Blinded by Proximity: Why Distance Reduction Cannot Preserve Meaning in High-Dimensional Multimodal Consensus
Year: 2026
Type: preprint
Abstract: Blinded by Proximity: Geometric Collapse and Boundary Analysis of Multimodal Consensus on Hyperspheres Version 2.0 | Preprint | CC BY 4.0 Summary This paper investigates the geometric mechanics of iterative consensus updates between image and text embeddings in contrastive vision-language models (CLIP). We demonstrate that all distance-reducing update rules — including Midpoint, Adaptive Scaling, and Gated Midpoint — systematically suffer from geometric collapse: they converge identically regardless of whether the image-text pair is semantically congruent or conflicting. Key Findings Geometric Collapse (N=100 validated): All update rules eliminate semantic distinctions. Near-category conflict (cat vs. "tiger", sim=0.1949) and far-category conflict (cat vs. "airplane", sim=0.1786) converge to within a 0.004-wide similarity band (0.9796–0.9830) after 20 steps. Mathematical Impossibility (Theorem 5.1–5.2, Corollary 5.4): We prove that no distance-reducing, isotropic, re-projecting update rule on S^{D-1} can distinguish pairs within O(1/√D) of each other. All real CLIP pairs occupy a 1.8/√D-wide band, falling precisely within this indistinguishability regime. Semantic Barrier Potential (870× improvement): Among four proposed frameworks, the Semantic Barrier Potential restores near-far discriminability by a factor of 870× over the Midpoint baseline (|Near−Far| = 0.607 vs. 0.001), with far-category pairs actively diverging to negative similarity (−0.511). Paradoxical Convergence: Conflicting conditions show larger agreement increases than congruent conditions (+0.801 vs. +0.717), the opposite of what a semantic consensus mechanism should produce. Experimental Setup Model: CLIP ViT-B/32 (OpenAI), frozen weights Data: 100 images from 10 STL-10 classes (6 animal + 4 vehicle categories) Conditions: Congruent (self-match), Near-category conflict, Far-category conflict Frameworks tested: Midpoint, Asymmetric Anchoring, Semantic Barrier Potential, Manifold-Constrained Hub, Orthogonal Subspace Projection Statistics: Paired t-tests, Cohen's d, bootstrap 95% CI, repeated-measures ANOVA (F(4,396)=799.4, p<10⁻¹⁰⁰, η²=0.89) Contents of This Deposit main_zenodo_final.tex — Full LaTeX source (13 pages + appendix) references.bib — Bibliography (28 references) figures/ — 8 publication-quality PDF figures (concentration histogram, violin plots, convergence curves, barrier dynamics, framework comparison, dimension effect) results/ — Experimental data in JSON format (Exp 5a: N=100 replication; Exp 5b: 5-framework comparison) README.md — Compilation instructions and citation information Core Principle Distance ≠ Meaning. In pre-trained contrastive spaces, reducing representational distance does not preserve semantic agreement. Consensus mechanisms must incorporate density-aware, category-conditional, or asymmetric geometric operations. How to Compile pdflatex main_zenodo_final.texbibtex main_zenodo_finalpdflatex main_zenodo_final.texpdflatex main_zenodo_final.tex Or upload to Overleaf for online compilation. Citation @misc{kim2026blinded, title = {Blinded by Proximity: Geometric Collapse and Boundary Analysis of Multimodal Consensus on Hyperspheres}, author = {Kim, Doo Shin and Su}, year = {2026}, version = {2.0}, publisher = {Zenodo}, doi = {10.5281/zenodo.XXXXXXX}, note = {Preprint}}
Authors: Doo Shin, kim, Su
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170067691
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