Related papers: Universal Approximation Theorems for Dynamical Sys…
Deep neural networks can be trained to be efficient and effective controllers for dynamical systems; however, the mechanics of deep neural networks are complex and difficult to guarantee. This work presents a general approach for providing…
Proximal policy optimization and trust region policy optimization (PPO and TRPO) with actor and critic parametrized by neural networks achieve significant empirical success in deep reinforcement learning. However, due to nonconvexity, the…
Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
A recent paradigm views deep neural networks as discretizations of certain controlled ordinary differential equations, sometimes called neural ordinary differential equations. We make use of this perspective to link expressiveness of deep…
Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of…
The stabilization of nonlinear systems under zero-state-detectability assumption or its analogues is considered. The proposed supervisory control provides a finite time practical stabilization of output and it is based on uniting local and…
This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…
We analyze the universal approximation constraints of narrow Residual Neural Networks (ResNets) both theoretically and numerically. For deep neural networks without input space augmentation, a central constraint is the inability to…
Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…
This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the…
In this paper, we provide the universal first-order methods of Composite Optimization with new complexity analysis. It delivers some universal convergence guarantees, which are not linked directly to any parametric problem class. However,…
We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more.…
We investigate the approximation capabilities of dense neural networks. While universal approximation theorems establish that sufficiently large architectures can approximate arbitrary continuous functions if there are no restrictions on…
We consider the notion of resilience for cyber-physical systems, that is, the ability of the system to withstand adverse events while maintaining acceptable functionality. We use finite temporal logic to express the requirements on the…
The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators,…
Neural ordinary differential equations (neural ODE) are powerful continuous-time machine learning models for depicting the behavior of complex dynamical systems, but their verification remains challenging due to limited reachability…
We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neural networks (DNNs). DNNs show remarkable generalization…
This work establishes a rigorous connection between stability properties of discrete-time algorithms (DTAs) and corresponding continuous-time dynamical systems derived through $ O(s^r) $-resolution ordinary differential equations (ODEs). We…