# Arithmetic Simplicity in Stochastic Gradient Methods

arXiv: https://arxiv.org/abs/2609.32240 · HTML: https://mlsanity.com/paper/2609.32240/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 10 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 4 of 4)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [AdaGrad stepsizes: Sharp convergence over nonconvex landscapes](https://mlsanity.com/paper/1806.01811/) (2018)
- [Linear Convergence of Adaptive Stochastic Gradient Descent](https://mlsanity.com/paper/1908.10525/) (2019)
- [Adaptivity via a Parallel Architecture for Stochastic Gradient Methods](https://mlsanity.com/paper/2607.28902/) (2026)

## Abstract (arXiv)

A gradient descent method is arithmetically simple if the operations are limited to +,-, ×, and division x/2t 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 xt+1=(1-λη)xt-fracη smt and Adam is the special case of AdamW with λ=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.