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

Bilateral body plans and functional lateralization coexist across animals, yet their computational relation remains unclear. Here we asked under what symmetry conditions a bilateral system can recover directional sign from paired sensory inputs. We formulated a minimal two-sensor inference framework with separate sensing and processing stages and analyzed it under a left-right reflection (Z2). Across auditory, binocular, and tactile models, bilaterally symmetric sensor placement produced Z2-equivariant Fisher-information profiles, indicating unbiased information uptake at the sensing stage. We then analyzed delay-based differential processing in the auditory case using cross-correlation readout kernels decomposed into even and odd components. Under symmetric placement and a symmetric source prior, purely even kernels preserved unsigned spatial information but failed to recover source sign, whereas introducing an odd kernel component restored sign-sensitive structure and strongly increased sign-recovery accuracy. This separation remained qualitatively robust across sensor noise, although quantitative performance depended on kernel width and source-angle range. These results identify a minimal division of labor in bilateral computation: body symmetry provides unbiased information uptake, whereas directional and lateralized information emerges at readout through symmetry-breaking processing.