Scale-Dependent Dimensionality Reveals a Common Structural Motif Across Representational Systems

AbstractUnderstanding how high-dimensional representations organize across scales is a central prob-lem in neuroscience and complex systems. Here, we analyze effective dimensionality as a functionof neighborhood scale across model-derived cortical representations and multiple synthetic sys-tems. We find that effective dimensionality follows a consistent growth–saturation profile: locallylow-dimensional structure expands with increasing scale before reaching a bounded plateau.After normalization, dimensionality curves exhibit strong cross-domain alignment (meanPearson correlation ≈ 0.90), indicating a shared structural motif across systems. However,systems differ quantitatively in growth rate (range: 0.23–0.82) and saturation behavior. TRIBE-derived cortical representations show pronounced compression (Deff ≈ 3–5, compression ratio= 0.49) and early saturation relative to synthetic systems.Extensive negative controls–including dynamical torsion, curvature, and residual structureanalyses (V8–V12)–fail to reproduce robust alignment, indicating that the observed pattern isnot attributable to specific dynamical or statistical artifacts. These results characterize scale-dependent dimensional growth with bounded saturation as a consistent structural pattern ob-served across diverse representational systems, while highlighting system-specific constraints onrepresentational capacity.