A steering direction's angular component becomes causally load-bearing only in a late prediction-centric depth phase

Haim & McNamee (2026) measure Participation Ratio and layer-wise Spearman correlation between representational distance (Euclidean vs. angular) and next-token-distribution KL divergence across real Llama-3.1-8B, Mistral-7B-v0.3, and Qwen2.5-7B, finding a consistent bi-phasic depth structure -- an early context-centric phase and a late prediction-centric phase, with phase-transition layer agreeing within 2.5% of depth across three tasks and three models [haim-mcnamee-2026-emergent-causal-geometric-dynamics-across-depth-in-large-language-models] Steering vectors decomposed into pure-angular vs. pure-norm interventions are causally effective (logit-preference shift) only when angular and only in the late phase; norm interventions are ineffective throughout [haim-mcnamee-2026-emergent-causal-geometric-dynamics-across-depth-in-large-language-models]