Recurrent Neural Networks

ReLU networks and admissible-ρ networks compute only primitive recursive functions under the stated bounds. For recurrent ReLU networks, integer threshold gates are exactly implemented by the difference of two ReLU terms. Admissible bounded activations require primitive recursive computable-analysis evaluation, a modulus of continuity, and a detector separating low and high input ranges. Recurrent ReLU computation iterates a fixed feedforward ReLU block from raw integer input and reads exact output after a primitive recursive observation time. Bounded-range admissible activation networks must use encoded inputs because their state space is compact.