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

Abstract: 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.

• The paper introduces a five-stage recursive process showing how persistent explanatory insufficiency triggers representational change.
• It integrates insights from AI, philosophy, and biological systems to define the conditions necessary for new representational frameworks.
• The study outlines implications for designing autonomous systems that self-assess and evolve their representations to address epistemic gaps.

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

Introduction and Motivation

The "Bootstrap Theory of Representational Emergence" (TBER) (2606.07303) presents a meta-theoretical framework elucidating how new representational structures arise in machine learning, artificial intelligence, adaptive systems, and the sciences. Unlike conventional approaches that treat representation learning as a process primarily driven by increased data, model size, or utility, this theory foregrounds explanatory insufficiency—the inability of current representations to render observations, transformations, or organizational principles intelligible—as the critical impetus for representational transitions.

The framework's central premise is that representational innovation is prompted not just by the search for increased predictive power, but also by persistent epistemic gaps exposed during empirical inquiry or autonomous system operation. This position provides a formal answer to the underexplored question: not merely how or how well to learn representations, but when and why new representational strata become necessary.

Theoretical Foundations and Five-Stage Model

TBER is articulated as a recursive bootstrap process, formalized in five stages, that captures the dynamics of representational change:

1. Stabilized Observation: The system operates under established representational schemes that allow for coherent data interpretation and manipulation.
2. Anomaly Detection: Accumulation of data surfaces anomalies—observations or transformations the existing framework cannot integrate seamlessly.
3. Recognition of Explanatory Insufficiency: Persistent anomalies are diagnosed as signals of representational, rather than parametric or methodological, insufficiency.
4. Representational Emergence: A new representational framework is introduced that resolves the previously irreducible anomalies, expanding the domain of intelligibility.
5. Provisional Stabilization: The new representation temporarily stabilizes explanations and predictions until future anomalies initiate another cycle.

This progression emphasizes that description (data summarization) can persist despite the breakdown of explanation (coherence of mechanisms or causality), and that a representation's utility may outlast its epistemic adequacy. Notably, the theory dissociates explanatory insufficiency from mere prediction error; a model may continue to predict accurately while remaining structurally or mechanistically opaque or insufficient.

Relation to Existing Theory and Practice

TBER positions itself at a meta-representational level, extending traditions from philosophy of science (notably Peirce, Bachelard, Foucault, Canguilhem, Simondon) to contemporary computational paradigms. It complements, rather than supersedes, current methods in representation learning [Bengio et al. 2013], self-organization [Kelso 1995], and world modeling [Ha & Schmidhuber 2018].

The framework is distinctly non-algorithmic; it does not specify learning architectures or optimization heuristics. Instead, it identifies the epistemic signals—anomalies interpreted as limits, not noise—that prompt shifts from observable-variable models, to latent embeddings, to world models, to structures like digital twins or multi-scale simulacra. These transitions are characterized as driven by qualitative rather than quantitative insufficiency.

By this account, historical shifts in science (e.g., classical mechanics to relativity), as well as recent transitions in AI (feature engineering to learned embeddings, static predictors to world models, local models to foundation models), are intelligible as responses to explanatory insufficiency. Furthermore, multiple representational levels may coexist; stratification rather than wholesale substitution is the norm.

Implications for Machine Learning and AI System Design

A key implication is the design of autonomous learning systems not only capable of optimizing within a representation, but also of recognizing and responding to the explanatory limits of their representations. This requires mechanisms for:

• Detecting persistent explanatory anomalies (distinguishing model error from representational failure).
• Diagnosing when anomalies signal irreducible limits of current representational assumptions.
• Initiating and constructing new representational architectures that reduce or eliminate such explanatory gaps.

This concept of representational intelligence extends conventional representation learning by endowing a system with meta-cognitive capabilities: self-assessment of representational adequacy and the autonomous construction of new explanatory frameworks.

The paper suggests that incorporating these capabilities is as critical to future AI as optimizing traditional loss functions. Applications include continual and open-ended learning, autonomous scientific discovery, and adaptive world modeling.

Empirical Origin and Biological Systems Analogy

TBER is motivated by empirical work in adaptive locomotor systems, where observed performance metrics proved unable to differentiate between underlying organizational states (Raynal et al., 1 May 2026, Raynal et al., 12 May 2026). Successive explanatory insufficiencies led researchers to introduce organizational, viability, and latent-space analyses in a sequence reflecting the TBER cycle. This exemplifies the broader claim: representational transitions are often triggered when existing explanatory frameworks cannot reconcile new organizational or behavioral phenomena, despite stable observables.

Biological systems, with their continual organizational reconfigurations under varying constraints, are posited as natural laboratories for empirical validation of TBER’s principles. The framework predicts that similar sequences—from performance, to organization, to viability, to latent representations, and finally to representational meta-reasoning—should recur across adaptive domains.

Limitations and Directions for Future Work

TBER is fundamentally theoretical and presently lacks operational criteria or algorithmic formalization for explanatory insufficiency. Its propositions must be tested via rigorous empirical studies that distinguish trivial model error from genuine representational inadequacy.

Developing practical diagnostics for explanatory insufficiency (e.g., via persistent instability under distribution shift, loss of transfer, mismatch between latent and observed organization) is highlighted as a core future direction. Integrating these diagnostics into learning systems could enable autonomous representational evolution.

Application to scientific discovery, continual learning, rehabilitation, and digital twins are suggested domains for empirical extension and validation.

Conclusion

The Bootstrap Theory of Representational Emergence (2606.07303) advances a conceptual framework for understanding the drivers and mechanisms underlying representational change in intelligent systems. It posits explanatory insufficiency—not merely error—as the key epistemic event catalyzing representational transitions, encapsulated by a recursive five-stage model. The framework’s main implication is that the development of next-generation AI systems will require explicit meta-representational capacities: the detection and resolution of their own explanatory limitations, leading not just to new representations, but to the open-ended evolution of forms of explanation themselves.