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Iterative artificial intelligence systems have become central to materials discovery, where machine learning models are repeatedly refined through cycles of training on incrementally accumulated data. This iterative nature introduces the concepts of model lineage—the traceable descent of model versions across generations—and knowledge inheritance—the mechanisms by which learned representations, parameters, or structural priors are transmitted from earlier to later models. This paper provides a conceptual exploration of these dynamics within materials AI, focusing on how lineage shapes the accumulation and evolution of knowledge rather than on specific implementation details. Drawing on recent advances in transfer learning, active learning, and sequential model refinement, the discussion examines interaction dynamics across successive model states, including the continuity of learned features, potential divergence in representational focus, and the epistemic implications of partial versus complete inheritance. A proposed conceptual framework organizes these elements into a systems-level view, emphasizing steering logics, trade-offs in retention versus adaptation, and feedback structures that influence long-term knowledge coherence. The framework offers interpretive insights into how lineage-aware perspectives can inform the design and interpretation of iterative processes, contributing to a deeper understanding of cumulative progress in materials AI without relying on empirical validation or predictive claims.