Optimizer-Induced Mode Connectivity: From AdamW to Muon

Fuente: arXiv
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Auteurs principaux: Zhang, Fangzhao, Kim, Sungyoon, Zhang, Erica, Jiang, Yiqi, Pilanci, Mert
Format: Preprint
Publié: 2026
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author Zhang, Fangzhao
Kim, Sungyoon
Zhang, Erica
Jiang, Yiqi
Pilanci, Mert
author_facet Zhang, Fangzhao
Kim, Sungyoon
Zhang, Erica
Jiang, Yiqi
Pilanci, Mert
contents Mode connectivity has been widely studied, yet the role of the optimizer remains underexplored. We revisit it through optimizer-induced implicit regularization, asking how connectivity behaves when restricted to solutions constrained by a given optimizer. For two-layer ReLU networks, we show that solutions from a single optimizer -- AdamW, Muon, or others in the Lion-$\mathcal{K}$ family -- form a connected set at sufficiently large width, a result not implied by prior work. We then characterize how optimizer-induced regions interact: at large width two different regions can be disjoint or overlap depending on regularization, while in our small-width example AdamW and Muon converge to disconnected zero-loss components separated by a provable loss barrier. Empirically, in GPT-2 pretraining, we observe same-optimizer paths preserve each model's spectrum while cross-optimizer paths traverse a smooth transition. Our results reveal optimizer-dependent structure beyond classical mode connectivity literature.
format Preprint
id arxiv_https___arxiv_org_abs_2605_09991
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Optimizer-Induced Mode Connectivity: From AdamW to Muon
Zhang, Fangzhao
Kim, Sungyoon
Zhang, Erica
Jiang, Yiqi
Pilanci, Mert
Artificial Intelligence
Machine Learning
Optimization and Control
Mode connectivity has been widely studied, yet the role of the optimizer remains underexplored. We revisit it through optimizer-induced implicit regularization, asking how connectivity behaves when restricted to solutions constrained by a given optimizer. For two-layer ReLU networks, we show that solutions from a single optimizer -- AdamW, Muon, or others in the Lion-$\mathcal{K}$ family -- form a connected set at sufficiently large width, a result not implied by prior work. We then characterize how optimizer-induced regions interact: at large width two different regions can be disjoint or overlap depending on regularization, while in our small-width example AdamW and Muon converge to disconnected zero-loss components separated by a provable loss barrier. Empirically, in GPT-2 pretraining, we observe same-optimizer paths preserve each model's spectrum while cross-optimizer paths traverse a smooth transition. Our results reveal optimizer-dependent structure beyond classical mode connectivity literature.
title Optimizer-Induced Mode Connectivity: From AdamW to Muon
topic Artificial Intelligence
Machine Learning
Optimization and Control
url https://arxiv.org/abs/2605.09991