Reservoir computing

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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, non-linear system called a reservoir. [1] 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. [1] The first key benefit of this framework is that training is performed only at the readout stage, as the reservoir dynamics are fixed. [1] The second is that the computational power of naturally available systems, both classical and quantum mechanical, can be used to reduce the effective computational cost. [2]

Contents

History

The concept of reservoir computing stems from the use of recursive connections within neural networks to create a complex dynamical system. [3] It is a generalisation of earlier neural network architectures such as recurrent neural networks, liquid-state machines and echo-state networks. Reservoir computing also extends to physical systems that are not networks in the classical sense, but rather continuous systems in space and/or time: e.g. a literal "bucket of water" can serve as a reservoir that performs computations on inputs given as perturbations of the surface. [4] 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. [3] However, training of recurrent neural networks is challenging and computationally expensive. [3] Reservoir computing reduces those training-related challenges by fixing the dynamics of the reservoir and only training the linear output layer. [3]

A large variety of nonlinear dynamical systems can serve as a reservoir that performs computations. In recent years semiconductor lasers have attracted considerable interest as computation can be fast and energy efficient compared to electrical components.

Recent advances in both AI and quantum information theory have given rise to the concept of quantum neural networks. [5] These hold promise in quantum information processing, which is challenging to classical networks, but can also find application in solving classical problems. [5] [6] In 2018, a physical realization of a quantum reservoir computing architecture was demonstrated in the form of nuclear spins within a molecular solid. [6] However, the nuclear spin experiments in [6] did not demonstrate quantum reservoir computing per se as they did not involve processing of sequential data. Rather the data were vector inputs, which makes this more accurately a demonstration of quantum implementation of a random kitchen sink [7] algorithm (also going by the name of extreme learning machines in some communities). In 2019, another possible implementation of quantum reservoir processors was proposed in the form of two-dimensional fermionic lattices. [6] In 2020, realization of reservoir computing on gate-based quantum computers was proposed and demonstrated on cloud-based IBM superconducting near-term quantum computers. [8]

Reservoir computers have been used for time-series analysis purposes. In particular, some of their usages involve chaotic time-series prediction, [9] [10] separation of chaotic signals, [11] and link inference of networks from their dynamics. [12]

Classical reservoir computing

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. [13]

Reservoirs can be virtual or physical. [13] Virtual reservoirs are typically randomly generated and are designed like neural networks. [13] [3] 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. [13] 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. [1]

Readout

The readout is a neural network layer that performs a linear transformation on the output of the reservoir. [1] 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 a linear regression or a Ridge regression. [1] As its implementation depends on spatiotemporal reservoir patterns, the details of readout methods are tailored to each type of reservoir. [1] 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. [1]

Types

Context reverberation network

An early example of reservoir computing was the context reverberation network. [14] 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

The Tree Echo State Network (TreeESN) model represents a generalization of the reservoir computing framework to tree structured data. [15]

Liquid-state machine

Chaotic Liquid State Machine

The liquid (i.e. reservoir) of a Chaotic Liquid State Machine (CLSM), [16] [17] or chaotic reservoir, is made from chaotic spiking neurons but which stabilize their activity by settling to a single hypothesis that describes the trained inputs of the machine. This is in contrast to general types of reservoirs that don’t stabilize. The liquid stabilization occurs via synaptic plasticity and chaos control that govern neural connections inside the liquid. CLSM showed promising results in learning sensitive time series data. [16] [17]

Nonlinear transient computation

This type of information processing is most relevant when time-dependent input signals depart from the mechanism’s internal dynamics. [18] These departures cause transients or temporary altercations which are represented in the device’s output. [18]

Deep reservoir computing

The extension of the reservoir computing framework towards Deep Learning, with the introduction of Deep Reservoir Computing and of the Deep Echo State Network (DeepESN) model [19] [20] [21] [22] allows to develop efficiently trained models for hierarchical processing of temporal data, at the same time enabling the investigation on the inherent role of layered composition in recurrent neural networks.

Quantum reservoir computing

Quantum reservoir computing may use the nonlinear nature of quantum mechanical interactions or processes to form the characteristic nonlinear reservoirs [5] [6] [23] [8] but may also be done with linear reservoirs when the injection of the input to the reservoir creates the nonlinearity. [24] The marriage of machine learning and quantum devices is leading to the emergence of quantum neuromorphic computing as a new research area. [25]

Types

Gaussian states of interacting quantum harmonic oscillators

Gaussian states are a paradigmatic class of states of continuous variable quantum systems. [26] Although they can nowadays be created and manipulated in, e.g, state-of-the-art optical platforms, [27] naturally robust to decoherence, it is well-known that they are not sufficient for, e.g., universal quantum computing because transformations that preserve the Gaussian nature of a state are linear. [28] Normally, linear dynamics would not be sufficient for nontrivial reservoir computing either. It is nevertheless possible to harness such dynamics for reservoir computing purposes by considering a network of interacting quantum harmonic oscillators and injecting the input by periodical state resets of a subset of the oscillators. With a suitable choice of how the states of this subset of oscillators depends on the input, the observables of the rest of the oscillators can become nonlinear functions of the input suitable for reservoir computing; indeed, thanks to the properties of these functions, even universal reservoir computing becomes possible by combining the observables with a polynomial readout function. [24] In principle, such reservoir computers could be implemented with controlled multimode optical parametric processes, [29] however efficient extraction of the output from the system is challenging especially in the quantum regime where measurement back-action must be taken into account.

2-D quantum dot lattices

In this architecture, randomized coupling between lattice sites grants the reservoir the “black box” property inherent to reservoir processors. [5] 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. [5]

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. [6] The reservoir is then excited by radiofrequency electromagnetic radiation tuned to the resonance frequencies of relevant nuclear spins. [6] Readout occurs by measuring the nuclear spin states. [6]

Reservoir computing on gate-based near-term superconducting quantum computers

The most prevalent model of quantum computing is the gate-based model where quantum computation is performed by sequential applications of unitary quantum gates on qubits of a quantum computer. [30] A theory for the implementation of reservoir computing on a gate-based quantum computer with proof-of-principle demonstrations on a number of IBM superconducting noisy intermediate-scale quantum (NISQ) computers [31] has been reported in. [8]

See also

Related Research Articles

<span class="mw-page-title-main">Artificial neural network</span> Computational model used in machine learning, based on connected, hierarchical functions

Artificial neural networks are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains.

<span class="mw-page-title-main">Quantum computing</span> Technology that uses quantum mechanics

A quantum computer is a computer that takes advantage of quantum mechanical phenomena.

In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is usually used for those algorithms which seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement.

A recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to the uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition. The term "recurrent neural network" is used to refer to the class of networks with an infinite impulse response, whereas "convolutional neural network" refers to the class of finite impulse response. Both classes of networks exhibit temporal dynamic behavior. A finite impulse recurrent network is a directed acyclic graph that can be unrolled and replaced with a strictly feedforward neural network, while an infinite impulse recurrent network is a directed cyclic graph that can not be unrolled.

Optical computing or photonic computing uses light waves produced by lasers or incoherent sources for data processing, data storage or data communication for computing. For decades, photons have shown promise to enable a higher bandwidth than the electrons used in conventional computers.

<span class="mw-page-title-main">Quantum neural network</span> Quantum Mechanics in Neural Networks

Quantum neural networks are computational neural network models which are based on the principles of quantum mechanics. The first ideas on quantum neural computation were published independently in 1995 by Subhash Kak and Ron Chrisley, engaging with the theory of quantum mind, which posits that quantum effects play a role in cognitive function. However, typical research in quantum neural networks involves combining classical artificial neural network models with the advantages of quantum information in order to develop more efficient algorithms. One important motivation for these investigations is the difficulty to train classical neural networks, especially in big data applications. The hope is that features of quantum computing such as quantum parallelism or the effects of interference and entanglement can be used as resources. Since the technological implementation of a quantum computer is still in a premature stage, such quantum neural network models are mostly theoretical proposals that await their full implementation in physical experiments.

Unconventional computing is computing by any of a wide range of new or unusual methods. It is also known as alternative computing.

A liquid state machine (LSM) is a type of reservoir computer that uses a spiking neural network. An LSM consists of a large collection of units. Each node receives time varying input from external sources as well as from other nodes. Nodes are randomly connected to each other. The recurrent nature of the connections turns the time varying input into a spatio-temporal pattern of activations in the network nodes. The spatio-temporal patterns of activation are read out by linear discriminant units.

<span class="mw-page-title-main">Echo state network</span> Type of reservoir computer

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. The connectivity and weights of hidden neurons are fixed and randomly assigned. The weights of output neurons can be learned so that the network can produce or reproduce specific temporal patterns. The main interest of this network is that although its behavior is non-linear, the only weights that are modified during training are for the synapses that connect the hidden neurons to output neurons. Thus, the error function is quadratic with respect to the parameter vector and can be differentiated easily to a linear system.

<span class="mw-page-title-main">Spiking neural network</span> Artificial neural network that mimics neurons

Spiking neural networks (SNNs) are artificial neural networks that more closely mimic natural neural networks. In addition to neuronal and synaptic state, SNNs incorporate the concept of time into their operating model. The idea is that neurons in the SNN do not transmit information at each propagation cycle, but rather transmit information only when a membrane potential—an intrinsic quality of the neuron related to its membrane electrical charge—reaches a specific value, called the threshold. When the membrane potential reaches the threshold, the neuron fires, and generates a signal that travels to other neurons which, in turn, increase or decrease their potentials in response to this signal. A neuron model that fires at the moment of threshold crossing is also called a spiking neuron model.

<span class="mw-page-title-main">Activation function</span> Artificial neural network node function

Activation function of a node in an artificial neural network is a function that calculates the output of the node. Nontrivial problems can be solved only using a nonlinear activation function. Modern activation functions include the smooth version of the ReLU, the GELU, which was used in the 2018 BERT model, the logistic (sigmoid) function used in the 2012 speech recognition model developed by Hinton et al, the ReLU used in the 2012 AlexNet computer vision model and in the 2015 ResNet model.

There are many types of artificial neural networks (ANN).

<span class="mw-page-title-main">Deep learning</span> Branch of machine learning

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<span class="mw-page-title-main">Quantum machine learning</span> Interdisciplinary research area at the intersection of quantum physics and machine learning

Quantum machine learning is the integration of quantum algorithms within machine learning programs.

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<span class="mw-page-title-main">Large width limits of neural networks</span> Feature of artificial neural networks

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<span class="mw-page-title-main">Physics-informed neural networks</span> Technique to solve partial differential equations

Physics-informed neural networks (PINNs) are a type of universal function approximators that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs). They overcome the low data availability of some biological and engineering systems that makes most state-of-the-art machine learning techniques lack robustness, rendering them ineffective in these scenarios. The prior knowledge of general physical laws acts in the training of neural networks (NNs) as a regularization agent that limits the space of admissible solutions, increasing the correctness of the function approximation. This way, embedding this prior information into a neural network results in enhancing the information content of the available data, facilitating the learning algorithm to capture the right solution and to generalize well even with a low amount of training examples.

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