Related papers: Approximation Theory for Lipschitz Continuous Tran…

We develop a switched nonlinear predictor-feedback control law to achieve global asymptotic stabilization for nonlinear systems with arbitrarily long input delay, under state quantization. The proposed design generalizes the nonlinear…

Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning…

The Transformer architecture has become a cornerstone of modern artificial intelligence, but its core self-attention mechanism suffers from a complexity bottleneck that scales quadratically with sequence length, severely limiting its…

We derive a Lipschitz continuity bound for quantum-classical conditional entropies with respect to angular distance, with a Lipschitz constant that is independent of the dimension of the conditioning system. This bound is sharper in some…

We offer a theoretical mathematical background through Lagrangian optimization on the unit hyperspherical manifold and its tangential collection with application to the Transformer and its token space. Our methods are catered to the…

This paper proposes a class of well-conditioned neural networks in which a unit amount of change in the inputs causes at most a unit amount of change in the outputs or any of the internal layers. We develop the known methodology of…

In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with…

Attention based neural networks are state of the art in a large range of applications. However, their performance tends to degrade when the number of layers increases. In this work, we show that enforcing Lipschitz continuity by normalizing…

Transformers have become the dominant architecture in modern machine learning, yet the theoretical understanding of their training dynamics remains limited. This paper develops a rigorous mathematical framework for analyzing gradient-based…

Obtaining sharp Lipschitz constants for feed-forward neural networks is essential to assess their robustness in the face of perturbations of their inputs. We derive such constants in the context of a general layered network model involving…

We propose an approach to design a Model Predictive Controller (MPC) for constrained Linear Time Invariant systems performing an iterative task. The system is subject to an additive disturbance, and the goal is to learn to satisfy state and…

In recent years, the development of multimodal autoencoders has gained significant attention due to their potential to handle multimodal complex data types and improve model performance. Understanding the stability and robustness of these…

Deep reinforcement learning approaches are becoming appealing for the design of nonlinear controllers for voltage control problems, but the lack of stability guarantees hinders their deployment in real-world scenarios. This paper constructs…

Recent research has demonstrated that transformers, particularly linear attention models, implicitly execute gradient-descent-like algorithms on data provided in-context during their forward inference step. However, their capability in…

Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…

Transformers are deep architectures that define ``in-context maps'' which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a set of patches for a vision transformer). In previous work, we…

The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…

Lipschitz learning is a graph-based semi-supervised learning method where one extends labels from a labeled to an unlabeled data set by solving the infinity Laplace equation on a weighted graph. In this work we prove uniform convergence…

ResNets constrained to be bi-Lipschitz, that is, approximately distance preserving, have been a crucial component of recently proposed techniques for deterministic uncertainty quantification in neural models. We show that theoretical…

Fixed-point equations with Lipschitz operators have been studied for more than a century, and are central to problems in mathematical optimization, game theory, economics, and dynamical systems, among others. When the Lipschitz constant of…