Transition Information Density: Morphological Trajectories, Synesthetic Perception, and Structured Interpolation in Neural Training (or: The Synesthetic AI)
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Computer Science > Machine Learning
arXiv:2607.03210 (cs)
[Submitted on 3 Jul 2026]
Title:Transition Information Density: Morphological Trajectories, Synesthetic Perception, and Structured Interpolation in Neural Training (or: The Synesthetic AI)
Authors:Sam Mao
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Abstract: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.
| Comments: | 38 pages, 9 figures, 4 tables. Empirical results from structured interpolation training across four representational mediums. Pipeline scripts, experimental data, and the Synesthesia Grid algorithm available upon reasonable request |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| ACM classes: | I.2.0; I.2.6; I.2.8 |
| Cite as: | arXiv:2607.03210 [cs.LG] |
| (or arXiv:2607.03210v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.03210
arXiv-issued DOI via DataCite (pending registration)
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