Memory-Efficient Subspace Optimization with Residual Correction: From Momentum SGD to Muon
Memory-efficient subspace optimization has emerged as a practical approach to reducing the memory cost of LLM training while preserving optimization performance. Previous algorithms typically rely on the leading singular subspace of stochastic gradients, yet the gradient noise may dominate the subspace in later training stages and can prevent convergence. To overcome this limitation, we adopt a residual correction framework, which maintains the optimizer states in the subspace and adds the orthogonal residual gradient to the parameter update. We first integrate this scheme into momentum SGD to develop SMRC, which attains an $O(T^{-1/4})$ convergence rate for a fixed orthonormal basis, mat...
| Authors | Sifan Yang, Hongyi Tao, Dingzhi Yu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
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