Related papers: Quantum Reservoir Computing and Risk Bounds

Quantum reservoir computing employs fixed quantum dynamics as a feature map for machine learning. Integrating multiple quantum reservoirs, however, raises a key question: how few inter-module connections are sufficient to match the…

We develop a general framework for margin-based multicategory classification in metric spaces. The basic work-horse is a margin-regularized version of the nearest-neighbor classifier. We prove generalization bounds that match the state of…

Realizing the promise of quantum information processing remains a daunting task, given the omnipresence of noise and error. Adapting noise-resilient classical computing modalities to quantum mechanics may be a viable path towards near-term…

Quantum machine learning offers a transformative approach to solving complex problems, but the inherent noise hinders its practical implementation in near-term quantum devices. This obstacle makes it difficult to understand the…

Quantum reservoir computing (QRC) is an emerging framework for near-term quantum machine learning that offers in-memory processing, platform versatility across analogue and digital systems, and avoids typical trainability challenges such as…

Quantum machine learning (QML) is expected to offer new opportunities to process high-dimensional data efficiently by exploiting the exponentially large state space of quantum systems. In this work, we apply quantum extreme reservoir…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

Quantum computers require precise control over parameters and careful engineering of the underlying physical system. In contrast, neural networks have evolved to tolerate imprecision and inhomogeneity. Here, using a reservoir computing…

Reservoir computing (RC) is a machine learning paradigm that harnesses dynamical systems as computational resources. In its quantum extension -- quantum reservoir computing (QRC) -- these principles are applied to quantum systems, whose…

We probabilistically bound the error of a solution to a radial network topology learning problem where both connectivity and line parameters are estimated. In our model, data errors are introduced by the precision of the sensors, i.e.,…

We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both…

In this work we consider the learning setting where, in addition to the training set, the learner receives a collection of auxiliary hypotheses originating from other tasks. We focus on a broad class of ERM-based linear algorithms that can…

This paper studies a quantum risk-sensitive estimation problem and investigates robustness properties of the filter. This is a direct extension to the quantum case of analogous classical results. All investigations are based on a discrete…

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…

Quantum Extreme Learning Machines (QELMs) have emerged as a promising framework for quantum machine learning. Their appeal lies in the rich feature map induced by the dynamics of a quantum substrate - the quantum reservoir - and the…

Many systems of interest in cryptography consist of equations of the same degree. Under the assumption that the degree of regularity is finite, we prove upper bounds on the degree of regularity of a system of equations of the same degree,…

Online learning methods yield sequential regret bounds under minimal assumptions and provide in-expectation risk bounds for statistical learning. However, despite the apparent advantage of online guarantees over their statistical…

The generalization gap of a classifier is related to the complexity of the set of functions among which the classifier is chosen. We study a family of low-complexity classifiers consisting of thresholding a random one-dimensional feature.…

Quantum machine learning models have shown successful generalization performance even when trained with few data. In this work, through systematic randomization experiments, we show that traditional approaches to understanding…

Following the seminal approach by Talagrand, the concept of Rademacher complexity for independent sequences of random variables is extended to Markov chains. The proposed notion of "block Rademacher complexity" (of a class of functions)…