Related papers: Do stable neural networks exist for classification…
Recent work has studied the reasons for the remarkable performance of deep neural networks in image classification. We examine batch normalization on the one hand and the dynamical systems view of residual networks on the other hand. Our…
Labelling of data for supervised learning can be costly and time-consuming and the risk of incorporating label noise in large data sets is imminent. When training a flexible discriminative model using a strictly proper loss, such noise will…
We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable robust control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural network to construct…
Lipschitz constrained networks have gathered considerable attention in the deep learning community, with usages ranging from Wasserstein distance estimation to the training of certifiably robust classifiers. However they remain commonly…
Despite apparent human-level performances of deep neural networks (DNN), they behave fundamentally differently from humans. They easily change predictions when small corruptions such as blur and noise are applied on the input (lack of…
Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…
We investigate robustness of deep feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
In this paper, we approach the task of determining sensitivity bounds for pose estimation neural networks. This task is particularly challenging as it requires characterizing the sensitivity of 3D rotations. We develop a sensitivity measure…
Empirically, modern deep learning training often occurs at the Edge of Stability (EoS), where the sharpness of the loss exceeds the threshold below which classical convergence analysis applies. Despite recent progress, existing theoretical…
Neural operators have emerged as a powerful, discretization-invariant framework for solving partial differential equations (PDEs). Although established approaches like the Deep Operator Network (DeepONet) have successfully achieved…
While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been…
We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically…
As deep neural networks are highly expressive, it is important to find solutions with small generalization gap (the difference between the performance on the training data and unseen data). Focusing on the stochastic nature of training, we…
This work considers the question: what convergence guarantees does the stochastic subgradient method have in the absence of smoothness and convexity? We prove that the stochastic subgradient method, on any semialgebraic locally Lipschitz…
State-of-the-art deep neural networks have achieved impressive results on many image classification tasks. However, these same architectures have been shown to be unstable to small, well sought, perturbations of the images. Despite the…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
The remarkable successes of neural networks in a huge variety of inverse problems have fueled their adoption in disciplines ranging from medical imaging to seismic analysis over the past decade. However, the high dimensionality of such…
This paper proposes a new notion of distributional Input-to-State Stability (dISS) for dynamic systems evolving in probability spaces over a domain. Unlike other norm-based ISS concepts, we rely on the Wasserstein metric, which captures…
In this work, a convergence lemma for function $f$ being finite compositions of analytic mappings and the maximum operator is proved. The lemma shows that the set of $\delta$-stationary points near an isolated local minimum point $x^*$ is…