Training-time Neuron Alignment through Permutation Subspace for Improving Linear Mode Connectivity and Model Fusion

In deep learning, stochastic gradient descent often yields functionally similar yet widely scattered solutions in the weight space even under the same initialization, causing barriers in the Linear Mode Connectivity (LMC) landscape. Overcoming these barriers is crucial for understanding deep learning dynamics and enhancing model-fusion algorithms. Previous studies highlight the role of permutation symmetry in reducing post-training barriers through network permutation. However, these post-hoc methods, demanding extra computations, are less effective for larger, complex models (e.g., ViT, LLM) due to numerous permutation matrices. Thus, in this paper, we study training-time neuron alignment. Our hypothesis suggests that training-time permutation subspace can reduce LMC barriers for free. We find that pruning at initialization supports this. Beyond pruning, we introduce TNA-PFN, a simple yet lossless algorithm using a partial gradient mask during training. TNA-PFN is theoretically and empirically validated for reducing LMC barriers. It excels in wide model fusion applications, especially in federated learning, two algorithms based on TNA-FPN that are proposed to show its prospects even under heterogeneous datasets. Moreover, TNA-PFN can enhance the generalization of model soup for vision transformers and ColD fusion for pretrained language models.