The Computational Capacity of LRC, Memristive and Hybrid Reservoirs

We extend the notion of memristive systems to capacitive and inductive elements, namely capacitors and inductors whose properties depend on the state and history of the system. All these elements show pinched hysteretic loops in the two constitutive variables that define them: current-voltage for the memristor, charge-voltage for the memcapacitor, and current-flux for the meminductor. We argue that these devices are common at the nanoscale where the dynamical properties of el...

Recent advancements in reservoir computing research have created a demand for analog devices with dynamics that can facilitate the physical implementation of reservoirs, promising faster information processing while consuming less energy and occupying a smaller area footprint. Studies have demonstrated that dynamic memristors, with nonlinear and short-term memory dynamics, are excellent candidates as information-processing devices or reservoirs for temporal classification and...

Reservoir computing (RC), first applied to temporal signal processing, is a recurrent neural network in which neurons are randomly connected. Once initialized, the connection strengths remain unchanged. Such a simple structure turns RC into a non-linear dynamical system that maps low-dimensional inputs into a high-dimensional space. The model's rich dynamics, linear separability, and memory capacity then enable a simple linear readout to generate adequate responses for variou...

Reservoir computing is a brain-inspired machine learning framework for processing temporal data by mapping inputs into high-dimensional spaces. Physical reservoir computers (PRCs) leverage native fading memory and nonlinearity in physical substrates, including atomic switches, photonics, volatile memristors, and, recently, memcapacitors, to achieve efficient high-dimensional mapping. Traditional PRCs often consist of homogeneous device arrays, which rely on input encoding met...

Reservoir computing is a computational framework suited for temporal/sequential data processing. It is derived from several recurrent neural network models, including echo state networks and liquid state machines. A reservoir computing system consists of a reservoir for mapping inputs into a high-dimensional space and a readout for pattern analysis from the high-dimensional states in the reservoir. The reservoir is fixed and only the readout is trained with a simple method su...

Advances in materials science have led to physical instantiations of self-assembled networks of memristive devices and demonstrations of their computational capability through reservoir computing. Reservoir computing is an approach that takes advantage of collective system dynamics for real-time computing. A dynamical system, called a reservoir, is excited with a time-varying signal and observations of its states are used to reconstruct a desired output signal. However, such ...

Reservoir computing is a recent trend in neural networks which uses the dynamical perturbations on the phase space of a system to compute a desired target function. We present how one can formulate an expectation of system performance in a simple class of reservoir computing called echo state networks. In contrast with previous theoretical frameworks, which only reveal an upper bound on the total memory in the system, we analytically calculate the entire memory curve as a fun...

In this work, we bound a machine's ability to learn based on computational limitations implied by physicality. We start by considering the information processing capacity (IPC), a normalized measure of the expected squared error of a collection of signals to a complete basis of functions. We use the IPC to measure the degradation under noise of the performance of reservoir computers, a particular kind of recurrent network, when constrained by physical considerations. First, w...

Networks of nanowires are currently being explored for a range of applications in brain-like (or neuromorphic) computing, and especially in reservoir computing (RC). Fabrication of real-world computing devices requires that the nanowires are deposited sequentially, leading to stacking of the wires on top of each other. However, most simulations of computational tasks using these systems treat the nanowires as 1D objects lying in a perfectly 2D plane - the effect of stacking o...

As one of the most important paradigms of recurrent neural networks, the echo state network (ESN) has been applied to a wide range of fields, from robotics to medicine, finance, and language processing. A key feature of the ESN paradigm is its reservoir --- a directed and weighted network of neurons that projects the input time series into a high dimensional space where linear regression or classification can be applied. Despite extensive studies, the impact of the reservoir ...