The Topology of Multimodal Fusion: Why Current Architectures Fail at Creative Cognition

TL;DR

This paper explores the topological limitations of current multimodal AI architectures, proposing a new geometric framework and benchmarks to improve creative cognition capabilities.

Contribution

It introduces a topological perspective on multimodal fusion, formalizes it mathematically, and proposes new implementations and benchmarks for advancing creative AI.

Findings

Identifies modal separability as a key topological limitation.

Proposes fiber bundle and Yang-Mills curvature formalism for multimodal fusion.

Introduces UOO implementation and new benchmarks for topological isomorphism.

Abstract

This paper identifies a structural limitation in current multimodal AI architectures that is topological rather than parametric. Contrastive alignment (CLIP), cross-attention fusion (GPT-4V/Gemini), and diffusion-based generation share a common geometric prior -- modal separability -- which we term contact topology. The argument rests on three pillars with philosophy as the generative center. The philosophical pillar reinterprets Wittgenstein's saying/showing distinction as a problem rather than a conclusion: where Wittgenstein chose silence, the Chinese craft epistemology tradition responded with xiang (operative schema) -- the third state emerging when saying and showing interpenetrate. A cruciform framework (dao/qi x saying/showing) positions xiang at the intersection, executing dual huacai (transformation-and-cutting) along both axes. This generates a dual-layer dynamics: chuanghua (creative transformation as spontaneous event) and huacai (its institutionalization into repeatable form). The cognitive science pillar reinterprets DMN/ECN/SN tripartite co-activation through the pathological mirror: overlap isomorphism vs. superimposition collapse in a 2D parameter space (coupling intensity x regulatory capacity). The mathematical pillar formalizes these via fiber bundles and Yang-Mills curvature, with the cruciform structure mapped to fiber bundle language. We propose UOO implementation via Neural ODEs with topological regularization, the ANALOGY-MM benchmark with error-type-ratio metric, and the META-TOP three-tier benchmark testing cross-civilizational topological isomorphism across seven archetypes. A phased experimental roadmap with explicit termination criteria ensures clean exit if falsified.