Embedding boolean circuits in a neural network

The proposal is to add a Boolean-circuit “sidecar” to a trained neural network, separating the task into representing logic gates and connecting them to the network’s real-valued activations. With binary inputs and a threshold-at-zero activation, individual neurons can implement basic gates: AND uses A + B − 1.5, OR uses A + B − 0.5, and NOT uses 0.5 − A. Since these gates can be composed into any Boolean expression, a circuit can be represented as a collection of neurons without changing the underlying logic.

The connection to the trained model uses thresholded inputs and additive outputs. A “probe” converts a chosen model neuron’s activation into a Boolean signal - for example, outputting 1 when a neuron exceeds a specified threshold. A “stim” uses a Boolean signal to add a signed amount along the output direction of a selected neuron, steering the model toward a desired behavior. Thresholds and steering magnitudes must be selected based on how the target neurons behave. Timing also matters: a probe must occur before the layer it stimulates, so a signal read from a later layer cannot affect an earlier one in the same forward pass. This is a conceptual design, not a tested implementation; it outlines how symbolic rules might be connected to learned model features.