RNNs Evolving on an Equilibrium Manifold: A Panacea for Vanishing and Exploding Gradients?

Recurrent neural networks (RNNs) are particularly well-suited for modeling long-term dependencies in sequential data, but are notoriously hard to train because the error backpropagated in time either vanishes or explodes at an exponential rate. While a number of works attempt to mitigate this effect through gated recurrent units, well-chosen parametric constraints, and skip-connections, we develop a novel perspective that seeks to evolve the hidden state on the equilibrium manifold of an ordinary differential equation (ODE). We propose a family of novel RNNs, namely {\em Equilibriated Recurrent Neural Networks} (ERNNs) that overcome the gradient decay or explosion effect and lead to recurrent models that evolve on the equilibrium manifold. We show that equilibrium points are stable, leading to fast convergence of the discretized ODE to fixed points. Furthermore, ERNNs account for long-term dependencies, and can efficiently recall informative aspects of data from the distant past. We show that ERNNs achieve state-of-the-art accuracy on many challenging data sets with 3-10x speedups, 1.5-3x model size reduction, and with similar prediction cost relative to vanilla RNNs.