# HomeAdam: Adam and AdamW Algorithms Sometimes Go Home to Obtain Better Provable Generalization

arXiv: https://arxiv.org/abs/2603.02649 · HTML: https://mlsanity.com/paper/2603.02649/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 46 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [Deep Reinforcement Learning for Robotics: A Survey of Real-World Successes](https://mlsanity.com/paper/2408.03539/) (2024)
- [On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization](https://mlsanity.com/paper/1808.02941/) (2018)
- [Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models](https://mlsanity.com/paper/2208.06677/) (2022)
- [A Simple Convergence Proof of Adam and Adagrad](https://mlsanity.com/paper/2003.02395/) (2020)
- [A Sufficient Condition for Convergences of Adam and RMSProp](https://mlsanity.com/paper/1811.09358/) (2018)
- [Improving Generalization Performance by Switching from Adam to SGD](https://mlsanity.com/paper/1712.07628/) (2017)
- [Why Transformers Need Adam: A Hessian Perspective](https://mlsanity.com/paper/2402.16788/) (2024)
- [Fine-Grained Analysis of Stability and Generalization for Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08157/) (2020)
- [Adam Can Converge Without Any Modification On Update Rules](https://mlsanity.com/paper/2208.09632/) (2022)
- [On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization](https://mlsanity.com/paper/1808.05671/) (2018)
- [Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks](https://mlsanity.com/paper/1806.06763/) (2018)
- [Implicit Bias of AdamW: ℓ_∞ Norm Constrained Optimization](https://mlsanity.com/paper/2404.04454/) (2024)
- [A Novel Convergence Analysis for Algorithms of the Adam Family](https://mlsanity.com/paper/2112.03459/) (2021)
- [Understanding the Generalization of Adam in Learning Neural Networks with Proper Regularization](https://mlsanity.com/paper/2108.11371/) (2021)
- [Closing the Gap Between the Upper Bound and the Lower Bound of Adam's Iteration Complexity](https://mlsanity.com/paper/2310.17998/) (2023)
- [Stability and Generalization of Stochastic Optimization with Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/2206.07082/) (2022)
- [Can We Remove the Square-Root in Adaptive Gradient Methods? A Second-Order Perspective](https://mlsanity.com/paper/2402.03496/) (2024)
- [On the Generalization of Stochastic Gradient Descent with Momentum](https://mlsanity.com/paper/1809.04564/) (2018)
- [ADOPT: Modified Adam Can Converge with Any β2 with the Optimal Rate](https://mlsanity.com/paper/2411.02853/) (2024)

## Built on by (most cited first, 1 of 1)

- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)

## Abstract (arXiv)

Adam and AdamW are a class of default optimizers for training deep learning models in machine learning. These adaptive algorithms converge faster but generalize worse compared to SGD. In fact, their proved generalization error O(frac1√N) also is larger than O(frac1N) of SGD, where N denotes training sample size. Recently, although some variants of Adam have been proposed to improve its generalization, their improved generalizations are still unexplored in theory. To fill this gap, in the paper, we restudy generalization of Adam and AdamW via algorithmic stability, and first prove that Adam and AdamW without square-root (i.e., Adam(W)-srf) have a generalization error O(frachatρ-2TN), where T denotes iteration number and hatρ>0 denotes the smallest element of second-order momentum plus a small positive number. To improve generalization, we propose a class of efficient clever Adam (i.e., HomeAdam(W)) algorithms via sometimes returning momentum-based SGD. Moreover, we prove that our HomeAdam(W) have a smaller generalization error O(frac1N) than O(frachatρ-2TN) of Adam(W)-srf, since hatρ is generally very small. In particular, it is also smaller than the existing O(frac1√N) of Adam(W). Meanwhile, we prove our HomeAdam(W) have a faster convergence rate of O(frac1T1/4) than O(fracbreveρ-1T1/4) of the Adam(W)-srf, where breveρ≤hatρ also is very small. Extensive numerical experiments demonstrate efficiency of our HomeAdam(W) algorithms.