As a distinct area, geometric group theory is relatively new, and became an identifiable branch of mathematics in the early 1990's. Geometric group theory closely interacts with low-dimensional topology, hyperbolic geometry, Lie groups and homogeneous spaces, algebraic topology, computational group theory, and differential geometry. There are also substantial connections with complexity theory, mathematical logic, dynamical systems, probability theory, K-theory, and other areas of mathematics.
The workshop will examine how to plan experiments in order to use information in a cost-optimal way. It will also include the application of these modalities to training complex models, such as deep architectures, and the transfer of these ideas to the generation of physically-relevant complex structures such as chemical structures, molecular structures, scalar or vector fields in fluid dynamics or electrodynamics, proposal steps for Markov chain Monte Carlo of physical systems etc.
This workshop will showcase how to employ mathematical aspects of statistical / information theoretic approaches in ML for the discovery of physical laws from data. Offering statistical guarantees along with the learned models is critical in physics and in areas such as aeronautics, climate science, chemistry, biology, and robotics. We will consider model selection, robust statistics, model-free and adaptive learning, and model validation in the context of both static and dynamic models, such as equations of motion.
In this workshop we will explore how to use physical intuition and ideas to design new classes of machine learning (ML) algorithms. Physics-inspired sampling algorithms could be used to train ML structures or sample the hyper-parameter space (e.g. deep Neural Networks). Additionally, physics-based models such as Ising/Potts models or energy-based models have influenced ML inference frameworks such as Markov Random Fields and Restricted Boltzmann Machines, and we want to continue the discussion to facilitate this innovation transfer. Finally, physical insight could be used to enhance learning in the situation of scarce data by enforcing smoothness, differentiability or other physical properties relevant to a given problem.
The program includes week-long workshops in Geometry and Topology, Algebra and Number Theory, and Dynamics and Probability, as well as master courses, seminars, and an art exhibition.
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