Shaping Persistent Representations from Independent Interactions

World models learn environment dynamics from interaction experience. How a system evolves depends not only on its current state and actions but also on properties that persist across interactions. Yet standard predictive training can lower error using local evidence alone, without organizing persistent information into reusable context. We introduce SPRII, a training principle that uses relations between interactions as weak supervision for persistent context while retaining the learner's native objective. SPRII pairs related interactions, such as different trajectories of the same system: states and actions can differ while persistent properties remain shared. This pairing guides context learning without numerical property labels. Two composable training components encourage related contexts to agree (Align) and use one interaction's context to predict another's future (Cross). We build an analysis framework tracing three linked stages: organizing accessible persistent information in context (Formation), using it in a fixed predictor (Use), and reducing task error (Value). Success at one stage does not guarantee the next. Controlled experiments show that more reliable relations yield better organization, yet requiring pairs to share an additional property can make a still-shared property less accessible. Substituting context changes a fixed predictor's outputs, while prediction horizon and readout shape the benefit obtained from history. SPRII yields average gains of over 10% in downstream task performance and over 15% in persistent-property readout relative to the corresponding baselines. Evaluations spanning thirteen settings, including controlled physical systems, public dynamics tasks, robotic and tactile data, and partner interaction, further demonstrate the principle's applicability across learner families and interaction settings.