fv-cyclic-mapping-impossibility-proof
IN premise — summaries/2026/08/24/todd-2023-function-vectors-s1-function-vectors-can-implement-complex-mappings-including-cy.md
Created 2026-08-25T02:58:40+00:00
No constant vector offset can implement a cyclic mapping such as antonymy: if w + v_a = antonym(w) for all w, then applying twice gives w + 2v_a = w, forcing v_a = 0 and w = antonym(w), a contradiction.
Summary
Antonymy (the relationship between opposite words) cannot be captured by a simple fixed shift in word-vector space, because applying such a shift twice should return you to the original word, which mathematically forces the shift to be zero and collapses every word into its own opposite. This means any system that tries to encode "opposite-of" as a single directional step in a geometric model is fundamentally broken, and must instead use a more complex relational or lookup structure.