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Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…

Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…

While training error of most deep neural networks degrades as the depth of the network increases, residual networks appear to be an exception. We show that the main reason for this is the Lyapunov stability of the gradient descent…

Predictive geometric models deliver excellent results for many Machine Learning use cases. Despite their undoubted performance, neural predictive algorithms can show unexpected degrees of instability and variance, particularly when applied…

Assessing the boundedness and stability of vector nonlinear systems with variable delays and coefficients remains a challenging problem with broad applications in science and engineering. Existing methods tend to produce overly conservative…

We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an…

Algorithmic stability is an important notion that has proven powerful for deriving generalization bounds for practical algorithms. The last decade has witnessed an increasing number of stability bounds for different algorithms applied on…

When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…

Adaptivity is an important feature of data analysis---the choice of questions to ask about a dataset often depends on previous interactions with the same dataset. However, statistical validity is typically studied in a nonadaptive model,…

Providing generalization guarantees for stochastic optimization algorithms remains a key challenge in learning theory. Recently, numerous works demonstrated the impact of the geometric properties of optimization trajectories on…

Robustness verification that aims to formally certify the prediction behavior of neural networks has become an important tool for understanding model behavior and obtaining safety guarantees. However, previous methods can usually only…

Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…

Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many…

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…

The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a…

The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent…

Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…

Many machine learning tasks can be formulated as a stochastic compositional optimization (SCO) problem such as reinforcement learning, AUC maximization, and meta-learning, where the objective function involves a nested composition…

We analyze a family of supervised learning algorithms based on sample compression schemes that are stable, in the sense that removing points from the training set which were not selected for the compression set does not alter the resulting…

Learned optimizers -- neural networks that are trained to act as optimizers -- have the potential to dramatically accelerate training of machine learning models. However, even when meta-trained across thousands of tasks at huge…