2025 – cmc.deusto.eus

SHAP values through General Fourier Representations: Theory and Applications

R. Morales (2025) SHAP values through General Fourier Representations: Theory and Applications Abstract. This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that…

Spiking Neural Networks: a theoretical framework for Universal Approximation and training

U. Biccari (2025) Spiking Neural Networks: a theoretical framework for Universal Approximation and training Abstract. Spiking Neural Networks (SNNs) are widely regarded as a biologically-inspired and energy-efficient alternative to classical…

Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels

K. Lyu, U. Biccari, J. Wang (2025) Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels Abstract. This paper investigates the mean square exponential stabilization problem for a…

A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints

Roberto Morales, U. Biccari (2025) A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints, Abstract. This article introduces a generalized framework for Decentralized Learning formulated as a Multi-Objective Optimization…

Sharp numerical approximation of the Hardy constant

L. Ignat, E. Zuazua (2025) Sharp numerical approximation of the Hardy constant Abstract. We study the P1 finite element approximation of the best constant in the classical Hardy inequality over…

Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis

A. Alcalde Zafra, G. Fantuzzi, E. Zuazua (2025) Clustering in Pure-Attention Hardmax Transformers and its Role in Sentiment Analysis, SIAM Mathematics of Data Science, SIMODS, arxiv: 2407.01602 Abstract. Transformers are…

A potential game perspective in Federated Learning

K. Liu, Z. Wang, E. Zuazua (2025) A potential game perspective in Federated Learning, arxiv:2411.11793 Abstract. Federated learning (FL) is an emerging paradigm for training machine learning models across distributed…

Regional and Partial Observability and Control of Waves

B. Dehman, S. Ervedoza, E. Zuazua (2025) Regional and Partial Observability and Control of Waves Abstract.We establish sharp regional observability results for solutions of the wave equation in a bounded…

Cluster-based classification with neural ODEs via control

A. Alvarez-Lopez, R. Orive-Illera, E. Zuazua (2025) Optimized classification with neural odes via separability, J. Mach. Learn., arXiv:2312.13807v2 Abstract.We address binary classification using neural ordinary differential equations from the perspective…

Optimal convergence rates for the finite element approximation of the Sobolev constant

L. Ignat, E. Zuazua (2025) Optimal convergence rates for the finite element approximation of the Sobolev constant Abstract. We establish optimal convergence rates for the P1 finite element approximation of…

Boundary observation and control for fractional heat and wave equations

U. Biccari, E. Zuazua (2025) Boundary observation and control for fractional heat and wave equations, https://doi.org/10.48550/arXiv.2504.17413 Abstract. We establish boundary observability and control for the fractional heat equation over arbitrary…

Almost periodic turnpike phenomenon for time-dependent systems

S. Zamorano (2025)Almost periodic turnpike phenomenon for time-dependent systems Systems and Control Letters, Vol. 199, pp. 106069, https://doi.org/10.1016/j.sysconle.2025.106069 Abstract. This paper explores the turnpike behavior of a controlled system with…

Turnpike in optimal control and beyond: A survey

E. Trélat, E. Zuazua (2025)Turnpike in optimal control and beyond: A survey https://hal.science/hal-05002039 Abstract. The turnpike principle is a fundamental concept in optimal control theory, stating that for a wide…

Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach

T. Crin-Barat, L. Liverani, Ly Shou, E. Zuazua (2025)Large-time asymptotics for hyperbolic systems with non-symmetric relaxation: An algorithmic approach, arXiv:2503.00236 Abstract. We study the stability of one-dimensional linear hyperbolic systems…

Pointwise constraints for scalar conservation laws with positive wave velocity

N. De Nitti, D. Serre, E. Zuazua (2025) Pointwise constraints for scalar conservation laws with positive wave velocity Abstract. We consider a conservation law with strictly positive wave velocity and…

Gaussian Beam ansatz for finite difference wave equations

U. Biccari, E. Zuazua (2025) Gaussian Beam ansatz for finite difference wave equations, Found Comput Math. , Vol. 25, pp. 1–54, https://doi.org/10.1007/s10208-023-09632-9 Abstract. This work is concerned with the construction…

Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics

K. Liu, E. Zuazua (2025) Representation and Regression Problems in Neural Networks: Relaxation, Generalization, and Numerics, Math. Models Methods Appl. Sci., Vol. 35, No. 6, pp. 1471-1521, arXiv:2412.01619v1, https://doi.org/10.1142/S0218202525500228 Abstract. In…

Exact Sequence Classification with Hardmax Transformers

A. Alcalde Zafra, G. Fantuzzi, E. Zuazua (2025) Exact Sequence Classification with Hardmax Transformers, arxiv: 2502.02270 Abstract. We prove that hardmax attention transformers perfectly classify datasets of $N$ labeled sequences…

On the decay of one-dimensional locally and partially dissipated and hyperbolic systems

T. Crin-Barat, N. De Nitti, E. Zuazua (2025) On the decay of one-dimensional locally and partially dissipated and hyperbolic systems, ESAIM:COCV, https://arxiv.org/abs/2206.00555 Abstract. We study the time-asymptotic behavior of linear…

Control of Hyperbolic and Parabolic Equations on Networks and Singular limits

J.A. Bárcena-Petisco, M. Cavalcante, G.M. Coclite, N. de Nitti, E. Zuazua (2025) Control of Hyperbolic and Parabolic Equations on Networks and Singular limits, MCRF, Vol. 15, No. 1, March 2025,…

FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning

Y. Song, Z. Wang, E. Zuazua (2025) FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning, Neural Networks, pp. 106-772, ISSN 0893-6080, https://doi.org/10.1016/j.neunet.2024.106772 Abstract. Federated learning (FL) is a promising…

Optimal L^p-approximation of convex sets by convex subsets

F. Zakaria, I. Ftouhi, E. Zuazua (2025) Optimal L^p-approximation of convex sets by convex subsets Abstract. Given a convex set Ω of R n, we consider the shape optimization problem…

Tracking controllability for the heat equation

J.A. Barcena-Petisco, E. Zuazua (2025) Tracking controllability for the heat equation, IEEE Trans. Autom. Control Abstract. We study the tracking or sidewise control- lability of the heat equation. More precisely,…

Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications

Z. Li, K. Liu, L. Liverani, E. Zuazua (2025)Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications, arXiv: 2407.17092 Abstract. In this paper, we introduce semi-autonomous neural ordinary…

Boundary sidewise observability of the wave equation

B. Dehman, E. Zuazua (2025) Boundary sidewise observability of the wave equation J. Eur. Math. Soc. (JEMS) Abstract. The wave equation on a bounded domain of Rn with non homogeneous…

Pattern control via diffusion interaction

D. Ruiz-Balet, E. Zuazua (2025) Pattern control via diffusion interaction Abstract. We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the…

Local Stability and Convergence of Unconstrained Model Predictive Control

D. Veldman, E. Zuazua (2025) Local Stability and Convergence of Unconstrained Model Predictive Control Abstract. The local stability and convergence for Model Predictive Control (MPC) of unconstrained nonlinear dynamics based…

Deep Neural Networks: Multi-Classification and Universal Approximation

M. Hernandez, E. Zuazua (2025)Deep Neural Networks: Multi-Classification and Universal Approximation arXiv:2409.06555 Abstract. We demonstrate that a ReLU deep neural network with a width of 2 and a depth of…

Approximate and Weighted Data Reconstruction Attack in Federated Learning

Z. Wang, Y. Song, E. Zuazua (2025) Approximate and Weighted Data Reconstruction Attack in Federated Learning arXiv:2308.06822 Abstract. Federated Learning (FL) is a distributed learning paradigm that enables multiple clients…

Tracking controllability for finite-dimensional linear systems

S. Zamorano, E. Zuazua (2025)Tracking controllability for finite-dimensional linear systems arXiv:2407.18641v2 Abstract. In this work, we present a functional analytic framework for tracking controllability in finite-dimensional linear systems. By leveraging…

Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings

GM. Coclite, N. De Nitti, F. Maddalena, G. Orlando, E. Zuazua (2025) Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings, Mathematical Models and Methods…

Large-time asymptotics in deep learning

C. Esteve, B. Geshkovski, D. Pighin, E. Zuazua (2025) Large-time asymptotics in deep learning, https://hal.archives-ouvertes.fr/hal-02912516 Abstract. We consider the neural ODE perspective of supervised learning and study the impact of the…