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Recurrent neural network architectures can have useful computationalproperties, with complex temporal dynamics and input-sensitive attractorstates. However, evaluation of recurrent dynamic architectures requiressolution of systems of differential equations, and the number of evaluationsrequired to determine their response to a given input can vary with the input,or can be indeterminate altogether in the case of oscillations or instability.In feed-forward networks, by contrast, only a single pass through the networkis needed to determine the response to a given input. Modern machine-learningsystems are designed to operate efficiently on feed-forward architectures. Wehypothesised that two-layer feedforward architectures with simple,deterministic dynamics could approximate the responses of single-layerrecurrent network architectures. By identifying the fixed-point responses of agiven recurrent network, we trained two-layer networks to directly approximatethe fixed-point response to a given input. These feed-forward networks thenembodied useful computations, including competitive interactions, informationtransformations and noise rejection. Our approach was able to find usefulapproximations to recurrent networks, which can then be evaluated in linear anddeterministic time complexity.

Feed-forward approximations to dynamic recurrent network architectures