In this work, we propose a novel, implicitly-defined neural network architecture and describe a method to compute its components. The proposed architecture forgoes the causality assumption used to formulate recurrent neural networks and instead couples the hidden states of the network, allowing improvement on problems with complex, long-distance dependencies. Initial experiments demonstrate the new architecture outperforms both the Stanford Parser and baseline bidirectional networks on the Penn Treebank Part-of-Speech tagging task and a baseline bidirectional network on an additional artificial random biased walk task.