Blinded by Proximity: Geometric Collapse and Boundary Analysis of Multimodal Consensus on Hyperspheres

While contrastive vision-language models like CLIP achieve remarkablecross-modal alignment, forming a dynamic consensus between image andtext embeddings without destroying their unique semantic identities remains a fundamental challenge. In this paper, we investigate the geometricmechanics of dual-channel consensus updates on the high-dimensional unithypersphere SD−1. We demonstrate that naive proximity reduction rules,including Gated Midpoint and Adaptive Scaling architectures, systematically suffer from geometric collapse—converging identically to an un-gatedbaseline under both near-category and far-category semantic conflict.Through rigorous mathematical diagnosis, we reveal that this collapseis driven by the concentration of measure on high-dimensional spheres andchordal contraction during linear interpolation. Furthermore, we empirically demonstrate that far-category pairs yield cosine similarities that remain within the same compressed range as near-category conflicts, and thatthe resulting DCH updates eliminate all semantic distinctions. For a cat image, DCH updates produced final agreements of 0.9782 (congruent), 0.9747(near), and 0.9751 (far), with the conflicting conditions showing larger increases than the congruent condition. For a rabbit image, we observed theidentical pattern: final agreements of 0.9816 (congruent), 0.9814 (near),and 0.9752 (far), with the far-category condition (airplane, +0.7977) againshowing a larger increase than the congruent condition (rabbit, +0.6617).These findings confirm that the inherent modality gap of contrastivespaces compresses all semantic divergences into a narrow cone, and thatdistance-reducing update rules systematically fail to preserve semantic distinctions across multiple image categories. Finally, to transcend these geometric limitations, we mathematically formulate four prospective, semanticpreserving frameworks—Asymmetric Reality Anchoring, Semantic BarrierPotential Dynamics, Manifold-Constrained Density Hubs, and OrthogonalSubspace Projection. Our work reframes a crucial empirical limitation intoa formal geometric boundary, tracing a clear theoretical trajectory for futuremultimodal representation dynamics.