Towards Understanding Adam Convergence on Highly Degenerate Polynomials
Adam is a widely used optimization algorithm in deep learning, yet the specific class of objective functions where it exhibits inherent advantages remains underexplored. Unlike prior studies requiring external schedulers and $β_2$ near 1 for convergence, this work investigates the ``natural'' auto-convergence properties of Adam. We identify a class of highly degenerate polynomials where Adam converges automatically without additional schedulers. Specifically, we derive theoretical conditions for local asymptotic stability on degenerate polynomials and demonstrate strong alignment between theoretical bounds and experimental results. We prove that Adam achieves local linear convergence on t...
| Authors | Zhiwei Bai, Jiajie Zhao, Zhangchen Zhou et al. |
|---|---|
| Primary category | cs.LG |
| Published | 10 March 2026 |
| Last updated at source | 25 May 2026 |
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