Related papers: Reservoir kernels and Volterra series
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…
Quantum reservoir computing is an emergent field in which quantum dynamical systems are exploited for temporal information processing. In previous work, it was found a feature that makes a quantum reservoir valuable: contractive dynamics of…
The universal approximation properties with respect to $L ^p $-type criteria of three important families of reservoir computers with stochastic discrete-time semi-infinite inputs is shown. First, it is proved that linear reservoir systems…
The popular qubit framework has dominated recent work on quantum kernel machine learning, with results characterising expressivity, learnability and generalisation. As yet, there is no comparative framework to understand these concepts for…
Reservoir Computing (RC) refers to a Recurrent Neural Networks (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
Reservoir Computing offers a great computational framework where a physical system can directly be used as computational substrate. Typically a "reservoir" is comprised of a large number of dynamical systems, and is consequently…
Quantum reservoir computing is a class of quantum machine learning algorithms involving a reservoir of an echo state network based on a register of qubits, but the dependence of its memory capacity on the hyperparameters is still rather…
We make an attempt to understanding convolutional neural network by exploring the relationship between (deep) convolutional neural networks and Volterra convolutions. We propose a novel approach to explain and study the overall…
In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert…
Computing the expectation of kernel functions is a ubiquitous task in machine learning, with applications from classical support vector machines to exploiting kernel embeddings of distributions in probabilistic modeling, statistical…
We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back…
The importance of inference in Machine Learning (ML) has led to an explosive number of different proposals in ML, and particularly in Deep Learning. In an attempt to reduce the complexity of Convolutional Neural Networks, we propose a…
Physical reservoir computing is a computational framework that implements spatiotemporal information processing directly within physical systems. By exciting nonlinear dynamical systems and creating linear models from their state, we can…
Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…
Quantum reservoir computing (QRC) is a highly promising computational paradigm that leverages quantum systems as a computational resource for nonlinear information processing. While its application to time-series analysis is eagerly…
We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture…
This paper addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented…
In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing…
Reservoir computing is a highly efficient machine learning framework for processing temporal data by extracting features from the input signal and mapping them into higher dimensional spaces. Physical reservoir layers have been realized…