Detecting Explanatory Insufficiency in Learned Representations: A Framework for Representational Vigilance

Learned representations are central to modern machine learning and are commonly evaluated through predictive performance, robustness, uncertainty estimation, or generalization. However, a learned representation may remain operationally successful while progressively failing to organize persistent residual structures that are not fully captured by conventional evaluation metrics. This article introduces VER, the Vigilant Evaluator of Representations, a conceptual framework for monitoring representational adequacy in learned representations. VER does not propose a new learning algorithm, loss function, or model architecture. Instead, it formalizes a diagnostic process through which persistent residual structures may be identified, analyzed, and interpreted as potential indicators of explanatory insufficiency. The framework distinguishes representational inadequacy from ordinary prediction error, uncertainty, noise, and distribution shift. It introduces a monitoring sequence based on representation identification, explanatory-domain delimitation, residual-structure detection, explanatory-resistance evaluation, and vigilance signaling. VER is intended as a contribution to representation diagnostics in machine learning. Its objective is not to replace existing evaluation methods but to complement them by treating representational adequacy as an explicit object of inquiry. A path toward empirical evaluation through representational-vigilance benchmarks is also outlined.

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.

From Performance to Viability: A Bootstrap Framework for Latent-Space Representation Learning in Adaptive Biological Systems

Observable performance is commonly used to characterize biological systems. In adaptive systems, however, similar performances may arise from distinct organizations, and configurations that appear comparable at a given time may follow different longitudinal trajectories. This limitation motivates a methodological framework for moving beyond performance-based interpretation without assuming a complete mechanistic model in advance. This article proposes a bootstrap framework for latent-space representation learning in adaptive biological systems. Here, bootstrap is used in a methodological and epistemological sense: new analytical levels are introduced when the preceding representation becomes insufficient to account for observed adaptive dynamics. The framework is organized around five levels: observable performance, dynamic organization, latent organization, longitudinal viability, and internal predictive approximation. The framework is illustrated by three previously reported gait--occlusion studies, used here only as a methodological case sequence and not as new experimental evidence. The article formalizes how performance analysis led to latent organization, how static latent organization led to longitudinal viability, and how observed viability led to internal predictive approximation. The contribution is not a new learning algorithm, clinical protocol, or dataset, but a bootstrap framework for latent-space representation learning describing how increasingly informative representations can emerge from observational insufficiencies in adaptive biological data.