#
Boltzmann machines

September 17 to September 21, 2018
at the

American Institute of Mathematics,
San Jose, California

organized by

Asja Fischer,
Guido Montufar,
and Jason Morton

## Original Announcement

This workshop will be devoted to the mathematics of Boltzmann machines. Since their debut in
the context of deep learning, Boltzmann machines have been studied intensively,
with significant leaps over the past six years, giving them a rare combination
of mathematical traction and practical machine learning relevance. Researchers
have been pushing tools in information theory, algebra, combinatorics, geometry,
and optimization to their limits to achieve the understanding we currently have
of these models. The result is a situation where further progress probably
requires a more intimate merger of these tools.
The workshop will analyze Boltzmann machines in terms of

- their representational power (compact representations, approximation errors,
geometry),
- parameter leaning and optimization (discrete dynamics, sampling, structure of
the loss function), and
- their connections to other models and generalizations (deep/ quantum/temporal
models).

Advancing on these topics will, so we hope, open new avenues to study
probabilistic graphical models with hidden variables in general, and contribute
to the mathematical foundations of machine learning.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

A list of open problems.

Workshop Videos

Papers arising from the workshop: