Optimizer-Induced Mode Connectivity: From AdamW to Muon
In a groundbreaking study recently released on arXiv, researchers delve into the intricate relationship between optimizers and mode connectivity in neural networks. The paper titled “Optimizer-Induced Mode Connectivity” (arXiv:2605.09991v1) explores how different optimization algorithms influence the connectivity of solutions within the landscape of neural networks, particularly focusing on two-layer ReLU networks.
Understanding Mode Connectivity
Mode connectivity refers to the phenomenon where multiple local minima of a neural network’s loss function can be connected through paths of lower loss, suggesting that these solutions share similar performance characteristics. While previous research has extensively examined mode connectivity, the role of optimizers in shaping these connections has received comparatively less attention.
Key Findings of the Study
The researchers have made several significant observations:
- Optimizer-Induced Implicit Regularization: The study posits that the choice of optimizer can impose implicit regularization that shapes the connectivity of solutions. This challenges the notion that mode connectivity is solely a property of the loss landscape.
- Connected Sets at Large Width: For sufficiently wide two-layer ReLU networks, the study demonstrates that solutions derived from a single optimizer—such as AdamW, Muon, and others in the Lion-$\mathcal{K}$ family—form a connected set. This finding extends the existing literature by showing that connectivity is dependent on the optimizer used.
- Interaction Between Optimizer-Induced Regions: At large widths, the research reveals that solutions from different optimizers may exhibit disjoint regions or overlap, depending on the regularization strategies employed. This duality highlights the complex nature of optimizer impacts.
- Disconnection at Small Width: In scenarios involving smaller networks, the analysis indicates that AdamW and Muon converge to distinct zero-loss components, which are separated by a provable loss barrier. This suggests that as networks narrow, the choice of optimizer becomes even more critical in determining performance.
- Empirical Observations in GPT-2 Pretraining: Utilizing GPT-2 pretraining, the researchers found that paths taken by the same optimizer preserve the model’s spectrum, whereas paths involving different optimizers lead to a smooth transition. This observation underscores the profound influence that optimizers exert on model training dynamics.
Implications for Future Research
The findings from this study not only enhance our understanding of mode connectivity but also suggest a new avenue for research focused on the implications of optimizer choice in neural network training. By characterizing how various optimizers induce different structures within the solution space, researchers can better tailor optimization strategies to improve model performance and generalization.
As the field of artificial intelligence continues to evolve, the insights gained from this research could lead to more effective training methodologies, making it a pivotal contribution to ongoing discussions surrounding neural network optimization.
Conclusion
The exploration of optimizer-induced mode connectivity opens new doors for understanding the complex interactions within neural networks. This research reinforces the notion that the choice of optimizer is not merely a technical detail but a fundamental factor that shapes the very architecture of the solution landscape. As researchers build upon these findings, the future of AI optimization looks to be more nuanced and sophisticated than ever before.
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