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= Reservoir Computing =

Overview
Reservoir computing is a framework for computation derived from recurrent neural network theory that maps input signals into higher dimensional computational spaces through the dynamics of a fixed, nonlinear system called a reservoir. After the input signal is fed into the reservoir, which is treated as a “black box,” a simple readout mechanism is trained to read the state of the reservoir and map it to the desired output. The first key benefit of this framework is that training is only performed at the output stage, as the reservoir dynamics remain fixed. The second is that the computational power of naturally available systems, both classical and quantum mechanical, can be utilized to reduce effective computational cost [existing Multiplex Network Source].

History
The concept of reservoir computing stems from the use of recursive connections within neural networks to create a complex dynamical system [existing Theory, Applications and Implementations...]. The resultant complexity of such recurrent neural networks was found to be useful in solving a variety of problems including language processing and dynamic system modeling [existing Theory, Applications and Implementations...]. However, training of recurrent neural networks is challenging and computationally expensive [existing Theory, Applications and Implementations...]. Reservoir computing reduces those training-related challenges by fixing the dynamics of the reservoir and only training the linear output layer [existing Theory, Applications and Implementations...].

Recent advances in both AI and quantum theory have given rise to the concept of quantum neural networks. These hold promise in quantum information processing, which is challenging to classical networks, but can also find application in solving classical problems. In 2018, a physical realization of a quantum reservoir computing architecture was demonstrated in the form of nuclear spins within a molecular solid. In 2019, another possible implementation of quantum reservoir processors was proposed in the form of two-dimensional fermionic lattices.

Reservoir
The ‘reservoir’ in reservoir computing is the internal structure of the computer, and must have two properties: it must be made up of individual, non-linear units, and it must be capable of storing information. The non-linearity describes the response of each unit to input, which is what allows reservoir computers to solve complex problems. Reservoirs are able to store information by connecting the units in recurrent loops, where the previous input affects the next response. The change in reaction due to the past allows the computers to be trained to complete specific tasks.

Reservoirs can be virtual or physical. Virtual reservoirs are typically randomly generated and are designed like neural networks [existing An overview of reservoir computing theory]. Virtual reservoirs can be designed to have non-linearity and recurrent loops, but, unlike neural networks, the connections between units are randomized and remain unchanged throughout computation. Physical reservoirs are possible because of the inherent non-linearity of certain natural systems. The interaction between ripples on the surface of water contains the nonlinear dynamics required in reservoir creation, and a pattern recognition RC was developed by first inputting ripples with electric motors then recording and analyzing the ripples in the readout.

Readout
The readout is a neural network layer that performs a linear transformation on the output of the reservoir. The weights of the readout layer are trained by analyzing the spatiotemporal patterns of the reservoir after excitation by known inputs, and by utilizing a training method such as linear regression or a Ridge regression. As its implementation depends on spatiotemporal reservoir patterns, the details of readout methods are tailored to each type of reservoir. For example, the readout for a reservoir computer using a container of liquid as its reservoir might entail observing spatiotemporal patterns on the surface of the liquid.

Context reverberation network [all of this text is existing]
An early example of reservoir computing was the context reverberation network. In this architecture, an input layer feeds into a high dimensional dynamical system which is read out by a trainable single-layer perceptron. Two kinds of dynamical system were described: a recurrent neural network with fixed random weights, and a continuous reaction-diffusion system inspired by Alan Turing’s model of morphogenesis. At the trainable layer, the perceptron associates current inputs with the signals that reverberate in the dynamical system; the latter were said to provide a dynamic "context" for the inputs. In the language of later work, the reaction-diffusion system served as the reservoir.

Echo state network
This reservoir computing framework can also be generalized to tree structured data, as demonstrated by the Tree Echo State Network (TreeESN) model [existing].

Liquid-state machine
This type of information processing is most relevant when time-dependent input signals depart from the mechanism’s internal dynamics. [existing Nonlinear transient computation] These departures cause transients or temporary altercations which are represented in the device’s output [source needed].

Quantum Reservoir Computing
Quantum reservoir computing utilizes the nonlinear nature of quantum mechanical interactions or processes to form the characteristic nonlinear reservoirs.

2-D Fermionic Lattices
In this architecture, randomized coupling between lattice sites grants the reservoir the “black box” property inherent to reservoir processors. The reservoir is then excited, which acts as the input, by an incident optical field. Readout occurs in the form of occupational numbers of lattice sites, which are naturally nonlinear functions of the input.

Nuclear Spins in a Molecular Solid
In this architecture, quantum mechanical coupling between spins of neighboring atoms within the molecular solid provides the non-linearity required to create the higher-dimensional computational space. The reservoir is then excited by radiofrequency electromagnetic radiation tuned to the resonance frequencies of relevant nuclear spins. Readout occurs by measuring the nuclear spin states.