提出轨迹信息密度概念，揭示结构化中间状态能显著压缩语言表征维度。
Transition Information Density: Morphological Trajectories, Synesthetic Perception, and Structured Interpolation in Neural Training (or: The Synesthetic AI)
- 定义过渡信息密度与位置身份，量化训练中中间状态的信息含量
- 语言/语义空间中结构化插值使内在维度从10.81降至3.33
- 该效应仅存在于语言类模态，适用于关注表征压缩的研究者
标准机器学习训练将数据视为离散的起点终点对，忽略了两者之间的结构。本文提出过渡信息密度（TID）——可从类别不同终点间的结构化中间状态恢复的信息量——及位置身份（Positional Identity），即中间状态在A到B连续体中的确定位置。两项概念基于三类实证背景：字形-颜色联觉、联觉网格（一种实现视觉形态空间中TID的边界轮廓变形算法）、四种表征介质上的四条件训练实验。在定义位置身份的结构化插值条件下（C3），语音/语言（C3: 3.33 vs. C2: 10.81）和语义描述（C3: 4.59 vs. C2: 8.67）介质中，探针的内在维度显著低于体积匹配对照组（C2）。视觉和跨模态介质未见此效应，确立了模态边界条件。固定样本数N=50的对比证实，位置身份结构而非样本量驱动该效应。分辨率随表示丰富度单调上升。合并两近邻分析显示，视觉空间全局坍缩（0.075），而语音空间全局一致（0.977）。论文贡献包括TID与位置身份的形式定义、九指标形状表征框架，以及分离轨迹结构、数据量与位置身份的四条件实验设计。
原文摘要 · Abstract (English)
Standard machine learning training presents data as discrete endpoint pairs, omitting the structure of the space between them. This paper introduces Transition Information Density (TID) -- the information content recoverable from structured intermediate states between categorically distinct training endpoints -- and Positional Identity, the defined location of an intermediate state on the A-to-B continuum. Both constructs are grounded in three empirical contexts: grapheme-color synesthesia, the Synesthesia Grid (a boundary-contour morphing algorithm instantiating TID in visual morphological space), and a four-condition training experiment across four representational mediums. Probes trained on structured interpolation at defined Positional Identities (C3) exhibit substantially lower intrinsic dimensionality than volume-matched controls (C2) in Phonetic/Linguistic (C3: 3.33 vs. C2: 10.81) and Semantic Description (C3: 4.59 vs. C2: 8.67) mediums. Visual and cross-modal mediums do not show this effect, establishing a modality boundary condition. A fixed-N=50 comparison confirms that Positional Identity structure, not sample count, drives the effect. Resolution N scales monotonically with representational richness. Pooled TwoNN analysis reveals globally collapsed representations in visual space (0.075) and globally consistent representations in phonetic space (0.977). The paper contributes a formal definition of TID and Positional Identity, a nine-metric shape characterization framework, and a four-condition experimental design isolating trajectory structure, data volume, and Positional Identity as distinct factors.
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