Momentum as Residual-Driven Multiplier Correction for Deep Learning Optimization
Momentum-based optimizers are widely used in modern deep learning, yet the relations among momentum recursion, update geometry, and acceleration remain only partially understood. We develop an $\textbf{A}$DMM-$\textbf{I}$nspired $\textbf{M}$omentum (AIM) framework based on residual-penalty variable splitting, which interprets momentum as a multiplier-like correction driven by the splitting residual. AIM recovers the exponential moving average of gradients from an ADMM-style multiplier update and separates two mechanisms that are usually intertwined in practical optimizers: the residual penalty determines the update geometry, whereas the approximation of the objective-related subproblem de...
| Authors | Zhixin Ren, Yao Lyu, Congrong Li et al. |
|---|---|
| Primary category | cs.LG |
| Published | 13 August 2026 |
| Last updated at source | 30 August 2026 |
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