Dynamical Isometry and a Mean Field Theory of LSTMs and GRUs
This work addresses training difficulties for researchers and practitioners using recurrent neural networks on long sequence tasks, offering a practical solution with incremental improvements over existing methods.
The authors tackled the problem of training instability in LSTM and GRU networks on long sequences by developing a mean field theory to analyze signal propagation and Jacobian properties, resulting in a novel initialization scheme that enables successful training and improves generalization, with standard initializations failing or being much slower.
Training recurrent neural networks (RNNs) on long sequence tasks is plagued with difficulties arising from the exponential explosion or vanishing of signals as they propagate forward or backward through the network. Many techniques have been proposed to ameliorate these issues, including various algorithmic and architectural modifications. Two of the most successful RNN architectures, the LSTM and the GRU, do exhibit modest improvements over vanilla RNN cells, but they still suffer from instabilities when trained on very long sequences. In this work, we develop a mean field theory of signal propagation in LSTMs and GRUs that enables us to calculate the time scales for signal propagation as well as the spectral properties of the state-to-state Jacobians. By optimizing these quantities in terms of the initialization hyperparameters, we derive a novel initialization scheme that eliminates or reduces training instabilities. We demonstrate the efficacy of our initialization scheme on multiple sequence tasks, on which it enables successful training while a standard initialization either fails completely or is orders of magnitude slower. We also observe a beneficial effect on generalization performance using this new initialization.