Zuazua Iriondo E (2026)
Publication Language: English
Publication Status: Submitted
Publication Type: Unpublished / Preprint
Future Publication Type: Article in Edited Volumes
Publication year: 2026
This proceedings note compresses several recent results at the interface of control theory and modern machine learning. We use a unified "flow control" viewpoint: (i) in shallow networks, selecting neurons is a static control/optimization problem, in agreement with the concept of turnpike, asserting that, in long time horizons, optimal control strategies are nearly static; (ii) in deep residual networks and Neural ODEs, weights act as time-dependent controls steering an ensemble of inputs as in ensemble or simulatenous control of dynamical systems; (iii) in attention layers, token interactions form a discrete dynamical system whose asymptotics simplify representation. We highlight four representative theorems: a no-gap convexification of $\ell^1$-regularized shallow-network interpolation with atomic extreme solutions; explicit simultaneous controllability of ReLU Neural ODEs with a depth-width trade-off; $L^1$-approximate controllability of the induced neural transport equation, relevant to normalizing flows; and asymptotic clustering for hardmax self-attention. We emphasize what these results say about architectural complexity, and we propose concrete directions connecting turnpike ideas, hybrid physics--data modeling, and diffusion-based generative mechanisms.
APA:
Zuazua Iriondo, E. (2026). Machine Learning and Control: A Unified Perspective. (Unpublished, Submitted).
MLA:
Zuazua Iriondo, Enrique. Machine Learning and Control: A Unified Perspective. Unpublished, Submitted. 2026.
BibTeX: Download