Geometric Evolution Maps: Extracting Stable Concept Probes from Transformer Residual Streams

A concept probe is only as reliable as the layer it is taken from. Probing at a fixed late layer, or at the peak of a separation curve, ignores a structural feature of how concepts form: the probe direction rotates substantially during assembly and does not settle until after the Concept Allocation Zone (CAZ) in which it forms. We introduce Geometric Evolution Maps (GEMs). A GEM records a concept's directional trajectory across one CAZ segment, takes the settled direction at that segment's final layer, and locates the handoff layer immediately beyond it - the first layer at which that direction can be evaluated outside the window it was estimated on. The handoff layer is derived from the segment boundary, not detected by a rotation criterion. A concept typically occupies several segments; we call that set its atlas. This rotation is substantial and consistent across architectures and concept types - a property of the representation, not an estimation artifact. The extracted direction is causal: ablating it suppresses far more separation than ablating a random direction, though no single site carries the effect alone. Probing after rotation completes is more precise than probing during it; a depth-matched control shows this advantage comes from probing at greater depth, not any privilege specific to the handoff boundary. A small number of structured exceptions are documented rather than left unaccounted for. A concept's atlas - its full set of GEMs, not any single one of them - is therefore the unit this method delivers for downstream use. GEM provides the ablation-targeting methodology used by the CAZ Validation paper in this program.