From Performance to Representational Adequacy: A Representational Bootstrap Framework for Adaptive Biological Systems

Representation learning is central to modern machine learning, but most research examines how representations are optimized after a framework has been selected. Less attention is given to when a new representational level becomes necessary. This article introduces the Bootstrap Theory of Representational Emergence (TBER), an initial conceptual theory and research program describing how new representations arise when existing ones become explanatorily insufficient. A representation may remain descriptively useful while failing to make certain observations, relations, transformations, or organizational properties intelligible. TBER treats this explanatory insufficiency as a positive signal for representational transition rather than as simple falsification or prediction error. The proposed recursive process follows five stages: stabilized observation, anomaly detection, recognition of explanatory insufficiency, representational emergence, and provisional stabilization. The framework concerns transitions between scientific or computational representations, not equivalent transitions within the physical systems being observed. Its scope includes representation learning, latent spaces, foundation models, world models, digital twins, adaptive biological systems, and scientific discovery. TBER does not propose a new algorithm, model architecture, benchmark, or optimization procedure. Its contribution is meta-representational: it provides a framework for interpreting when and why new representational levels become necessary. A possible implication for future artificial intelligence is the development of systems able to detect when their own internal representations have reached explanatory limits and to initiate representational refinement or transition.

In biomechanical systems, observable performance is often used as a proxy for underlying organization, although similar outputs may arise from different adaptive configurations. This study considers the vertical dimension of occlusion (VDO) as a constraint applied to an adaptive neuromechanical system. A single-case design in a patient with Parkinson's disease enabled repeated intra-individual gait observations under six occlusal probes. Three complementary analytical levels were examined: (i) an aggregated scalar score of observable performance, (ii) a conceptual dynamical systems framework, and (iii) an exploratory UMAP representation of 55 standardized biomechanical variables from 270 M1 observations. The revised Level 1 analysis showed that the relative ranking of OC2.5 and OC3 depended on score construction, while their scalar distributions remained close. The Level 3 embedding showed substantial overlap among all six probes and did not identify independently separated condition-specific clusters. OC2.5 and OC3 displayed limited centroid displacement but broad observation-level overlap. The principal result is therefore representational non-identifiability: neither the aggregated score nor the selected low-dimensional embedding uniquely identifies an occlusal-condition-specific system state. VDO is interpreted as a constraint parameter rather than a causal determinant. The findings are exploratory, model dependent, and non causal. They do not establish distinct physiological states, an optimal VDO, clinical thresholds, or diagnostic, predictive, mechanistic, or prescriptive validity.

Understanding adaptive biomechanical systems requires distinguishing observable performance, static multivariate representation, longitudinal displacement, and internal approximation of observed change. This study introduces Level 5, which examines whether the M1-M2 transformation observed in a single-subject gait dataset can be approximated within a selected PCA representation. Gait was recorded with instrumented insoles in a participant with Parkinson's disease under six occlusal observational probes during two sessions eleven weeks apart. A simplified feed-forward neural network was trained to approximate M2 PC1-PC2 coordinates from M1 coordinates, occlusal-probe descriptors, and the longitudinal-transition indicator. In the core analysis aligned with Level 4, the model preserved the Euclidean centroid-displacement hierarchy dOC3 < dONL < dOC2.5. In the extended six-probe analysis, it preserved the broad structure of the exploratory ordering. Held-out M2 and leave-condition-out analyses provided internal tests beyond the full-dataset fit, while a within-session analysis described probe positions relative to ONL. The term predictive is used only in a restricted methodological sense. The model does not provide prospective clinical prediction, patient-level forecasting, or generalization to unseen individuals. Occlusal conditions are treated as observational probes applied during measurement, not as continuous causal drivers of longitudinal evolution. The findings are exploratory, retrospective, representation dependent, and non causal. They do not establish causal occlusal effects, validated viability thresholds, therapeutic superiority, distinct physiological states, or generalizable predictive validity.