Cross-Context Neural Transport

We give a geometric account of how object tuning measured with controlled images relates to object representation during natural vision, in the same brains, and find the relation- ship is carried mostly by ambient visual geometry rather than by object-specific axes. The account is organised by a symmetry: a linear neural readout is invariant under the gauge group acting on the feature basis (GL(d) for least squares, O(d) for ridge), so representa- tional claims are claims about points on a Grassmannian of subspaces, not about coordi- nates. This dictates the design, comparing behaviour-derived, PCA, and random rank-66 subspaces, and forbids per-dimension claims. Within that discipline we introduce a same- participant benchmark aligning controlled object-image fMRI (CNeuroMod-THINGS) and naturalistic movie fMRI (Movie10) on one cortical surface, and a frozen-tuning transport model. Three geometric findings, replicated in four individuals, and one observation we flag as tentative. (i) Image-fit tuning transports zero-shot to movies, film-robustly and lo- calised to ventral temporal cortex, but against a null of random rank-66 subspaces the behavioural axes earn a specific advantage only in place cortex, at the parahippocampal place area in all four subjects; a random subspace retaining 9 percent of the backbone variance transports as well everywhere else. (ii) The geometry is shared across brains up to a per-subject gauge, one person’s tuning predicting another’s movies at about 60 percent of within-person strength, peaking in place cortex. (iii) The movie-specific tuning change is a low-rank deformation whose leading directions form a subspace shared across individuals. We also observe a fourfold image-to-movie transport asymmetry, but leave its direction open pending symmetric, O(d)-invariant tests. Two further bounds: object-centric pool- ing underperforms whole-scene geometry, and image pretraining gives no few-shot savings. What controlled-image encoding models measure that survives into natural vision is thus largely ambient visual geometry, object-specific mainly for place and scene cortex. We release the benchmark and the frozen-transport model.