Generalized Linear Mode Connectivity for Transformers
Alexander Theus, Alessandro Cabodi, Sotiris Anagnostidis, Antonio Orvieto, Sidak Pal Singh, Valentina Boeva
Understanding the geometry of neural network loss landscapes is a central question in deep learning, with implications for generalization and optimization. A striking phenomenon is $\textit{linear mode connectivity}$ (LMC), where independently trained models can be connected by low- or zero-loss paths, despite appearing to lie in separate basins. However, this is often obscured by symmetries in parameter space—such as neuron permutations—which make functionally equivalent models appear dissimilar. Prior work has predominantly focused on neuron re-ordering through permutations, but such approaches are limited in scope and fail to capture the richer symmetries exhibited by modern architectures such as Transformers. In this work, we introduce a unified framework that captures four symmetry classes—permutations, semi-permutations, orthogonal transformations, and general invertible maps—broadening the set of valid reparameterizations and subsuming many previous approaches as special cases. Crucially, this generalization enables, for the first time, the discovery of low- and zero-barrier linear interpolation paths between independently trained Vision Transformers and GPT-2 models. These results reveal deeper structure in the loss landscape and underscore the importance of symmetry-aware analysis for understanding model space geometry.