Capacity and Trainability in Recurrent Neural Networks

TL;DR

This paper investigates the capacity and trainability of various RNN architectures, showing they have similar capacity bounds but differ in training difficulty, and introduces two new architectures that improve training for deep stacks.

Contribution

The study reveals that common RNNs share similar capacity limits and introduces two novel architectures that are easier to train in deep stacking scenarios.

Findings

All RNN architectures have similar capacity bounds.

Capacity is approximately 5 bits per parameter and one input value per hidden unit.

Vanilla RNNs are harder to train but have slightly higher capacity.

Abstract

Two potential bottlenecks on the expressiveness of recurrent neural networks (RNNs) are their ability to store information about the task in their parameters, and to store information about the input history in their units. We show experimentally that all common RNN architectures achieve nearly the same per-task and per-unit capacity bounds with careful training, for a variety of tasks and stacking depths. They can store an amount of task information which is linear in the number of parameters, and is approximately 5 bits per parameter. They can additionally store approximately one real number from their input history per hidden unit. We further find that for several tasks it is the per-task parameter capacity bound that determines performance. These results suggest that many previous results comparing RNN architectures are driven primarily by differences in training effectiveness, rather than differences in capacity. Supporting this observation, we compare training difficulty for several architectures, and show that vanilla RNNs are far more difficult to train, yet have slightly higher capacity. Finally, we propose two novel RNN architectures, one of which is easier to train than the LSTM or GRU for deeply stacked architectures.