Related papers: Hypothesis Set Stability and Generalization

We study the notion of a generalization bound being uniformly tight, meaning that the difference between the bound and the population loss is small for all learning algorithms and all population distributions. Numerous generalization bounds…

This paper introduces a framework for analyzing a general class of uncertain nonlinear discrete-time systems with given state-, control-, and disturbance constraints. In particular, we propose a set-theoretic generalization of the concept…

In reactive synthesis, the goal is to automatically generate an implementation from a specification of the reactive and non-terminating input/output behaviours of a system. Specifications are usually modelled as logical formulae or automata…

We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class - in our case, empirical Rademacher complexity - to what extent can we (a…

Graph neural networks (GNNs) have emerged as a fundamental tool for learning from graph-structured data, achieving strong performance across a wide range of applications. However, understanding their generalization capabilities remains…

Deriving generalization bounds for stable algorithms is a classical question in learning theory taking its roots in the early works by Vapnik and Chervonenkis (1974) and Rogers and Wagner (1978). In a series of recent breakthrough papers by…

Recent advances in deep learning have given us some very promising results on the generalization ability of deep neural networks, however literature still lacks a comprehensive theory explaining why heavily over-parametrized models are able…

We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…

Offset Rademacher complexities have been shown to provide tight upper bounds for the square loss in a broad class of problems including improper statistical learning and online learning. We show that the offset complexity can be generalized…

Understanding generalization in reinforcement learning (RL) is a significant challenge, as many common assumptions of traditional supervised learning theory do not apply. We focus on the special class of reparameterizable RL problems, where…

The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…

We present an extensive analysis of relative deviation bounds, including detailed proofs of two-sided inequalities and their implications. We also give detailed proofs of two-sided generalization bounds that hold in the general case of…

Despite the celebrated popularity of Graph Neural Networks (GNNs) across numerous applications, the ability of GNNs to generalize remains less explored. In this work, we propose to study the generalization of GNNs through a novel…

Gradient-based optimization methods have shown remarkable empirical success, yet their theoretical generalization properties remain only partially understood. In this paper, we establish a generalization bound for gradient flow that aligns…

Machine learning technologies have been used in a wide range of practical systems. In practical situations, it is natural to expect the input-output pairs of a machine learning model to satisfy some requirements. However, it is difficult to…

With the desire to apply the Dempster-Shafer theory to complex real world problems where the evidential strength is often imprecise and vague, several attempts have been made to generalize the theory. However, the important concept in the…

We introduce Transductive Local Complexity (TLC) to extend the classical Local Rademacher Complexity (LRC) to the transductive setting, incorporating substantial and novel components. Although LRC has been used to obtain sharp…

We consider a random network of nonlinear maps exhibiting a wide range of local dynamics, with the links having normally distributed interaction strengths. The stability of such a system is examined in terms of the asymptotic fraction of…

This paper explores a theory of generalization for learning problems on product distributions, complementing the existing learning theories in the sense that it does not rely on any complexity measures of the hypothesis classes. The main…

Under necessary compatibility condition, and some mild regularity assumptions on the interior and the boundary data, we prove the existence, uniqueness, and stability of the solution of generalized Dary-Forchheimer model.