Topology and Machine Learning:
Workshop in Shonan (2023)

A workshop on machine learning and topology will be held in Shonan Village Center scheduled from August 3, 2023 to August 5, 2023.  Both of machine learning and topology will be discussed: the application of machine learning to topology, and vice versa.  One example is the persistent homology which is useful to extract topological features from the data distribution.  The successful cases include the possible characterization of materials without well-defined order parameters.  For instance, confinement in non-Abelian gauge theories (Yang-Mills theories) is a quite nontrivial phenomenon in physics and it is hard to identify the order parameter.  It has been demonstrated that the Betti number associated with the persistent homology for gauge configurations is sensitive to the phase transition of confinement/deconfinement.  See: "Confinement in non-Abelian lattice gauge theory via persistent homology" by Spitz, Urban, and Pawlowski.
The scope of the workshop will also include the implementation of the normalizing flow which connects two probability distributions by an invertible and differentiable function.  For an application to the sign problem in quantum field theory, see: "Flow-based density of states for complex actions" by Pawlowski and Urban.  The topology or the homotopy requires continuous mapping and we are expecting the application of the normalizing flow to find topological invariants efficiently.

In this workshop, the B03 group will welcome three visitors from Germany:

• Jan Pawlowski (Heidelberg Univ.)

• Jan Horak  (Heidelberg Univ.)

• Len Brandes (Technical Univ. of Munich)

They are experts on the quantum field theory, machine learning, and data analysis based on the probabilistic method (Bayesian analysis), and the technique of the normalizing flow.  Also, the B03 group will invite:

• Akinori Tanaka (RIKEN AIP)

to deliver an intensive lecture on the foundation of the normalizing flow.  Dr. Tanaka is a leader of the B01 group which focuses on Mathematics and Application to of Deep Learning.  We are expecting inter-group discussions.

The aim of the workshop is to explore new directions for the application of machine learning techniques, especially something related to topology.  So far, the persistent homology is widely used to deal with the data and is partially combined with the graph neural network to improve the performance for the graph classification.  We will be seeking for some alternatives to the persistent homology and/or more active usages of the data topology to quantify the machine learning efficiency.  We will also discuss how to implement the normalizing flow for the purpose of characterizing the topological features.

Participation in this workshop is by invitation only.

Confirmed Participants

• Len Brandes   (Technical Univ. of Munich, Ph.D. student)

• Kenji Fukushima   (Univ. of Tokyo, Professor)

• Yuji Hirono   (Kyoto Univ., Associate Professor)

• Jan Horak   (Heidelberg Univ., Ph.D. student)

• Syo Kamata   (Univ. of Tokyo, Assistant Professor)

• Tatsuhiro Misumi   (Kindai Univ., Associate Professor)

• Koichi Murase   (Yukawa Institute for Theoretical Physics, Assistant Professor)

• (Lecturer) Jan Pawlowski   (Heidelberg Univ., Professor)

• Ken Shiozaki   (Yukawa Institute for Theoretical Physics, Assistant Professor)

• (Lecturer) Akinori Tanaka   (RIKEN, AIP, Senior Research Scientist)

Schedule