Architectural Complexity Measures of Recurrent Neural Networks
This work addresses the need for systematic architectural analysis in RNNs, which is incremental as it builds on existing concepts to provide new measures.
The paper tackles the problem of analyzing and measuring the architectural complexity of recurrent neural networks (RNNs) by proposing a graph-theoretic framework and three complexity measures, with experimental results showing that larger recurrent depth, feedforward depth, and recurrent skip coefficient can improve performance, such as boosting performance on long-term dependency problems.
In this paper, we systematically analyze the connecting architectures of recurrent neural networks (RNNs). Our main contribution is twofold: first, we present a rigorous graph-theoretic framework describing the connecting architectures of RNNs in general. Second, we propose three architecture complexity measures of RNNs: (a) the recurrent depth, which captures the RNN's over-time nonlinear complexity, (b) the feedforward depth, which captures the local input-output nonlinearity (similar to the "depth" in feedforward neural networks (FNNs)), and (c) the recurrent skip coefficient which captures how rapidly the information propagates over time. We rigorously prove each measure's existence and computability. Our experimental results show that RNNs might benefit from larger recurrent depth and feedforward depth. We further demonstrate that increasing recurrent skip coefficient offers performance boosts on long term dependency problems.