Population-Level Representation Variability and Triplet-Derived Model-Level Representation Descriptors

Independently trained neural networks can develop different representations under the same learning conditions, motivating a population-level view of learned representations. Yet, most analyses focus on pairwise comparisons, limiting characterization of population variability and individual representations. We address both levels with Representational Dispersion (RD), a measure of population-level variability, and the Triplet-Derived Representation Descriptor (TRD), which characterizes each model's representation through relative distances over shared observations. We show that RD captures consistent variability patterns across learning conditions and training stochasticity, while TRD preserves Centered Kernel Alignment (CKA)-based relationships between models despite differences in their representation spaces. We further introduce Compact TRD and Surrogate-Guided Subset Optimization (SGSO), which efficiently optimizes an observation subset under a fixed budget to construct a compact TRD that preserves model-level representation geometry. Together, these tools extend representation analysis from pairwise similarity to population structure and provide a basis for large-scale model characterization, organization, and selection.