for the handling and characterization of large amounts of data, paving the way for addressing some of the most pressing issues facing the current big data paradigm.

Reservoir computing with noise

This paper investigates in detail the effects of measurement noise on the performance of reservoir computing. We focus on an application in which reservoir computers are used to learn the relationship between different state variables of a chaotic system. We recognize that noise can affect the training and testing phases differently. We find that the best performance of the reservoir is achieved when the strength of the noise that affects the input signal in the training phase equals the strength of the noise that affects the input signal in the testing phase. For all the cases we examined, we found that a good remedy to noise is to low-pass filter the input and the training/testing signals; this typically preserves the performance of the reservoir, while reducing the undesired effects of noise.

Deriving task specific performance from the information processing capacity of a reservoir computer

In the reservoir computing literature, the information processing capacity is frequently used to characterize the computing capabilities of a reservoir. However, it remains unclear how the information processing capacity connects to the performance on specific tasks. We demonstrate on a set of standard benchmark tasks that the total information processing capacity correlates poorly with task specific performance. Further, we derive an expression for the normalized mean square error of a task as a weighted function of the individual information processing capacities. Mathematically, the derivation requires the task to have the same input distribution as used to calculate the information processing capacities. We test our method on a range of tasks that violate this requirement and find good qualitative agreement between the predicted and the actual errors as long as the task input sequences do not have long autocorrelation times. Our method offers deeper insight into the principles governing reservoir computing performance. It also increases the utility of the evaluation of information processing capacities, which are typically defined on i.i.d. input, even if specific tasks deliver inputs stemming from different distributions. Moreover, it offers the possibility of reducing the experimental cost of optimizing physical reservoirs, such as those implemented in photonic systems.