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SUMMARY:Markos Katsoulakis\, "Optimal Control and Proximal Optimal Transpo
 rt Divergences for Robust Machine Learning"
DTSTART;VALUE=DATE-TIME:20260122T133000Z
DTEND;VALUE=DATE-TIME:20260122T143000Z
DTSTAMP;VALUE=DATE-TIME:20260306T184100Z
UID:indico-event-918@indico.gssi.it
DESCRIPTION:Abstract: Training many modern deep learning models\, such as
  generative models\, residual networks\, and transformers\, can be natural
 ly formulated as optimal control problems\, where the dynamics of learning
  and architecture design are governed by control objectives in high-dimens
 ional spaces. In this setting\, Hamilton–Jacobi (HJ) equations and Mean-
 Field Games (MFGs) provide a mathematical framework for analyzing and impr
 oving training dynamics and model architectures. We first show how fundame
 ntal classes of generative flows\, including continuous-time normalizing f
 lows and score-based diffusion models\, emerge intrinsically from MFG form
 ulations with varying particle dynamics\, cost functionals\, divergences\,
  and probability metrics. The forward–backward PDE structure of MFGs yie
 lds analytical insight and guides the design of robust\, data-efficient tr
 aining algorithms. Moreover\, proximal optimal transport divergences serve
  as natural regularizers within the MFG/optimal-control formulation\, stab
 ilizing the forward–backward dynamics and enabling faster\, more robust 
 learning. The regularity theory of HJ equations\, combined with model-unce
 rtainty quantification\, provides provable performance and robustness guar
 antees for both generative models and complex neural architectures such as
  transformers. Our theoretical analysis is supported by extensive numerica
 l experiments\, with applications to likelihood-free inference\, foundatio
 n models for PDEs\, the solution of high-dimensional control problems\, an
 d comprehensive validations on widely used ML benchmarks.\n\nhttps://indic
 o.gssi.it/event/918/
LOCATION:Ex-ISEF/Building-Main Lecture Hall (GSSI)
URL:https://indico.gssi.it/event/918/
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