no code implementations • 6 Feb 2024 • Yikun Bai, Rocio Diaz Martin, Abihith Kothapalli, Hengrong Du, Xinran Liu, Soheil Kolouri
We establish that PGW is a well-defined metric between mm-spaces and discuss its theoretical properties, including the existence of a minimizer for the PGW problem and the relationship between PGW and GW, among others.
no code implementations • 4 Feb 2024 • Huy Tran, Yikun Bai, Abihith Kothapalli, Ashkan Shahbazi, Xinran Liu, Rocio Diaz Martin, Soheil Kolouri
Comparing spherical probability distributions is of great interest in various fields, including geology, medical domains, computer vision, and deep representation learning.
no code implementations • 8 Jun 2023 • Ashkan Shahbazi, Abihith Kothapalli, Xinran Liu, Robert Sheng, Soheil Kolouri
Our findings reveal that: 1) complex pooling methods, such as transport-based or attention-based poolings, can significantly boost the performance of simple backbones, but the benefits diminish for more complex backbones, 2) even complex backbones can benefit from pooling layers in low data scenarios, 3) surprisingly, the choice of pooling layers can have a more significant impact on the model's performance than adjusting the width and depth of the backbone, and 4) pairwise combination of pooling layers can significantly improve the performance of a fixed backbone.
1 code implementation • 6 Jun 2023 • Abihith Kothapalli, Mudassir Shabbir, Xenofon Koutsoukos
The minimum dominating set problem seeks to find a dominating set of minimum cardinality and is a well-established NP-hard combinatorial optimization problem.