## The PIMS Postdoctoral Fellow Seminar: Jakwang Kim

- Date: 09/27/2023

Online

Understanding adversarial robustness via optimal transport perspective.

In this talk, I will present the recent progress of understanding adversarial multiclass classification problems, motivated by the empirical observation of the sensitivity of neural networks by small adversarial attacks. From the perspective of optimal transport theory, I will give equivalent reformulations of this problem in terms of 'generalized barycenter problems' and a family of multimarginal optimal transport problems. These new theoretical results reveal a rich geometric structure of adversarial learning problems in multiclass classification and extend recent results restricted to the binary classification setting. Furthermore, based on this optimal transport approach I will give the result of the existence of optimal robust classifiers which not only extends the binary setting to the general one but also provides shorter proof and an interpretation between adversarial training problems and related generalized barycenter problems.

Research plan:

The application of the Schrodinger bridge problem to computer sciences and statistics is of interest to me. It is well-known that the Schrodinger bridge problem is the entropic regularized optimal transport problem. On the other hand, rich studies about it from the probabilistic perspectives are known. So, combining these two viewpoints will provide a numerous implication for both theoretical and practical purposes. In particular, I want to understand this problem in the hypercube and connect it to Oliver's Ricci curvature and geodesic convexity arguments.

Try to understand various discrete Ricci's curvature definitions of Markov chains on finite cases(spin systems etc.), how to integrate them and connect to verify nice implications(e.g. log-Sobolev inequalities) on finite cases.

**Speaker biography:** Jakwang Kim is a PIMS Postdoctoral fellow at the University of British Columbia, under the sponsorship of the PIMS Research Network - Kanotrovich Initiative. His area of research is in Optimal Transport, as well as high-dimensional inference problems like stochastic block models, planted clique problems, and graph matching problems. In particular, statistical-information phase transition will play an important role to understand not only these toy models of random optimization but also real-world problems, e.g. success of deep learning, LLM etc.

This event is part of the Emergent Research: The PIMS Postdoctoral Fellow Colloquium Series.

This seminar takes places across multiple time zones: 9:30 AM Pacific/ 10:30 AM Mountain / 11:30 AM Central

Register via Zoom to receive the link (and reminders) for this event and the rest of the series.

See past seminar recordings on MathTube.