Arithmetic Simplicity in Stochastic Gradient Methods
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 $x_{t+1}=(1-λη)x_t-\frac{η}{s}m_t$ 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.
| Authors | Bin Fu, Pengfei Gu, Jose Nunez et al. |
|---|---|
| Primary category | cs.LG |
| Published | 26 September 2026 |
| Last updated at source | 26 September 2026 |
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