Back-propagation (BP) is widely used learning algorithm for neural network optimization. However, BP requires enormous computation cost and is too slow to train in central processing unit (CPU). Therefore current neural network optimizaiton is performed in graphical processing unit (GPU) with compute unified device architecture (CUDA) programming. In this paper, we propose a light, fast learning algorithm on CPU that is fast as CUDA acceleration on GPU. This algorithm is based on forward-propagating method, using concept of dual number in algebraic geometry.

翻译：反向传播（BP）是神经网络优化中广泛使用的学习算法。然而，BP需要巨大的计算成本，且在中央处理器（CPU）上训练速度过慢。因此，当前的神经网络优化需在采用统一计算设备架构（CUDA）编程的图形处理器（GPU）上执行。本文提出一种在CPU上运行的轻量级快速学习算法，其速度可与GPU上的CUDA加速相媲美。该算法基于前向传播方法，并利用代数几何中的对偶数概念。