Rethinking the Relationship between Recurrent and Non-Recurrent Neural Networks: A Study in Sparsity

Neural networks (NN) can be divided into two broad categories, recurrent and non-recurrent. Both types of neural networks are popular and extensively studied, but they are often treated as distinct families of machine learning algorithms. In this position paper, we argue that there is a closer relationship between these two types of neural networks than is normally appreciated. We show that many common neural network models, such as Recurrent Neural Networks (RNN), Multi-Layer Perceptrons (MLP), and even deep multi-layer transformers, can all be represented as iterative maps. The close relationship between RNNs and other types of NNs should not be surprising. In particular, RNNs are known to be Turing complete, and therefore capable of representing any computable function (such as any other types of NNs), but herein we argue that the relationship runs deeper and is more practical than this. For example, RNNs are often thought to be more difficult to train than other types of NNs, with RNNs being plagued by issues such as vanishing or exploding gradients. However, as we demonstrate in this paper, MLPs, RNNs, and many other NNs lie on a continuum, and this perspective leads to several insights that illuminate both theoretical and practical aspects of NNs.