7 papers
Constructive interpolation and generalization rates for neural ODEs: a control perspective
Antonio Ãlvarez-López, Lorenzo Liverani, Enrique Zuazua
We study supervised regression with neural ODEs (NODEs) from a control-theoretic perspective to derive explicit population-risk bounds. We focus on a widely used class of non-auton…
Perceptrons and localization of attention's mean-field landscape
Antonio Ãlvarez-López, Borjan Geshkovski, Domènec Ruiz-Balet
The forward pass of a Transformer can be seen as an interacting particle system on the unit sphere: time plays the role of layers, particles that of token embeddings, and the unit…
Gaussian mixture models in Hilbert spaces via kernel methods
Daniel López-Montero, Antonio Ãlvarez-López, Marcos Matabuena
Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally…
Continuous-Time Learning of Probability Distributions: A Case Study in a Digital Trial of Young Children with Type 1 Diabetes
Antonio Ãlvarez-López, Marcos Matabuena
Understanding how biomarker distributions evolve over time is a central challenge in digital health and chronic disease monitoring. In diabetes, changes in the distribution of gluc…
Convergence, design and training of continuous-time dropout as a random batch method
Antonio Ãlvarez-López, MartÃn Hernández
We study dropout regularization in continuous-time models through the lens of random-batch methods -- a family of stochastic sampling schemes originally devised to reduce the compu…
Continuous Temporal Learning of Probability Distributions via Neural ODEs with Applications in Continuous Glucose Monitoring Data
Antonio Ãlvarez-López, Marcos Matabuena
Modeling the dynamics of probability distributions from time-dependent data samples is a fundamental problem in many fields, including digital health. The goal is to analyze how th…