Bootstrap Theory of Representational Emergence: Explanatory Insufficiency as a Driver of Representation Learning and World Models

Representation learning is central to modern machine learning, enabling transitions from handcrafted features to learned embeddings, latent spaces, foundation models, world models, and digital twins. Yet most research examines how representations are optimized after a representational framework has been selected, while less attention is given to when a new level of representation becomes necessary. We introduce the Bootstrap Theory of Representational Emergence (TBER), a framework describing how new representations arise when existing ones become explanatorily insufficient. In this view, representational innovation is not only driven by more data, larger models, or greater computational power, but also by persistent explanatory gaps: situations in which a representation can still describe observations but can no longer make their organization or transformations intelligible. TBER identifies explanatory insufficiency as a positive signal for representational transition. A representation becomes insufficient not because it is necessarily false, but because its explanatory domain has been exceeded. The bootstrap dynamic follows a recursive sequence: observations reveal anomalies; anomalies expose insufficiencies; insufficiencies motivate new representations; and these new representations generate further observations and possible new insufficiencies.We formalize this process through five stages: stabilized observation, anomaly detection, recognition of explanatory insufficiency, representational emergence, and provisional stabilization. We discuss applications to representation learning, latent spaces, foundation models, world models, digital twins, adaptive biological systems, and scientific discovery. TBER suggests that future AI systems may benefit from mechanisms for detecting the explanatory limits of their own internal representations.