Invited Talk #4: Landscaping Linear Mode Connectivity: The Geometry of Barriers

While Linear Mode Connectivity (LMC) reveals linear paths between neural network solutions, the geometric origins of these paths --- and the barriers that obstruct them --- remain poorly understood. This talk introduces a topographical model of the loss landscape to explain how LMC occurs. Concretely, we present empirical experiments on forked training trajectories that indicate a distinct structure governing these paths. We use the perspective of ridges to tie together these observed geometric features. Further, to complement this, we present a theoretical analysis of LMC barrier heights that highlights the critical role played by curvature. Finally, we will outline future work on how to mathematically formalize these landscape ridges as restricted local maxima.