Related papers: Lyapunov-Stable Deep Equilibrium Models
A retrovirus dynamic model is proposed. We pay attention to the case when viral pathogenicity is low and the infected cells are able to reproduce. Using Lyapunov function method we study stability properties of an inner equilibrium of the…
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…
A deep equilibrium model (DEQ) is implicitly defined through an equilibrium point of an infinite-depth weight-tied model with an input-injection. Instead of infinite computations, it solves an equilibrium point directly with root-finding…
In this paper, we introduce a novel class of neural differential equation, which are intrinsically Lyapunov stable, exponentially stable or passive. We take a recently proposed Polyak Lojasiewicz network (PLNet) as an Lyapunov function and…
Many tasks in deep learning involve optimizing over the \emph{inputs} to a network to minimize or maximize some objective; examples include optimization over latent spaces in a generative model to match a target image, or adversarially…
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…
Equivariant imaging (EI) enables training signal reconstruction models without requiring ground truth data by leveraging signal symmetries. Deep equilibrium models (DEQs) are a powerful class of neural networks where the output is a fixed…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
Deep equilibrium models (DEQs) have recently emerged as a powerful paradigm for training infinitely deep weight-tied neural networks that achieve state of the art performance across many modern machine learning tasks. Despite their…
Implicit-depth models such as Deep Equilibrium Networks have recently been shown to match or exceed the performance of traditional deep networks while being much more memory efficient. However, these models suffer from unstable convergence…
The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a…
Human posture control models are used to analyse neurological experiments and control of humanoid robots. This work focuses on a well-known nonlinear posture control model, the DEC (Disturbance estimate and Compensation). In order to…
The Lyapunov inequality is an indispensable tool for stability analysis in linear control theory. It provides a necessary and sufficient condition for the stability of an autonomous linear-time invariant system in terms of the existence of…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…
Implicit models such as Deep Equilibrium Models (DEQs) have garnered significant attention in the community for their ability to train infinite layer models with elegant solution-finding procedures and constant memory footprint. However,…
Deep neural networks (DNNs) are vulnerable to subtle adversarial perturbations applied to the input. These adversarial perturbations, though imperceptible, can easily mislead the DNN. In this work, we take a control theoretic approach to…