Related papers: Localmax dynamics for attention in transformers an…
Control of network systems with uncertain local dynamics has remained an open problem for a long time. In this paper, a distributed minimax adaptive control algorithm is proposed for such networks whose local dynamics has an uncertain…
We develop an indirect-adaptive model predictive control algorithm for uncertain linear systems subject to constraints. The system is modeled as a polytopic linear parameter varying system where the convex combination vector is constant but…
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…
We study local (also referred to as small-signal) stability of a network of identical DC/AC converters having a rotating degree of freedom. We develop a stability theory for a class of partitioned linear systems with symmetries that has…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Understanding the intricate non-convex training dynamics of softmax-based models is crucial for explaining the empirical success of transformers. In this article, we analyze the gradient flow dynamics of the value-softmax model, defined as…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
We study an agent-based model of self-propelled particles with a velocity-dependent alignment rule. This interaction is orientation weighted and acts along the line connecting neighboring particles. Tuning the alignment strength produces…
In this paper, we study the controllability and stabilizability properties of the Kolmogorov forward equation of a continuous time Markov chain (CTMC) evolving on a finite state space, using the transition rates as the control parameters.…
We focus on the solutions of second-order stable linear difference equations and demonstrate that their behavior can be non-monotone and exhibit peak effects depending on initial conditions. The results are applied to the analysis of the…
Lyapunov functions are essential tools in dynamical systems, as they allow the stability analysis of equilibrium points without the need to explicitly solve the system's equations. Despite their importance, no systematic method exists for…
Time series forecasting is essential for many practical applications, with the adoption of transformer-based models on the rise due to their impressive performance in NLP and CV. Transformers' key feature, the attention mechanism,…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
Fixed-budget nonconvex optimization can fail not because local descent is unstable, but because it is too stable: after reaching a nearby stationary point, an optimizer may spend the remaining evaluations refining an uninformative local…
Sequence models lie at the heart of modern deep learning. However, rapid advancements have produced a diversity of seemingly unrelated architectures, such as Transformers and recurrent alternatives. In this paper, we introduce a unifying…
Most approaches that model time-series data in human activity recognition based on body-worn sensing (HAR) use a fixed size temporal context to represent different activities. This might, however, not be apt for sets of activities with…
Existing research largely attributes the global sequence modeling capability of Transformers to the explicit computation of attention weights, a process that inherently incurs quadratic computational complexity. In this work, we offer a…
This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…
In this paper, a new approach based on convex analysis is introduced to solve the $H_\infty$ problem for discrete-time nonlinear stochastic systems. A stochastic version of bounded real lemma is proved and the state feedback $H_\infty$…
We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic…