cross-lingual-pivot-language-structure
IN premise — summaries/2026/08/24/park-2023-linear-representation-s5-he-was-known-as-the-warrior.md
Created 2026-08-24T17:11:03+00:00
Cross-lingual concepts sharing a pivot language (e.g., English→French and French→German) show high causal inner product with each other, while concepts not sharing a pivot (English→French vs. German→Spanish) are nearly orthogonal under the causal inner product, validating the geometric structure of multilingual concept directions.
Summary
When multilingual concept representations share a common intermediate language, their directional structure lines up closely, while pairs with no shared language are essentially unrelated in direction. This matters because it means cross-lingual concept geometry is predictable and anchored by shared pivot languages, so the system can rely on these structural regularities when reasoning across multiple languages rather than treating each language pair as an isolated case.