Related papers: Reservoir kernels and Volterra series

A new approach suitable for distributed quantum machine learning and exhibiting memory is proposed for a photonic platform. This measurement-based quantum reservoir computing takes advantage of continuous variable cluster states as the main…

Approximation capability of reservoir systems whose reservoir is a recurrent neural network (RNN) is discussed. We show what we call uniform strong universality of RNN reservoir systems for a certain class of dynamical systems. This means…

Reservoir computing is a machine learning paradigm that uses a structure called a reservoir, which has nonlinearities and short-term memory. In recent years, reservoir computing has expanded to new functions such as the autonomous…

Reservoir computers are a type of neuromorphic computer that may be built a an analog system, potentially creating powerful computers that are small, light and consume little power. Typically a reservoir computer is build by connecting…

In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for…

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…

We analyze the properties of a quantum system composed of two coherently coupled quantum oscillators and show through simulations that it fulfills the two properties required for reservoir computing: non-linearity and fading memory. We…

Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approximation of the Laplace kernel, generated by a computationally…

Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner…

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…

The generalization properties of Gaussian processes depend heavily on the choice of kernel, and this choice remains a dark art. We present the Neural Kernel Network (NKN), a flexible family of kernels represented by a neural network. The…

Recurrent Neural Networks (RNNs) have been a prominent concept within artificial intelligence. They are inspired by Biological Neural Networks (BNNs) and provide an intuitive and abstract representation of how BNNs work. Derived from the…

Reservoir Computing is an emerging machine learning framework which is a versatile option for utilising physical systems for computation. In this paper, we demonstrate how a single node reservoir, made of a simple electronic circuit, can be…

Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances…

Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing…

From logical reasoning to mental simulation, biological and artificial neural systems possess an incredible capacity for computation. Such neural computers offer a fundamentally novel computing paradigm by representing data continuously and…

Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that…

We develop a framework for function classes generated by parametric ridge kernels: one-dimensional kernels composed with affine projections and averaged over a parameter measure. The induced kernels are positive definite, and the resulting…

We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…

Quantum reservoir computing is a machine learning framework that offers ease of training compared to other quantum neural networks, as it does not rely on gradient-based optimization. Learning is performed in a single step on the output…