Related papers: Tight Generalization Bound for Supervised Quantum …
Modern deep neural networks (DNNs) represent a formidable challenge for theorists: according to the commonly accepted probabilistic framework that describes their performance, these architectures should overfit due to the huge number of…
PAC-Bayesian is an analysis framework where the training error can be expressed as the weighted average of the hypotheses in the posterior distribution whilst incorporating the prior knowledge. In addition to being a pure generalization…
It remains unclear whether quantum machine learning (QML) has real advantages when dealing with practical and meaningful tasks. Encoding classical data into quantum states is one of the key steps in QML. Amplitude encoding has been widely…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
We study the generalization error of stochastic learning algorithms from an information-theoretic perspective, with a particular emphasis on deriving sharper bounds for differentially private algorithms. It is well known that the…
The mechanisms by which certain training interventions, such as increasing learning rates and applying batch normalization, improve the generalization of deep networks remains a mystery. Prior works have speculated that "flatter" solutions…
Several important models of machine learning algorithms have been successfully generalized to the quantum world, with potential speedup to training classical classifiers and applications to data analytics in quantum physics that can be…
Continual learning (CL) has emerged as a dominant paradigm for acquiring knowledge from sequential tasks while avoiding catastrophic forgetting. Although many CL methods have been proposed to show impressive empirical performance, the…
Since the celebrated works of Russo and Zou (2016,2019) and Xu and Raginsky (2017), it has been well known that the generalization error of supervised learning algorithms can be bounded in terms of the mutual information between their input…
Data representation is crucial for the success of machine learning models. In the context of quantum machine learning with near-term quantum computers, equally important considerations of how to efficiently input (encode) data and…
Established approaches to obtain generalization bounds in data-driven optimization and machine learning mostly build on solutions from empirical risk minimization (ERM), which depend crucially on the functional complexity of the hypothesis…
In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our…
Data-driven algorithms can adapt their internal structure or parameters to inputs from unknown application-specific distributions, by learning from a training sample of inputs. Several recent works have applied this approach to problems in…
We derive generalization error bounds for the training of two-layer neural networks without assuming boundedness of the loss function, using Wasserstein distance estimates on the discrepancy between a probability distribution and its…
Quantum noise is conventionally viewed as a fundamental obstacle in near-term quantum computing, motivating extensive error correction and mitigation strategies. We present numerical evidence that challenges this consensus. Through…
Generalization beyond a training dataset is a main goal of machine learning, but theoretical understanding of generalization remains an open problem for many models. The need for a new theory is exacerbated by recent observations in deep…
In this paper, the worst-case probability measure over the data is introduced as a tool for characterizing the generalization capabilities of machine learning algorithms. More specifically, the worst-case probability measure is a Gibbs…
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…
Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we…