Symmetric sensing and symmetry-breaking processing as a minimal principle for directional inference

Bilateral animals often combine symmetric body plans with lateralized neural processing, but the computational relation between these features remains unclear. We used a minimal two-sensor framework to separate sensing from readout. Across auditory, binocular, and tactile models, symmetric sensor placement produced Z₂-equivariant Fisher-information profiles, indicating matched local estimation precision for opposite sides of the body midline. Because Fisher information does not directly establish sign recovery, we separately measured total information, sign information, unsigned spatial information, and balanced sign accuracy. In an auditory cross-correlation model, an even scalar readout preserved unsigned source eccentricity but remained nearly sign-blind. Increasing the odd readout component selectively increased sign information, balanced accuracy, correlation magnitude, and odd conditional-mean structure, while reducing unsigned information. A decoder trained on the full cross-correlation also acquired an almost purely odd weight profile. These results show that symmetric sensing balances input precision, whereas antisymmetric readout recovers directional sign.