Related papers: Risk bounds for reservoir computing
Reservoir Computing is a class of Recurrent Neural Networks with internal weights fixed at random. Stability relates to the sensitivity of the network state to perturbations. It is an important property in Reservoir Computing as it directly…
Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become…
We establish empirical risk minimization principles for active learning by deriving a family of upper bounds on the generalization error. Aligning with empirical observations, the bounds suggest that superior query algorithms can be…
The paradigm of reservoir computing exploits the nonlinear dynamics of a physical reservoir to perform complex time-series processing tasks such as speech recognition and forecasting. Unlike other machine-learning approaches, reservoir…
Reservoir computing (RC) harnesses the intrinsic dynamics of a chaotic system, called the reservoir, to perform various time-varying functions. An important use-case of RC is the generation of target temporal sequences via a trainable…
Reservoir computing - information processing based on untrained recurrent neural networks with random connections - is expected to depend on the nonlinear properties of the neurons and the resulting oscillatory, chaotic, or fixpoint…
Reservoir computing is a well-established approach for processing data with a much lower complexity compared to traditional neural networks. Despite two decades of experimental progress, the core properties of reservoir computing (namely…
We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…
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…
We present a series of new and more favorable margin-based learning guarantees that depend on the empirical margin loss of a predictor. We give two types of learning bounds, both distribution-dependent and valid for general families, in…
Reservoir Computing is an Unconventional Computation model to perform computation on various different substrates, such as recurrent neural networks or physical materials. The method takes a 'black-box' approach, training only the outputs…
Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay…
A minimal model for reservoir computing is studied. We demonstrate that a reservoir computer exists that emulates given coupled maps by constructing a modularized network. We describe a possible mechanism for collapses of the emulation in…
Reservoir computing approximation and generalization bounds are proved for a new concept class of input/output systems that extends the so-called generalized Barron functionals to a dynamic context. This new class is characterized by the…
We study finite episodic Markov decision processes incorporating dynamic risk measures to capture risk sensitivity. To this end, we present two model-based algorithms applied to \emph{Lipschitz} dynamic risk measures, a wide range of risk…
This paper proposes a simple approach to derive efficient error bounds for learning multiple components with sparsity-inducing regularization. We show that for such regularization schemes, known decompositions of the Rademacher complexity…
The dramatic increase of autonomous systems subject to variable environments has given rise to the pressing need to consider risk in both the synthesis and verification of policies for these systems. This paper aims to address a few…
In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum…
This guide provides a reference for high-probability regret bounds in empirical risk minimization (ERM). The presentation is modular: we begin with intuition and general proof strategies, then state broadly applicable guarantees under…
We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds…