维特根斯坦表示假说：语言是否是多模态收敛的吸引子？
The Wittgensteinian Representation Hypothesis: Is Language the Attractor of Multimodal Convergence?
AI总结：
研究探讨了为何不同模态的神经网络收敛于共享表示，发现语言模态对其他模态有显著方向性吸引，提出维特根斯坦表示假说。
摘要：
理解为何独立训练的不同模态神经网络收敛于共享表示，以及这种收敛导致何处，仍然是表示学习中的开放问题。现有所有证据均依赖对称相似性度量，虽然可以检测收敛，但结构上对方向性无能为力。我们引入利用cycle-kNN的定向收敛分析，一种非对称对齐度量，应用于数十个独立训练的单模态模型，涵盖点云、视觉和语言。我们发现一致的方向不对称性：非语言模态显著比反方向更趋向语言的邻域结构，且这种模式在所有模型家族和尺度上均成立——然而完全无法被对称度量察觉。机制分析将方向性追溯到特征密度不对称性，其中语言表示占据表征空间最紧凑的区域。信息瓶颈框架提供了原理性解释：在压缩优化下，表示趋向于语言特有的离散、组合结构。我们将此正式化为维特根斯坦表示假说：语言的语义结构是多模态表示收敛的渐近吸引子。
英文摘要：
Understanding why independently trained neural networks from different modalities converge toward shared representations, and where this convergence leads, remains an open question in representation learning. All existing evidence relies on symmetric similarity measures, which can detect convergence but are structurally blind to its direction. We introduce directional convergence analysis using cycle-kNN, an asymmetric alignment measure, applied across dozens of independently trained unimodal models spanning point clouds, vision, and language. We uncover a consistent directional asymmetry: non-language modalities move toward the neighborhood structure of language significantly more than the reverse, and this pattern holds across all model families and scales--yet is entirely invisible to symmetric measures. Mechanistic analysis traces the directionality to feature density asymmetry, whereby language representations occupy the most compact regions of representational space. The Information Bottleneck framework provides a principled interpretation: optimization under compression drives representations toward discrete, compositional structures characteristic of language. We formalize this as the Wittgensteinian Representation Hypothesis: the semantic structure of language is the asymptotic attractor of multimodal representation convergence.
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