Gating Enables Long-Range Recall in Recurrent Logic Gate Networks

Logic Gate Networks (LGNs) learn a circuit of two-input Boolean gates by gradient descent and run as raw logic at inference, making them extremely cheap on CPUs and FPGAs. The existing recurrent LGNs all carry state by concat-recurrence, recomputing the hidden state from scratch at every step; none has a gating mechanism, a gap that two of the three groups explicitly name as future work. We build a gated recurrent cell in which a learned two-to-one multiplexer per hidden bit implements a keep/write choice whose keep path carries gradients through time unattenuated: the mechanism that makes LSTMs and GRUs trainable on long dependencies, realized in Boolean logic. On two long-range recall tasks the control fails outright (its write-step gradient is exactly zero), while the gated cell still recovers a digit held through 100 blank steps three times as often as chance (accuracy 0.30 vs.\ 0.10). To our knowledge, this is the first learned gated recurrent LGN.