Residual-stream layer-to-layer transitions decompose into a model-dependent but condition-stable rotation/displacement curve across depth

- Bhattacharya & Kolli measure real residual-stream transitions in six instruction-tuned models (Qwen3-0.6B/1.7B/4B/8B, Gemma-2-2B-IT, StableLM-2-1.6B-Chat) via relative displacement (how far representations move between consecutive layers) plus orthogonal Procrustes decomposition of each transition into a rigid rotation and a non-rigid residual. [bhattacharya-kolli-2026-residual-stream-geometry-transformer-depth] - Relative displacement is strongly layer-dependent -- larger early and late, quieter in the middle third -- and is nearly invariant across the two tested conditions (code generation, cross-lingual translation) within each model; rotation magnitude stays nearly constant across depth while the Procrustes residual and angle concentration remain depth-modulated, peaking at the final transition. [bhattacharya-kolli-2026-residual-stream-geometry-transformer-depth] - During generation, non-English targets show larger final-layer displacement and residual than English targets; the authors frame these as descriptive geometric regularities, not causal or effort measures, and state "Curvature is used only descriptively and is not included in our statistical tests" (Sec. 5.3), so the curvature-profile tag rests on descriptive curves only. [bhattacharya-kolli-2026-residual-stream-geometry-transformer-depth]