Unitary Evolution Recurrent Neural Networks
This addresses a fundamental problem in training RNNs for long-term dependencies, offering a novel solution that could benefit machine learning practitioners working with sequential data.
The paper tackled the difficulty of training recurrent neural networks (RNNs) due to vanishing and exploding gradients by proposing a new architecture that learns a unitary weight matrix with eigenvalues of absolute value 1, achieving state-of-the-art results in tasks with very long-term dependencies.
Recurrent neural networks (RNNs) are notoriously difficult to train. When the eigenvalues of the hidden to hidden weight matrix deviate from absolute value 1, optimization becomes difficult due to the well studied issue of vanishing and exploding gradients, especially when trying to learn long-term dependencies. To circumvent this problem, we propose a new architecture that learns a unitary weight matrix, with eigenvalues of absolute value exactly 1. The challenge we address is that of parametrizing unitary matrices in a way that does not require expensive computations (such as eigendecomposition) after each weight update. We construct an expressive unitary weight matrix by composing several structured matrices that act as building blocks with parameters to be learned. Optimization with this parameterization becomes feasible only when considering hidden states in the complex domain. We demonstrate the potential of this architecture by achieving state of the art results in several hard tasks involving very long-term dependencies.