topological-not-metric-cross-modal-alignment
IN premise — summaries/2026/08/24/aristotelian-2026-sR-references-chunk-3.md
Created 2026-08-24T17:10:51+00:00
Cross-modal models agree on which points are neighbors (topological/ordinal structure, shown by mKNN alignment at all k values) but not on how close they are (metric/cardinal structure, shown by CKA-RBF yielding no calibrated alignment at σ=0.1)
Summary
When different types of representations are compared, the models consistently agree on which items rank as neighbors to each other, but they do not agree on the actual distance values between those items. This means the system can safely rely on relative ordering for decisions like retrieval or clustering, but it should not treat similarity magnitudes as interchangeable across modalities or use them for threshold-based judgments.