Simple Recurrent Networks are Interactive

There is disagreement among cognitive scientists as to whether a key computational framework - the Simple Recurrent Network (SRN; Elman, Machine Learning, 7(2), 195-225, 1991; Elman, Cognitive Science, 14(2), 179-211, 1990) - is a feedforward system. SRNs have been essential tools in advancing theories of learning, development, and processing in cognitive science for more than three decades. If SRNs were feedforward systems, there would be pervasive theoretical implications: Anything an SRN can do would therefore be explainable without interaction (feedback). However, despite claims that SRNs (and by extension recurrent neural networks more generally) are feedforward (Norris, 1993), this is not the case. Feedforward networks by definition are acyclic graphs - they contain no loops. SRNs contain loops - from hidden units back to hidden units with a time delay - and are therefore cyclic graphs. As we demonstrate, they are interactive in the sense normally implied for networks with feedback connections between layers: In an SRN, bottom-up inputs are inextricably mixed with previous model-internal computations. Inputs are transmitted to hidden units by multiplying them by input-to-hidden weights. However, hidden units simultaneously receive their own previous activations as input via hidden-to-hidden connections with a one-step time delay (typically via context units). These are added to the input-to-hidden values, and the sums are transformed by an activation function. Thus, bottom-up inputs are mixed with the products of potentially many preceding transformations of inputs and model-internal states. We discuss theoretical implications through a key example from psycholinguistics where the status of SRNs as feedforward or interactive has crucial ramifications.