# Adaptive Moment Estimation Optimization Algorithm Using Projection Gradient for Deep Learning

arXiv: https://arxiv.org/abs/2503.10005 · HTML: https://mlsanity.com/paper/2503.10005/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Adaptive Gradient Methods with Dynamic Bound of Learning Rate](https://mlsanity.com/paper/1902.09843/) (2019)
- [On the Convergence of A Class of Adam-Type Algorithms for Non-Convex Optimization](https://mlsanity.com/paper/1808.02941/) (2018)
- [Improving Generalization Performance by Switching from Adam to SGD](https://mlsanity.com/paper/1712.07628/) (2017)
- [Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks](https://mlsanity.com/paper/1806.06763/) (2018)
- [Variants of RMSProp and Adagrad with Logarithmic Regret Bounds](https://mlsanity.com/paper/1706.05507/) (2017)
- [AdaX: Adaptive Gradient Descent with Exponential Long Term Memory](https://mlsanity.com/paper/2004.09740/) (2020)

## Abstract (arXiv)

Training deep neural networks is challenging. To accelerate training and enhance performance, we propose PadamP, a novel optimization algorithm. PadamP is derived by applying the adaptive estimation of the p-th power of the second-order moments under scale invariance, enhancing projection adaptability by modifying the projection discrimination condition. It is integrated into Adam-type algorithms, accelerating training, boosting performance, and improving generalization in deep learning. Combining projected gradient benefits with adaptive moment estimation, PadamP tackles unconstrained non-convex problems. Convergence for the non-convex case is analyzed, focusing on the decoupling of first-order moment estimation coefficients and second-order moment estimation coefficients. Unlike prior work relying on , our proof generalizes the convergence theorem, enhancing practicality. Experiments using VGG-16 and ResNet-18 on CIFAR-10 and CIFAR-100 show PadamP's effectiveness, with notable performance on CIFAR-10/100, especially for VGG-16. The results demonstrate that PadamP outperforms existing algorithms in terms of convergence speed and generalization ability, making it a valuable addition to the field of deep learning optimization.