The Cost of Interpretability: Auditable User Representations via Archetypes

Collaborative filtering embeddings underpin personalization across web platforms but are opaque: a user's dense vector cannot explain their behavioral profile to a regulator or the user themselves, and retraining produces arbitrarily rotated coordinates that defeat archival and longitudinal comparison—capabilities that GDPR Article 22, the EU AI Act, and the Digital Services Act increasingly demand of web information systems. We propose AURA, a two-layer interpretable user representation, together with an operational definition of interpretability as three testable properties: readable axes, plausible components, and temporal identity. Layer 1 applies archetypal analysis to behavioral features, expressing each user as a convex combination of extreme behavioral profiles (e.g., "40% blockbuster enthusiast, 25% documentary veteran"): the convex-hull constraint makes every archetype a plausible profile, and the simplex coordinates give every user a direct mixture-of-archetypes reading. Layer 2 lifts these coordinates to a density matrix encoding both the mean profile and its temporal variability, yielding built-in confidence diagnostics, representations two to three times more stable than point estimates, and a low-cost purity-adaptive routing mechanism. Experiments on MovieLens-32M and Amazon CDs & Vinyl show that archetype coordinates achieve the highest component coherence among tested decompositions—confirmed by a 21-participant user study—and that purity-adaptive routing outperforms uniform-strategy baselines by 12-15%. This interpretability comes at a measurable, domain-dependent cost in reconstruction and stability, which we characterize.