Related papers: Generalization Bounds for Quantum Learning via R\'…
We are motivated by the problem of providing strong generalization guarantees in the context of meta-learning. Existing generalization bounds are either challenging to evaluate or provide vacuous guarantees in even relatively simple…
Understanding the theoretical capabilities and limitations of quantum machine learning (QML) models to solve machine learning tasks is crucial to advancing both quantum software and hardware developments. Similarly to the classical setting,…
In a certain sense we generalize the recently introduced and extensively studied notion called quantum R\'enyi divergence (in another name, sandwiched R\'enyi relative entropy) and describe the structures of corresponding symmetries. More…
Adversarial robustness and generalization are both crucial properties of reliable machine learning models. In this paper, we study these properties in the context of quantum machine learning based on Lipschitz bounds. We derive…
Generalization under distribution shift remains a core challenge in modern machine learning, yet existing learning bound theory is limited to narrow, idealized settings and is non-estimable from samples. In this paper, we bridge the gap…
The ultimate limits for the quantum machine learning of quantum data are investigated by obtaining a generalisation of the celebrated No Free Lunch (NFL) theorem. We find a lower bound on the quantum risk (the probability that a trained…
We introduce an alternative closed form lower bound on the Gaussian process ($\mathcal{GP}$) likelihood based on the R\'enyi $\alpha$-divergence. This new lower bound can be viewed as a convex combination of the Nystr\"om approximation and…
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…
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…
Estimating divergences in a consistent way is of great importance in many machine learning tasks. Although this is a fundamental problem in nonparametric statistics, to the best of our knowledge there has been no finite sample exponential…
Previous research on PAC-Bayes learning theory has focused extensively on establishing tight upper bounds for test errors. A recently proposed training procedure called PAC-Bayes training, updates the model toward minimizing these bounds.…
We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing…
Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role…
We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output. The bounds provide an information-theoretic understanding of generalization in learning problems,…
Minimising upper bounds on the population risk or the generalisation gap has been widely used in structural risk minimisation (SRM) -- this is in particular at the core of PAC-Bayesian learning. Despite its successes and unfailing surge of…
In this work, our prime objective is to study the phenomena of quantum chaos and complexity in the machine learning dynamics of Quantum Neural Network (QNN). A Parameterized Quantum Circuits (PQCs) in the hybrid quantum-classical framework…
The entropy accumulation theorem, and its subsequent generalized version, is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size…
Uniform stability of a learning algorithm is a classical notion of algorithmic stability introduced to derive high-probability bounds on the generalization error (Bousquet and Elisseeff, 2002). Specifically, for a loss function with range…
Convergence bounds are one of the main tools to obtain information on the performance of a distributed machine learning task, before running the task itself. In this work, we perform a set of experiments to assess to which extent, and in…
Similarity learning has received a large amount of interest and is an important tool for many scientific and industrial applications. In this framework, we wish to infer the distance (similarity) between points with respect to an arbitrary…