Structured Interpolation Enhances Neural Network Representation Learning

Standard machine learning training typically feeds data to models as discrete, disconnected endpoint pairs, neglecting the inherent structure of the space that lies between these points. This research introduces two novel concepts: Transition Information Density (TID), which quantifies the information recoverable from structured intermediate states along a trajectory between distinct training endpoints, and Positional Identity, which defines the precise location of an intermediate state on a continuum from point A to point B. These constructs are grounded in empirical observations, including grapheme-color synesthesia and a visual morphing algorithm called the Synesthesia Grid. A four-condition training experiment across various representational mediums demonstrated significant findings. Neural probes trained with structured interpolation at defined Positional Identities (Condition 3) exhibited substantially lower intrinsic dimensionality compared to volume-matched controls (Condition 2) in phonetic/linguistic and semantic description tasks. This effect was not observed in visual or cross-modal mediums, establishing a modality-specific boundary condition. The study concludes that the structure provided by Positional Identity, rather than just the sample count, is the driving force behind these more collapsed and efficient representations, particularly in abstract linguistic spaces.