From SGD to Muon: Adaptive Optimization via Schatten-p Norms
The article introduces a new adaptive optimization framework that utilizes Schatten-p norms for deep neural networks. This framework dynamically selects optimal update geometries based on runtime data, improving upon traditional fixed geometries. The proposed method demonstrates competitive performance against established optimizers like Muon and AdamW across various training scenarios.
- ▪Modern optimizers impose matrix-wise geometry constraints on updates.
- ▪The new framework allows for dynamic selection of proxy-optimal update geometries.
- ▪It achieves only a 3% runtime overhead on highly optimized baselines.
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| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.19781 |
| Publication time | Wed, 20 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-20T04:04:59.484Z |
| Last seen | 2026-05-20T04:04:59.484Z |
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Computer Science > Artificial Intelligence arXiv:2605.19781 (cs) [Submitted on 19 May 2026] Title:From SGD to Muon: Adaptive Optimization via Schatten-p Norms Authors:Thomas Massena (IRIT, DTIPG - SNCF, UT3), Corentin Friedrich, Mathieu Serrurier (IRIT) View a PDF of the paper titled From SGD to Muon: Adaptive Optimization via Schatten-p Norms, by Thomas Massena (IRIT and 4 other authors View PDF Abstract:Modern optimizers, like Muon, impose matrix-wise geometry constraints on their updates. These matrix-wise constraints can be unified under Linear Minimization Oracle (LMO) theory. However, all current methods impose fixed LMO geometries for the update rules, chosen by-design or empirically, which are not necessarily optimal according to the problem's geometry.
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