Exploring Neural Network Landscapes: Star-Shaped and Geodesic Connectivity
Abstract: One of the most intriguing findings in the structure of neural network landscapes is the phenomenon of mode connectivity: For two typical global minima, there exists a path connecting them without barrier. This concept of mode connectivity has played a crucial role in understanding important phenomena in deep learning.
In this paper, we conduct a fine-grained analysis of this connectivity phenomenon. First, we demonstrate that in the overparameterized case, the connecting path can be as simple as a two-piece linear path, and the path length can be nearly equal to the Euclidean distance. This finding suggests that the landscape should be nearly convex in a certain sense. Second, we uncover a surprising star-shaped connectivity: For a finite number of typical minima, there exists a center on the minima manifold that connects all of them simultaneously via linear paths. These results are provably valid for linear networks and two-layer ReLU networks under a teacher-student setup, and are empirically supported by models trained on MNIST and CIFAR-10.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Serguei_Barannikov1
Submission Number: 2686
Loading