Today we had an involving discussion with Bo Zhao about her work on applying topological notions in order to understand the linear mode connectivity and structure of the minima on the loss surface. In particular, using the topological tools One can define the symmetries and build algorithmically low-loss connection ways between minima, which can even be very close to linear curvature. This discussion was mainly based on the ICML 2025 paper “Understanding Mode Connectivity via Parameter Space Symmetry.

Presentation can be found here.