It is a known fact that training recurrent neural networks for tasks that
have long term dependencies is challenging. One of the main reasons is the
vanishing or exploding gradient problem, which prevents gradient information
from propagating to early layers. In this paper we propose a simple recurrent
architecture, the Fourier Recurrent Unit (FRU), that stabilizes the gradients
that arise in its training while giving us stronger expressive power.
Specifically, FRU summarizes the hidden states $h^{(t)}$ along the temporal
dimension with Fourier basis functions. This allows gradients to easily reach
any layer due to FRU's residual learning structure and the global support of
trigonometric functions. We show that FRU has gradient lower and upper bounds
independent of temporal dimension. We also show the strong expressivity of
sparse Fourier basis, from which FRU obtains its strong expressive power. Our
experimental study also demonstrates that with fewer parameters the proposed
architecture outperforms other recurrent architectures on many tasks.

本文提出了一种简单的循环神经网络架构，即傅里叶循环单元 (FRU)，它稳定了训练中出现的梯度，同时为我们提供了更强的表现能力。具体而言，FRU 使用傅里叶基函数概括了沿时间维度的隐藏状态 $h^{(t)}$，使得由于残差学习结构和三角函数的全局支持，梯度可以轻松地到达任何层。我们还展示了 FRU 具有与时间维度无关的梯度下限和上限，以及得到 FRU 强表现力的稀疏傅里叶基的优势。我们的实验研究还表明，与其他循环架构相比，所提出的架构在许多任务上具有更少的参数且表现更好。