190 citations · 643 across the 41 of their papers we have counts for
52 papers
From NeurODEs to AutoencODEs: a mean-field control framework for width-varying Neural Networks
Cristina Cipriani, Massimo Fornasier, Alessandro Scagliotti
The connection between Residual Neural Networks (ResNets) and continuous-time control systems (known as NeurODEs) has led to a mathematical analysis of neural networks which has pr…
Gradient is All You Need? How Consensus-Based Optimization can be Interpreted as a Stochastic Relaxation of Gradient Descent
Konstantin Riedl, Timo Klock, Carina Geldhauser +1
In this paper, we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO),…
Finite Sample Identification of Wide Shallow Neural Networks with Biases
Massimo Fornasier, Timo Klock, Marco Mondelli +1
Artificial neural networks are functions depending on a finite number of parameters typically encoded as weights and biases. The identification of the parameters of the network fro…
Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces
Massimo Fornasier, Giuseppe Savaré, Giacomo Enrico Sodini
We prove a general criterion for the density in energy of suitable subalgebras of Lipschitz functions in the metric-Sobolev space associated wi…
Convergence of Anisotropic Consensus-Based Optimization in Mean-Field Law
Massimo Fornasier, Timo Klock, Konstantin Riedl
In this paper we study anisotropic consensus-based optimization (CBO), a multi-agent metaheuristic derivative-free optimization method capable of globally minimizing nonconvex and…
A Measure Theoretical Approach to the Mean-field Maximum Principle for Training NeurODEs
Benoît Bonnet, Cristina Cipriani, Massimo Fornasier +1
In this paper we consider a measure-theoretical formulation of the training of NeurODEs in the form of a mean-field optimal control with -regularization of the control. We der…