Year: 2021
Type: preprint
Abstract: Adam is an adaptive gradient method that has experienced widespread adoption due to its fast and reliable training performance. Recent approaches have not offered significant improvement over Adam, often because they do not innovate upon one of its core features: normalization by the root mean square (RMS) of recent gradients. However, as noted by Kingma and Ba (2015), any number of $L^p$ normalizations are possible, with the RMS corresponding to the specific case of $p=2$. In our work, we theoretically and empirically characterize the influence of different $L^p$ norms on adaptive gradient methods for the first time. We show mathematically how the choice of $p$ influences the size of the steps taken, while leaving other desirable properties unaffected. We evaluate Adam with various $L^p$ norms on a suite of deep learning benchmarks, and find that $p > 2$ consistently leads to improved learning speed and final performance. The choices of $p=3$ or $p=6$ also match or outperform state-of-the-art methods in all of our experiments.
Source: arXiv (Cornell University)
Authors: Daley, Brett, Amato, Christopher
Institution: Northeastern University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3165904201