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Differential Equations and Continuous-Time Deep Learning (Dagstuhl Seminar 22332)

Authors: David Duvenaud, Markus Heinonen, Michael Tiemann, and Max Welling

Published in: Dagstuhl Reports, Volume 12, Issue 8 (2023)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 22332 "Differential Equations and Continuous-Time Deep Learning". Neural ordinary-differential equations and similar continuous model architectures have gained interest in recent years, due to the existence of a vast literature in calculus and numerical analysis. Thus, continuous models might lead to architectures with finer control over prior assumptions or theoretical understanding. In this seminar, we have sought to bring together researchers from traditionally disjoint areas - machine learning, numerical analysis, dynamical systems and their "consumers" - to try and develop a joint language about this novel modeling paradigm. Through talks & group discussions, we have identified common interests and we hope that this first seminar is but the first step on a joint journey.

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David Duvenaud, Markus Heinonen, Michael Tiemann, and Max Welling. Differential Equations and Continuous-Time Deep Learning (Dagstuhl Seminar 22332). In Dagstuhl Reports, Volume 12, Issue 8, pp. 20-30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{duvenaud_et_al:DagRep.12.8.20,
  author =	{Duvenaud, David and Heinonen, Markus and Tiemann, Michael and Welling, Max},
  title =	{{Differential Equations and Continuous-Time Deep Learning (Dagstuhl Seminar 22332)}},
  pages =	{20--30},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{12},
  number =	{8},
  editor =	{Duvenaud, David and Heinonen, Markus and Tiemann, Michael and Welling, Max},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.8.20},
  URN =		{urn:nbn:de:0030-drops-177131},
  doi =		{10.4230/DagRep.12.8.20},
  annote =	{Keywords: deep learning, differential equations}
}

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DOI: 10.4230/DagRep.12.4.13

Recent Advancements in Tractable Probabilistic Inference (Dagstuhl Seminar 22161)

Authors: Priyank Jaini, Kristian Kersting, Antonio Vergari, and Max Welling

Published in: Dagstuhl Reports, Volume 12, Issue 4 (2022)

Abstract

In several real-world scenarios, decision making involves advanced reasoning under uncertainty, i.e. the ability to answer probabilistic queries. Typically, it is necessary to compute these answers in a limited amount of time. Moreover, in many domains, such as healthcare and economical decision making, it is crucial that the result of these queries is reliable, i.e. either exact or comes with approximation guarantees. In all these scenarios, tractable probabilistic inference and learning are becoming increasingly important. Research on representations and learning algorithms for tractable inference embraces very different fields, each one contributing its own perspective. These include automated reasoning, probabilistic modeling, statistical and Bayesian inference and deep learning. Among the many recent emerging venues in these fields there are: tractable neural density estimators such as autoregressive models and normalizing flows; deep tractable probabilistic circuits such as sum-product networks and sentential decision diagrams; approximate inference routines with guarantees on the quality of the approximation. Each of these model classes occupies a particular spot in the continuum between tractability and expressiveness. That is, different model classes might offer appealing advantages in terms of efficiency or representation capabilities while trading-off other of these aspects. So far, clear connections and a deeper understanding of the key differences among them have been hindered by the different languages and perspectives adopted by the different "souls" that comprise the tractable probabilistic modeling community. This Dagstuhl Seminar brought together experts from these sub-communities and provided the perfect venue to exchange perspectives, deeply discuss the recent advancements and build strong bridges that can greatly propel interdisciplinary research.

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Priyank Jaini, Kristian Kersting, Antonio Vergari, and Max Welling. Recent Advancements in Tractable Probabilistic Inference (Dagstuhl Seminar 22161). In Dagstuhl Reports, Volume 12, Issue 4, pp. 13-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{jaini_et_al:DagRep.12.4.13,
  author =	{Jaini, Priyank and Kersting, Kristian and Vergari, Antonio and Welling, Max},
  title =	{{Recent Advancements in Tractable Probabilistic Inference (Dagstuhl Seminar 22161)}},
  pages =	{13--25},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{12},
  number =	{4},
  editor =	{Jaini, Priyank and Kersting, Kristian and Vergari, Antonio and Welling, Max},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.12.4.13},
  URN =		{urn:nbn:de:0030-drops-172785},
  doi =		{10.4230/DagRep.12.4.13},
  annote =	{Keywords: approximate inference with guarantees, deep generative models, probabilistic circuits, Tractable inference}
}

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Documents authored by Welling, Max

Differential Equations and Continuous-Time Deep Learning (Dagstuhl Seminar 22332)

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Recent Advancements in Tractable Probabilistic Inference (Dagstuhl Seminar 22161)

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