Blinded by Proximity: Why Distance Reduction Cannot Preserve Meaning in High-Dimensional Multimodal Consensus

<h2>Blinded by Proximity: Geometric Collapse and Boundary Analysis of Multimodal Consensus on Hyperspheres</h2> <strong>Version 2.0</strong> | Preprint | CC BY 4.0 <h3>Summary</h3> 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 <em>geometric collapse</em>: they converge identically regardless of whether the image-text pair is semantically congruent or conflicting. <h3>Key Findings</h3> <ul><li><strong>Geometric Collapse (N=100 validated):</strong> 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.</li> <li><strong>Mathematical Impossibility (Theorem 5.1–5.2, Corollary 5.4):</strong> 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.</li> <li><strong>Semantic Barrier Potential (870× improvement):</strong> 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).</li> <li><strong>Paradoxical Convergence:</strong> Conflicting conditions show <em>larger</em> agreement increases than congruent conditions (+0.801 vs. +0.717), the opposite of what a semantic consensus mechanism should produce.</li></ul> <h3>Experimental Setup</h3> <ul><li><strong>Model:</strong> CLIP ViT-B/32 (OpenAI), frozen weights</li><li><strong>Data:</strong> 100 images from 10 STL-10 classes (6 animal + 4 vehicle categories)</li><li><strong>Conditions:</strong> Congruent (self-match), Near-category conflict, Far-category conflict</li><li><strong>Frameworks tested:</strong> Midpoint, Asymmetric Anchoring, Semantic Barrier Potential, Manifold-Constrained Hub, Orthogonal Subspace Projection</li><li><strong>Statistics:</strong> Paired t-tests, Cohen's d, bootstrap 95% CI, repeated-measures ANOVA (F(4,396)=799.4, p&lt;10⁻¹⁰⁰, η²=0.89)</li></ul> <h3>Contents of This Deposit</h3> <ul><li><code>main_zenodo_final.tex</code> — Full LaTeX source (13 pages + appendix)</li><li><code>references.bib</code> — Bibliography (28 references)</li><li><code>figures/</code> — 8 publication-quality PDF figures (concentration histogram, violin plots, convergence curves, barrier dynamics, framework comparison, dimension effect)</li><li><code>results/</code> — Experimental data in JSON format (Exp 5a: N=100 replication; Exp 5b: 5-framework comparison)</li><li><code>README.md</code> — Compilation instructions and citation information</li></ul> <h3>Core Principle</h3> <blockquote><strong>Distance ≠ Meaning.</strong> 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.</blockquote> <h3>How to Compile</h3> <pre>pdflatex main_zenodo_final.texbibtex main_zenodo_finalpdflatex main_zenodo_final.texpdflatex main_zenodo_final.tex</pre> Or upload to <a href="https://www.overleaf.com">Overleaf</a> for online compilation. <h3>Citation</h3> <pre>@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}}</pre>