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.
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机译：众所周知，培训具有长期依赖性的任务的经常性神经网络是具有挑战性的。其中一个主要原因是消失或爆炸梯度问题，这可以防止梯度信息传播到早期层。在本文中，我们提出了一种简单的经常性架构，傅里叶复发单元（FRU），其稳定在其培训中产生的梯度，同时给予我们更强大的表现力。具体来说，FRU总结了具有傅立叶基函数的时间维度的隐藏状态$ h ^ {（t）} $。这允许梯度由于FRU的剩余学习结构和三角函数的全球支持而轻松地达到任何层。我们表明FRU与颞尺寸无关的渐变下限和上限。我们还阐述了稀疏傅立叶的强烈表现，从中获得了强大的表现力。我们的实验研究还展示了较少的参数，所提出的体系结构在许多任务中优于其他经常性架构。
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