Abstract
Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure degrades. We show that geometric stability, the consistency of a representation's pairwise distance structure, addresses both. Supervised Shesha variants that measure task-aligned geometric stability predict linear steerability with near-perfect accuracy (\rho = 0.89-0.97) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial \rho = 0.62-0.76). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks (\rho \approx 0.10), revealing that task alignment is essential for controllability prediction. However, unsupervised stability excels at drift detection, measuring nearly 2\times greater geometric change than CKA during post-training alignment (up to 5.23\times in Llama) while providing earlier warning in 73\% of models and maintaining a 6\times lower false alarm rate than Procrustes. Together, supervised and unsupervised stability form complementary diagnostics for the LLM deployment lifecycle: one for pre-deployment controllability assessment, the other for post-deployment monitoring.
