Related papers: Do stable neural networks exist for classification…

This work investigates the detection of instabilities that may occur when utilizing deep learning models for image reconstruction tasks. Although neural networks often empirically outperform traditional reconstruction methods, their usage…

Designing neural networks with bounded Lipschitz constant is a promising way to obtain certifiably robust classifiers against adversarial examples. However, the relevant progress for the important $\ell_\infty$ perturbation setting is…

Graph neural networks (GNNs), consisting of a cascade of layers applying a graph convolution followed by a pointwise nonlinearity, have become a powerful architecture to process signals supported on graphs. Graph convolutions (and thus,…

The Lipschitz constant of a neural network is connected to several important properties of the network such as its robustness and generalization. It is thus useful in many settings to estimate the Lipschitz constant of a model. Prior work…

Relying on the premise that the performance of a binary neural network can be largely restored with eliminated quantization error between full-precision weight vectors and their corresponding binary vectors, existing works of network…

We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator Am depending non-linearly on a parameter m and operating on a function u. In the…

Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to…

In this work, we assess the theoretical limitations of determining guaranteed stability and accuracy of neural networks in classification tasks. We consider classical distribution-agnostic framework and algorithms minimising empirical risks…

A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…

In the context of deep learning research, where model introductions continually occur, the need for effective and efficient evaluation remains paramount. Existing methods often emphasize accuracy metrics, overlooking stability. To address…

Graph neural networks (GNNs) have recently been demonstrated to perform well on a variety of network-based tasks such as decentralized control and resource allocation, and provide computationally efficient methods for these tasks which have…

We study the problem of reconstructing solutions of inverse problems when only noisy measurements are available. We assume that the problem can be modeled with an infinite-dimensional forward operator that is not continuously invertible.…

The local Lipschitz constant of a neural network is a useful metric with applications in robustness, generalization, and fairness evaluation. We provide novel analytic results relating the local Lipschitz constant of nonsmooth vector-valued…

Lipschitz constant is a fundamental property in certified robustness, as smaller values imply robustness to adversarial examples when a model is confident in its prediction. However, identifying the worst-case adversarial examples is known…

Training a deep neural network (DNN) often involves stochastic optimization, which means each run will produce a different model. Several works suggest this variability is negligible when models have the same performance, which in the case…

One of the arguments to explain the success of deep learning is the powerful approximation capacity of deep neural networks. Such capacity is generally accompanied by the explosive growth of the number of parameters, which, in turn, leads…

This paper presents a formal definition of stability for node centrality measures in weighted graphs. It is shown that the commonly used measures of degree, closeness and eigenvector centrality are stable whereas betweenness centrality is…

Stability is a general notion that quantifies the sensitivity of a learning algorithm's output to small change in the training dataset (e.g. deletion or replacement of a single training sample). Such conditions have recently been shown to…

Existing bounds on the generalization error of deep networks assume some form of smooth or bounded dependence on the input variable, falling short of investigating the mechanisms controlling such factors in practice. In this work, we…

This work studies the adversarial robustness of parametric functions composed of a linear predictor and a non-linear representation map. % that satisfies certain stability condition. Our analysis relies on \emph{sparse local Lipschitzness}…