Empirical Discovery of Cross-Lingual Concept Geometry: Stable Semantic Attractors, Zero-Token Robustness, and Domain-Invariant Language Partitions in Multilingual Embedding Spaces
Year: 2026
Type: preprint
Abstract: This paper reports the empirical discovery of cross-lingual concept geometry in multilingual embedding spaces, proving that semantic meaning is represented as stable geometric attractors independent of surface language. Using LaBSE as a probe, we construct (concept, language) centroid vectors from 10 representative words each across 44 concepts, 5 semantic domains, and 6 diverse languages (representing 5 language families). Our primary contribution is the demonstration that these centroids form tight, language-agnostic semantic clusters under fully unsupervised conditions. Main results: (1) Unsupervised agglomerative clustering of 264 centroids yields 97.3% purity, representing a massive 34.2 percentage point gap (55.6σ, p < 0.0001) above a rigorous, matched permutation null baseline (63.2%). (2) To rule out surface-token confounding, we present a zero-shared-token experiment (Stage 9b v2) where 12,000 composed phrases with zero shared tokens across languages cluster at 99.96% purity (random baseline 10.0%), confirming that semantic proximity, not lexical overlap, drives the geometry. (3) We discover a domain-invariant within-concept language partition—[EN·ES·ZH] · [FR] · [FA] · [AR]—stable across all 44 concepts, which reflects training-corpus topology rather than genetic linguistic kinship. Rather than asserting a fully built system, we show how this discovered geometry motivates and constrains a proposed 4-layer concept-native language system architecture (Hash-X), including the specific requirement for language-conditioned satellite nodes to accommodate Arabic and Persian. We discuss open questions regarding holistic composition rules (Layer 2) and the semantic relation graph (Layer 3) motivated by these findings.
Author: Towfigh, Nasser
Language: English
Topic: Topic Modeling
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161936668
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