5 citations · 13 across the 18 of their papers we have counts for
15 papers · 1 filter
Constructive conditional normalizing flows
Borjan Geshkovski, Domènec Ruiz-Balet
Motivated by applications in conditional sampling, given a probability measure and a diffeomorphism , we consider the problem of simultaneously approximating and the pus…
Attention's forward pass and Frank-Wolfe
Albert Alcalde, Borjan Geshkovski, Domènec Ruiz-Balet
We study the hardmax limit of self-attention dynamics for token embeddings obtained in the zero-temperature () regime, and relate it to the finite- setting. In this…
Constructive approximate transport maps with normalizing flows
Antonio Álvarez-López, Borjan Geshkovski, Domènec Ruiz-Balet
We study an approximate controllability problem for the continuity equation and its application to constructing transport maps with normalizing flows. Specifically, we construct ti…
A total variation flow scheme for ergodic mean field games
Dante Kalise, Alessio Oliviero, Domènec Ruiz-Balet
Motivated by recent developments in mean field games in ecology, in this paper we introduce a connection between the best response dynamics in evolutionary game theory, the minimiz…
Measure-to-measure interpolation using Transformers
Borjan Geshkovski, Philippe Rigollet, Domènec Ruiz-Balet
Transformers are deep neural network architectures that underpin the recent successes of large language models. Unlike more classical architectures that can be viewed as point-to-p…
Pattern control via Diffussion interaction
Domènec Ruiz-Balet, Enrique Zuazua
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. W…
Control of neural transport for normalizing flows
Domènec Ruiz-Balet, Enrique Zuazua
Inspired by normalizing flows, we analyze the bilinear control of neural transport equations by means of time-dependent velocity fields restricted to fulfill, at any time instance,…
Spatial ecology, optimal control and game theoretical fishing problems
Idriss Mazari, Domènec Ruiz-Balet
Of paramount importance in both ecological systems and economic policies are the problems of harvesting of natural resources. A paradigmatic situation where this question is raised…
Interpolation and approximation via Momentum ResNets and Neural ODEs
Domènec Ruiz-Balet, Elisa Affili, Enrique Zuazua
In this article, we explore the effects of memory terms in continuous-layer Deep Residual Networks by studying Neural ODEs (NODEs). We investigate two types of models. On one side,…
Neural ODE control for classification, approximation and transport
Domènec Ruiz-Balet, Enrique Zuazua
We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main properties and paradigms of Deep Learning (DL), in part…
Quantitative stability for eigenvalues of Schrödinger operator, Quantitative bathtub principle \& Application to the turnpike property for a bilinear optimal control problem
Idriss Mazari, Domenec Ruiz-Balet
This work is concerned with two optimisation problems that we tackle from a qualitative perspective. The first one deals with quantitative inequalities for spectral optimisation pr…
Constrained control of gene-flow models
Idriss Mazari, Domenec Ruiz-Balet, Enrique Zuazua
In ecology and population dynamics, gene-flow refers to the transfer of a trait from one population to another. This phenomenon appears in studying the evolution of social features…
A fragmentation phenomenon for a non-energetic optimal control problem: optimisation of the total population size in logistic diffusive models
Idriss Mazari, Domenec Ruiz-Balet
Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spa…
Control under constraints for multi-dimensional reaction-diffusion monostable and bistable equations
Domènec Ruiz-Balet, Enrique Zuazua
Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical…
A parabolic approach to the control of opinion spreading
Domènec Ruiz-Balet, Enrique Zuazua
We analyze the problem of controlling to consensus a nonlinear system modeling opinion spreading. We derive explicit exponential estimates on the cost of approximately controlling…