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Found 26 papers, 4 papers with code
State-Space Systems as Dynamic Generative Models
The results in this paper constitute a significant stochastic generalization of sufficient conditions for the deterministic echo state property to hold, in the sense that the stochastic echo state property can be satisfied under contractivity conditions that are strictly weaker than those in deterministic situations.
A Structure-Preserving Kernel Method for Learning Hamiltonian Systems
A structure-preserving kernel ridge regression method is presented that allows the recovery of potentially high-dimensional and nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields.
Invariant kernels on Riemannian symmetric spaces: a harmonic-analytic approach
This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter.
Geometric Learning with Positively Decomposable Kernels
Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS).
Learning multi-modal generative models with permutation-invariant encoders and tighter variational bounds
To encode latent variables from different modality subsets, Product-of-Experts (PoE) or Mixture-of-Experts (MoE) aggregation schemes have been routinely used and shown to yield different trade-offs, for instance, regarding their generative quality or consistency across multiple modalities.
Memory of recurrent networks: Do we compute it right?
Numerical evaluations of the memory capacity (MC) of recurrent neural networks reported in the literature often contradict well-established theoretical bounds.
Infinite-dimensional reservoir computing
The reservoir architectures used for the approximation and estimation of elements in the new class are randomly generated echo state networks with either linear or ReLU activation functions.
The Gaussian kernel on the circle and spaces that admit isometric embeddings of the circle
On Euclidean spaces, the Gaussian kernel is one of the most widely used kernels in applications.
Reservoir kernels and Volterra series
A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space.
Reservoir Computing for Macroeconomic Forecasting with Mixed Frequency Data
Macroeconomic forecasting has recently started embracing techniques that can deal with large-scale datasets and series with unequal release periods.
Transport in reservoir computing
Stochastic state contractivity can be satisfied by systems that are not state-contractive, which is a need typically evoked to guarantee the echo state property in reservoir computing.
Expressive Power of Randomized Signature
We consider the question whether the time evolution of controlled differential equations on general state spaces can be arbitrarily well approximated by (regularized) regressions on features generated themselves through randomly chosen dynamical systems of moderately high dimension.
Learning strange attractors with reservoir systems
This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space.
Fading memory echo state networks are universal
Echo state networks (ESNs) have been recently proved to be universal approximants for input/output systems with respect to various $L ^p$-type criteria.
Discrete-time signatures and randomness in reservoir computing
A new explanation of geometric nature of the reservoir computing phenomenon is presented.
Dimension reduction in recurrent networks by canonicalization
Many recurrent neural network machine learning paradigms can be formulated using state-space representations.
Memory and forecasting capacities of nonlinear recurrent networks
The notion of memory capacity, originally introduced for echo state and linear networks with independent inputs, is generalized to nonlinear recurrent networks with stationary but dependent inputs.
Approximation Bounds for Random Neural Networks and Reservoir Systems
This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights.
Risk bounds for reservoir computing
We analyze the practices of reservoir computing in the framework of statistical learning theory.
Differentiable reservoir computing
That research is complemented in this paper with the characterization of the differentiability of reservoir filters for very general classes of discrete-time deterministic inputs.
Reservoir Computing Universality With Stochastic Inputs
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.
Echo state networks are universal
This paper shows that echo state networks are universal uniform approximants in the context of discrete-time fading memory filters with uniformly bounded inputs defined on negative infinite times.
Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems
A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing.
Singular ridge regression with homoscedastic residuals: generalization error with estimated parameters
This paper characterizes the conditional distribution properties of the finite sample ridge regression estimator and uses that result to evaluate total regression and generalization errors that incorporate the inaccuracies committed at the time of parameter estimation.
Nonlinear memory capacity of parallel time-delay reservoir computers in the processing of multidimensional signals
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.
Quantitative evaluation of the performance of discrete-time reservoir computers in the forecasting, filtering, and reconstruction of stochastic stationary signals
This paper extends the notion of information processing capacity for non-independent input signals in the context of reservoir computing (RC).
