Related papers: Reservoir kernels and Volterra series
A new explanation of geometric nature of the reservoir computing phenomenon is presented. Reservoir computing is understood in the literature as the possibility of approximating input/output systems with randomly chosen recurrent neural…
Much effort has been devoted in the last two decades to characterize the situations in which a reservoir computing system exhibits the so-called echo state (ESP) and fading memory (FMP) properties. These important features amount, in…
Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the…
The Volterra signature extends the classical path signature by incorporating general matrix-valued kernel into its iterated integral structure, yielding a flexible notion of memory for time series. Its components can be viewed as successive…
This work proposes a time series prediction method based on the kernel view of linear reservoirs. In particular, the time series motifs of the reservoir kernel are used as representational basis on which general readouts are constructed. We…
Reservoir computing is a versatile paradigm in computational neuroscience and machine learning, that exploits the non-linear dynamics of a dynamical system - the reservoir - to efficiently process time-dependent information. Since its…
Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems…
Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse…
This work focuses on quantum reservoir computing and, in particular, on quantum Wiener architectures (qWiener), consisting of quantum linear dynamic networks with weak continuous measurements and classical nonlinear static readouts. We…
Several topological and analytical notions of continuity and fading memory for causal and time-invariant filters are introduced, and the relations between them are analyzed. A significant generalization of the convolution theorem that…
Volterra series representation is a powerful mathematical model for nonlinear circuits. However, the difficulties in determining higher-order Volterra kernels limited its broader applications. In this work, a systematic approach that…
Since its introduction, the Discrete Variable Representation (DVR) basis set has become an invaluable representation of state vectors and Hermitian operators in non-relativistic quantum dynamics and spectroscopy calculations. On the other…
Higher-order learning is fundamentally rooted in exploiting compositional features. It clearly hinges on enriching the representation by more elaborate interactions of the data which, in turn, tends to increase the model complexity of…
Quantum reservoir computing offers a promising route for time series learning by modelling sequential data via rich quantum dynamics while the only training required happens at the level of a lightweight classical readout. However, studies…
Next-generation reservoir computing (NG-RC) has attracted much attention due to its excellent performance in spatio-temporal forecasting of complex systems and its ease of implementation. This paper shows that NG-RC can be encoded as a…
Recurrent neural networks (RNNs) are brain-inspired models widely used in machine learning for analyzing sequential data. The present work is a contribution towards a deeper understanding of how RNNs process input signals using the response…
Reservoir computation models form a subclass of recurrent neural networks with fixed non-trainable input and dynamic coupling weights. Only the static readout from the state space (reservoir) is trainable, thus avoiding the known problems…
The Volterra series can be used to model a large subset of nonlinear, dynamic systems. A major drawback is the number of coefficients required model such systems. In order to reduce the number of required coefficients, Laguerre polynomials…
Volterra analysis and its variants have long been prominent among methods for modeling multi-input non-linear systems. The product of Volterra analysis, the Volterra kernels, are particularly suited to quantifying intra- and inter-input…
We continue our earlier investigation on generalized reproducing kernels, in connection with the complex geometry of $C^*$- algebra representations, by looking at them as the objects of an appropriate category. Thus the correspondence…