Related papers: The Price of Robustness: Stable Classifiers Need O…

The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…

In the plane, we consider the problem of reconstructing a domain from the normal derivative of its Green's function (with fixed pole) relative to the Dirichlet problem for the Laplace operator. By means of the theory of conformal mappings,…

Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…

Recent research has highlighted a critical issue known as ``robust fairness", where robust accuracy varies significantly across different classes, undermining the reliability of deep neural networks (DNNs). A common approach to address this…

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…

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…

The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…

For linear classifiers, the relationship between (normalized) output margin and generalization is captured in a clear and simple bound -- a large output margin implies good generalization. Unfortunately, for deep models, this relationship…

In this paper we develop a new perspective on generalization of neural networks by proposing and investigating the concept of a neural network stiffness. We measure how stiff a network is by looking at how a small gradient step in the…

Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample…

The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…

This paper investigates the theory of robustness against adversarial attacks. We focus on randomized classifiers (\emph{i.e.} classifiers that output random variables) and provide a thorough analysis of their behavior through the lens of…

While generalizing well over natural inputs, neural networks are vulnerable to adversarial inputs. Existing defenses against adversarial inputs have largely been detached from the real world. These defenses also come at a cost to accuracy.…

Thanks to their extensive capacity, over-parameterized neural networks exhibit superior predictive capabilities and generalization. However, having a large parameter space is considered one of the main suspects of the neural networks'…

The notion of developing statistical methods in machine learning which are robust to adversarial perturbations in the underlying data has been the subject of increasing interest in recent years. A common feature of this work is that the…

We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…

We study the problem of assessing the robustness of counterfactual explanations for deep learning models. We focus on $\textit{plausible model shifts}$ altering model parameters and propose a novel framework to reason about the robustness…

Common practice in modern machine learning involves fitting a large number of parameters relative to the number of observations. These overparameterized models can exhibit surprising generalization behavior, e.g., ``double descent'' in the…

We study the generalization of over-parameterized deep networks (for image classification) in relation to the convex hull of their training sets. Despite their great success, generalization of deep networks is considered a mystery. These…

A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…