Universal approximation power of deep residual neural networks through the lens of control
P Tabuada, B Gharesifard - IEEE Transactions on Automatic …, 2022 - ieeexplore.ieee.org
In this article, we show that deep residual neural networks have the power of universal
approximation by using, in an essential manner, the observation that these networks can be …
approximation by using, in an essential manner, the observation that these networks can be …
Control of neural transport for normalising flows
D Ruiz-Balet, E Zuazua - Journal de Mathématiques Pures et Appliquées, 2024 - Elsevier
Inspired by normalising flows, we analyse the bilinear control of neural transport equations
by means of time-dependent velocity fields restricted to fulfil, at any time instance, a simple …
by means of time-dependent velocity fields restricted to fulfil, at any time instance, a simple …
Learning robust state observers using neural odes
Relying on recent research results on Neural ODEs, this paper presents a methodology for
the design of state observers for nonlinear systems based on Neural ODEs, learning …
the design of state observers for nonlinear systems based on Neural ODEs, learning …
Observer-based control barrier functions for safety critical systems
This paper considers the safety-critical control design problem with output measurements.
An observer-based safety control framework that integrates the estimation error quantified …
An observer-based safety control framework that integrates the estimation error quantified …
A measure theoretical approach to the mean-field maximum principle for training NeurODEs
In this paper we consider a measure-theoretical formulation of the training of NeurODEs in
the form of a mean-field optimal control with L 2-regularization of the control. We derive first …
the form of a mean-field optimal control with L 2-regularization of the control. We derive first …
Deep residual neural network (ResNet)-based adaptive control: A Lyapunov-based approach
Deep Neural Network (DNN)-based controllers have emerged as a tool to compensate for
unstructured uncertainties in nonlinear dynamical systems. A recent breakthrough in the …
unstructured uncertainties in nonlinear dynamical systems. A recent breakthrough in the …
Mad max: Affine spline insights into deep learning
R Balestriero, RG Baraniuk - Proceedings of the IEEE, 2020 - ieeexplore.ieee.org
We build a rigorous bridge between deep networks (DNs) and approximation theory via
spline functions and operators. Our key result is that a large class of DNs can be written as a …
spline functions and operators. Our key result is that a large class of DNs can be written as a …
Neural tangent kernel analysis of deep narrow neural networks
The tremendous recent progress in analyzing the training dynamics of overparameterized
neural networks has primarily focused on wide networks and therefore does not sufficiently …
neural networks has primarily focused on wide networks and therefore does not sufficiently …
Achieve the minimum width of neural networks for universal approximation
Y Cai - arXiv preprint arXiv:2209.11395, 2022 - arxiv.org
The universal approximation property (UAP) of neural networks is fundamental for deep
learning, and it is well known that wide neural networks are universal approximators of …
learning, and it is well known that wide neural networks are universal approximators of …
Feedforward neural networks and compositional functions with applications to dynamical systems
In this paper we develop an algebraic framework for analyzing neural network
approximation of compositional functions, a rich class of functions that are frequently …
approximation of compositional functions, a rich class of functions that are frequently …