Arithmetic Simplicity in Stochastic Gradient Methods

Abstract:A gradient descent method is arithmetically simple if the operations are limited to $+,-, \times$, and division $x/2^t$ with integer $t$. An arthmetically simple gradient method is easy to implement in chip design. We show how to transform AdaGrad, Adam, and AdamW into arithmetically simple. AdamW is based on the recursion $x_{t+1}=(1-\lambda\eta)x_t-\frac{\eta }{s}m_t$ and Adam is the special case of AdamW with $\lambda=0$. We transform them into a static case with $s=S(T)$, where $T$ is the number of iterations, and $S(T)$ is a fixed function. The convergence analysis is given for a static Adam, which is also arithmetically simple.

Machine Learning (cs.LG)

arXiv:2609.32240 [cs.LG]

(or arXiv:2609.32240v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.32240 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.