过渡信息密度：神经训练中的形态轨迹、联觉感知和结构化插值（或：联觉人工智能）
Transition Information Density: Morphological Trajectories, Synesthetic Perception, and Structured Interpolation in Neural Training (or: The Synesthetic AI)
AI总结：
介绍过渡信息密度及位置标识，基于联觉等实证背景研究。通过结构化插值训练的探针在语音/语言和语义描述媒介中维度更低，贡献相关定义、框架及实验设计，区分轨迹结构等因素。
摘要：
标准机器学习训练将数据呈现为离散端点对，忽略其间空间结构。本文引入过渡信息密度（TID）和位置标识。二者基于三种实证背景，经实验发现特定训练探针在部分媒介中维度更低，贡献TID等定义、框架及实验设计。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
