Geometric map between perceptual and control manifolds in cortex

Determine the map relating the dually flat manifold of stationary visitation measures and log-policies for planning to the dually flat manifold of expectation and natural parameters used in predictive-coding models, thereby establishing whether the cortex implements a sensorimotor duality.

Background

The paper compares its control-side geometry—pairing stationary visitation measures with log-policies—to a predictive-coding geometry for sensory processing—pairing expectation and natural parameters under a log-partition function.

It identifies the precise correspondence between these two manifolds as unresolved and explicitly leaves the problem for future work. The question is motivated by the possibility that shared cortical architecture reflects a geometric perception–action duality.

References

Whether cortex implements a sensorimotor duality then becomes the geometric question of what map relates these two dually flat manifolds, which we leave to future work.

— The Dually Flat Geometry of Planning as Inference  (2609.04005 - Milosevic et al., 3 Sep 2026) in Section 3, subsection “Application in theoretical neuroscience,” paragraph “Perception--action duality in the cortex”