Simple arithmetic methods make popular gradient optimizers easier to build
Arithmetic Simplicity in Stochastic Gradient Methods
Machine Learning
Summary
Gradient descent methods help computers learn by adjusting settings step by step, but some use complex math that’s hard to build into hardware chips. The authors found a way to simplify popular methods like AdaGrad, Adam, and AdamW using only basic arithmetic operations like addition, subtraction, multiplication, and division by powers of two. This makes these learning methods easier to implement in chip design. They also showed how the simpler Adam method still works well with a fixed step size.
What this means in practice
- •For chip designers: Design chips that implement popular gradient algorithms more efficiently using only simple arithmetic operations.
- •For embedded system developers: Implement more power- and resource-efficient machine learning optimizers on embedded or edge hardware using arithmetic simple algorithms.
Authors
Bin Fu, Pengfei Gu, Jose Nunez, Fabian Vazquez
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 $x_{t+1}=(1-λη)x_t-\frac{η}{s}m_t$ 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.