Aggregated predictors are obtained by making a set of basic predictors vote according to
some weights, that is, to some probability distribution. Randomized predictors are obtained …

A fundamental question in theoretical machine learning is generalization. Over the past
decades, the PAC-Bayesian approach has been established as a flexible framework to …

In recent years, there has been an explosion of research into develo** more robust deep
neural networks against adversarial examples. Adversarial training appears as one of the …

Deep learning is usually described as an experiment-driven field under continuous criticizes
of lacking theoretical foundations. This problem has been partially fixed by a large volume of …

We provide an information-theoretic framework for studying the generalization properties of
machine learning algorithms. Our framework ties together existing approaches, including …

An information-theoretic upper bound on the generalization error of supervised learning
algorithms is derived. The bound is constructed in terms of the mutual information between …

The dominant term in PAC-Bayes bounds is often the Kullback-Leibler divergence between
the posterior and prior. For so-called linear PAC-Bayes risk bounds based on the empirical …

The information-theoretic framework of Russo and Zou (2016) and Xu and Raginsky (2017)
provides bounds on the generalization error of a learning algorithm in terms of the mutual …

The noise in stochastic gradient descent (SGD) provides a crucial implicit regularization
effect for training overparameterized models. Prior theoretical work largely focuses on …

We study the generalization properties of the popular stochastic optimization method known
as stochastic gradient descent (SGD) for optimizing general non-convex loss functions. Our …