Related papers: Quantum Reservoir Computing and Risk Bounds
We simulate the nonlinear chaotic dynamics of Lorenz-type models for a classical two-dimensional thermal convection flow with 3 and 8 degrees of freedom by a hybrid quantum--classical reservoir computing model. The high-dimensional quantum…
Quantum computers are known to provide speedups over classical state-of-the-art machine learning methods in some specialized settings. For example, quantum kernel methods have been shown to provide an exponential speedup on a learning…
Many machine learning models are vulnerable to adversarial attacks; for example, adding adversarial perturbations that are imperceptible to humans can often make machine learning models produce wrong predictions with high confidence.…
Recent advances in quantum computing have demonstrated its potential to significantly enhance the analysis and forecasting of complex classical data. Among these, quantum reservoir computing has emerged as a particularly powerful approach,…
Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for…
Quantum reservoir computing is a computing approach which aims at utilising the complexity and high-dimensionality of small quantum systems, together with the fast trainability of reservoir computing, in order to solve complex tasks. The…
Quantum reservoir computing uses the dynamics of quantum systems to process temporal data, making it particularly well-suited for machine learning with noisy intermediate-scale quantum devices. Recent developments have introduced…
In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…
We introduce the technique of generic chaining and majorizing measures for controlling sequential Rademacher complexity. We relate majorizing measures to the notion of fractional covering numbers, which we show to be dominated in terms of…
We investigate approaches to regularisation during fine-tuning of deep neural networks. First we provide a neural network generalisation bound based on Rademacher complexity that uses the distance the weights have moved from their initial…
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…
We investigate the capacity control provided by dropout in various machine learning problems. First, we study dropout for matrix completion, where it induces a data-dependent regularizer that, in expectation, equals the weighted trace-norm…
In this paper, we propose a new framework to study the generalization property of classifier chains trained over observations associated with multiple and interdependent class labels. The results are based on large deviation inequalities…
Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
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 identify a hidden bottleneck in the information processing capacity of linear reservoir computers. When the measured features evolve linearly in the reservoir and the output is formed by linear readout with bias, we show that the…
In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat…
Quantum Reservoir Computing (QRC) harnesses quantum systems to tackle intricate computational problems with exceptional efficiency and minimized energy usage. This paper presents a QRC framework that utilizes a minimalistic quantum…
We study Rademacher processes where the coefficients are functions evaluated at fixed, but arbitrary covariables. Specifically, we assume the function class under consideration to be parametrized by the standard cocube in l dimensions and…