Behavioral Entanglement in Transformers: Grassmann Geometry of Rho-Guided Supervised Fine-Tuning

We track behavioral subspaces throughout rho-guided SFT on Qwen 2.5-7B-Instruct under three protection conditions (gamma=0.03, gamma=0.10, anneal). The central finding is that surgery operates by compression, not rotation: pairwise Grassmann angles remain within 2-3 degrees of baseline across all conditions and layers, while effective dimensionality of target behaviors compresses 40-60% within the first 25 training steps. The protection strength gamma controls collateral compression: at gamma=0.10, factual dimensionality collapses to 1 at all layers, explaining weaker behavioral outcomes despite stronger protection. Compression is irreversible once established.