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Found 17 papers, 4 papers with code
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.
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.
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.
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.
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).
