Anon: Extrapolating Adaptivity Beyond SGD and Adam

• URL: http://arxiv.org/abs/2605.02317v2
• Date: Wed, 06 May 2026 13:42:00 GMT
• Title: Anon: Extrapolating Adaptivity Beyond SGD and Adam
• Abstract summary: Anon provides the first unified and reliable framework capable of bridging the gap between classical and moderns.<n>Anon is more flexible than hard-tracking and enhances gradient robustness to noise.
• Score: 25.876261427108673
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Adaptive optimizers such as Adam have achieved great success in training large-scale models like large language models and diffusion models. However, they often generalize worse than non-adaptive methods, such as SGD on classical architectures like CNNs. We identify a key cause of this performance gap: adaptivity in pre-conditioners, which limits the optimizer's ability to adapt to diverse optimization landscapes. To address this, we propose Anon (Adaptivity Non-restricted Optimizer with Novel convergence technique), a novel optimizer with continuously tunable adaptivity in R, allowing it to interpolate between SGD-like and Adam-like behaviors and even extrapolate beyond both. To ensure convergence across the entire adaptivity spectrum, we introduce incremental delay update (IDU), a novel mechanism that is more flexible than AMSGrad's hard max-tracking strategy and enhances robustness to gradient noise. We theoretically establish convergence guarantees under both convex and non-convex settings. Empirically, Anon consistently outperforms state-of-the-art optimizers on representative image classification, diffusion, and language modeling tasks. These results demonstrate that adaptivity can serve as a valuable tunable design principle, and Anon provides the first unified and reliable framework capable of bridging the gap between classical and modern optimizers and surpassing their advantageous properties.

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