Convolutional unitary or orthogonal recurrent neural networks
This work addresses training difficulties in convolutional RNNs for machine learning practitioners, offering an incremental improvement over existing orthogonal/unitary methods.
The authors tackled the vanishing gradient problem in recurrent neural networks by introducing convolutional exponential operations that transform antisymmetric or anti-Hermitian kernels into orthogonal or unitary ones, enabling efficient training with computational complexity matching the network iteration.
Recurrent neural networks are extremely powerful yet hard to train. One of their issues is the vanishing gradient problem, whereby propagation of training signals may be exponentially attenuated, freezing training. Use of orthogonal or unitary matrices, whose powers neither explode nor decay, has been proposed to mitigate this issue, but their computational expense has hindered their use. Here we show that in the specific case of convolutional RNNs, we can define a convolutional exponential and that this operation transforms antisymmetric or anti-Hermitian convolution kernels into orthogonal or unitary convolution kernels. We explicitly derive FFT-based algorithms to compute the kernels and their derivatives. The computational complexity of parametrizing this subspace of orthogonal transformations is thus the same as the networks' iteration.