Understanding Mode Connectivity via Parameter Space Symmetry
Keywords: symmetry, mode connectivity
Abstract: Neural network minima have been observed to be connected by curves along which train and test loss remain nearly constant, a phenomenon known as mode connectivity.
While this has enabled applications such as model merging and fine-tuning, its theoretical explanation remains unclear.
We propose a new approach to exploring the connectedness of minima using parameter space symmetry.
By linking the topology of symmetry groups to that of the minima, we derive the number of connected components of the minima of linear networks and show that skip connections reduce this number.
We then examine when mode connectivity and linear mode connectivity hold or fail, using parameter symmetries which account for a significant part of the minimum.
Finally, we provide explicit expressions for connecting curves in the minima induced by symmetry.
Using the curvature of these curves, we derive conditions under which linear mode connectivity approximately holds.
Our analysis highlights the role of continuous symmetries in understanding the neural network loss landscape.
Primary Area: learning theory
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 12981
Loading