  Recent work has shown that topological enhancements to recurrent neural
networks (RNNs) can increase their expressiveness and representational
capacity. Two popular enhancements are stacked RNNs, which increases the
capacity for learning non-linear functions, and bidirectional processing, which
exploits acausal information in a sequence. In this work, we explore the
delayed-RNN, which is a single-layer RNN that has a delay between the input and
output. We prove that a weight-constrained version of the delayed-RNN is
equivalent to a stacked-RNN. We also show that the delay gives rise to partial
acausality, much like bidirectional networks. Synthetic experiments confirm
that the delayed-RNN can mimic bidirectional networks, solving some acausal
tasks similarly, and outperforming them in others. Moreover, we show similar
performance to bidirectional networks in a real-world natural language
processing task. These results suggest that delayed-RNNs can approximate
topologies including stacked RNNs, bidirectional RNNs, and stacked
bidirectional RNNs - but with equivalent or faster runtimes for the
delayed-RNNs.
