Transition Information Density: Morphological Trajectories, Synesthetic Perception, and Structured Interpolation in Neural Training (or: The Synesthetic AI)
2026-07-03 • Machine Learning
Machine LearningArtificial IntelligenceComputation and Language
AI summaryⓘ
The authors explain that typical machine learning only looks at clear start-and-end examples but misses what happens in between. They introduce Transition Information Density (TID), which captures the important info found in the steps between two points, and Positional Identity, which marks where you are along that path. Their experiments show that in language-related tasks, focusing on these in-between steps makes the system simpler and more organized, but this doesn't happen in visual tasks. They also provide ways to measure and test these ideas systematically.
Transition Information DensityPositional Identityintrinsic dimensionalitygrapheme-color synesthesiarepresentational mediummorphological spacestructured interpolationTwoNN analysisphonetic spacemachine learning training
Authors
Sam Mao
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.