Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer
Aratrika Mustafi, Soumya Mukherjee, Bharath K. Sriperumbudur
Key claim
Muon optimizer achieves exponential convergence in probabilistic settings.
This paper presents a new gradient flow for optimizing matrix-valued parameters using a regularized version of the Muon optimizer. The key result is the establishment of a damped Hamiltonian dynamics that ensures energy dissipation and convergence rates under certain conditions, which could enhance training in neural networks.
The paper extends the Muon optimizer to a probabilistic framework, introducing new dynamics.
The methodology is solid with rigorous derivations and convergence guarantees.
Deep reliability assessment
The methodology supports the development of a Hamiltonian probability flow that effectively captures the dynamics of the Muon optimizer, but claims of exponential convergence rates may be overly optimistic without sufficient empirical validation. The theoretical results are promising but require practical testing to confirm their applicability in real-world scenarios.
Reproducibility
No, there is no mention of open source code or datasets provided in the paper.
Discussion questions
- How does the assumption of matrix-valued parameters influence the generalizability of the Muon optimizer to other types of neural network architectures?
- What are the practical implications of implementing the regularized Muon optimizer in large-scale machine learning models, particularly in terms of computational efficiency?
- What specific conditions or scenarios would lead to a breakdown of the claimed exponential convergence rates in practice?
Key figure
Figure 1 illustrates the performance of the Muon optimizer in two synthetic experiments, showcasing the convergence of the objective and Hamiltonian energies over time.