Git Re-Basin: Merging Models modulo Permutation Symmetries (2209.04836v6)

Abstract: The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

• The paper reveals that permutation symmetry transforms complex loss landscapes into a near-convex basin, explaining the surprising success of SGD.
• It introduces three algorithms that reorder network weights to merge independently trained models, achieving zero-barrier linear mode connectivity.
• Empirical results show clear links between model width and training dynamics, offering practical insights for efficient model interpolation and federated learning.

An Analytical Overview of "Git Re-Basin: Merging Models Modulo Permutation Symmetries"

The paper "Git Re-Basin: Merging Models Modulo Permutation Symmetries," authored by Ainsworth et al., explores the intriguing phenomenon of permutation symmetries within the neural network training process. It examines how simple algorithms, particularly those based on stochastic gradient descent (SGD), inexplicably thrive in optimizing large, non-convex loss landscapes. The authors propose that the surprising success of these algorithms is due to an underlying near-single basin structure of loss landscapes when accounting for permutation symmetries.

Core Contributions

1. Permutation Symmetry in Neural Networks: The paper builds on the conjecture by Entezari et al., extending the idea that neural networks' loss landscapes can be transformed such that they approximate a single convex basin after addressing all permutation symmetries of hidden units. This theoretical perspective provides insight into why different SGD solutions can be linearly connected without significant barriers, a phenomenon termed linear mode connectivity (LMC).
2. Proposed Algorithms for Model Merging: The authors introduce three innovative algorithms to permute and align the weights of two independently trained models to merge them in weight space. These algorithms leverage combinatorial optimization techniques to re-order network neurons, achieving a functionally equivalent set of weights that bring the two models into an approximately convex region. Notably, the paper highlights an emergent property of training procedures related to LMC, experimentally verifying these ideas with remarkable results across various architectures and datasets.
3. Zero-Barrier Linear Mode Connectivity: A substantial empirical contribution is the demonstration of zero-barrier LMC using the proposed methods, particularly between independently trained ResNet models on the CIFAR-10 dataset. This result lends robust support to the hypothesis of a single basin structure and advances practical applications of model interpolation and merging.
4. Analyzing Model Width and Training Dynamics: The experiments underscore intriguing relationships between model width, training time, and the facilitation of LMC. These findings suggest that wider models might naturally align more closely to the permutation invariant hypothesis, guiding practical deployment of these algorithms in architectures where training efficiency and model robustness are critical.
5. Addressing Limitations and Counterexamples: The authors also acknowledge and explore the boundaries of their linear mode connectivity hypothesis. By constructing counterexamples, they demonstrate that linear mode connectivity is not guaranteed in all cases, emphasizing that SGD's implicit search bias is a notable factor in achieving such connectivity.

Theoretical and Practical Implications

The work lays down pivotal theoretical groundwork for understanding the meta-geometry of learned solutions in deep learning, specifically in the context of permutation symmetries. Practically, the insights and algorithms proposed have wide-ranging implications, from advancing federated learning methodologies to enabling efficient model patching and ensemble techniques without incurring additional computational costs.

The intersection of permutation symmetries and SGD properties raises critical questions about how we conceptualize the robustness and generalization potential of neural networks. It opens up avenues for further exploration in symmetry breaking, alternative optimization algorithms, and potentially more adaptive training procedures that exploit this underlying loss landscape geometry.

Future Research Directions

The paper invites further investigation into the nature of these symmetries and their interplay with various optimization protocols beyond SGD. Additionally, exploring the confluence of such invariance structures with emerging models like ConvNeXt and architectures involving extensive depth-wise convolutions could offer new insights into architectural adjustments that naturally support or hinder these phenomena.

In summary, "Git Re-Basin" marries theoretical inquiry with experimental validation, pushing the envelope of our understanding of neural network training dynamics and their structural invariances. It sets a foundation for exploring more nuanced geometric and algebraic properties of neural models, with significant implications for future AI developments.