A Measurement Framework for Divergence in Representation Stability Under Transformation Complexity

We introduce a measurement framework for analyzing how neural representations diverge under transformations of increasing complexity. Rather than proposing a universal theory of representation learning or invariance, we define a single observable, $\Delta(c)$, which measures inter-model variance in representation stability across heterogeneous neural architectures. The framework is designed as an empirical instrument: it specifies how to measure divergence, how to control for parameterization artifacts, and how to evaluate whether regime-like structure exists in representation sensitivity. We define a transition scale $c^*$ operationally from the behavior of $\Delta(c)$ and provide a set of robustness stress-tests intended to distinguish structural effects from smooth nonlinear or metric-induced artifacts. We do not assume the existence of universal scaling laws, critical phenomena, or phase transitions. Instead, we propose a falsifiable protocol for determining whether structured divergence regimes emerge consistently across architectures, transformation families, and representation metrics. The contribution of this work is therefore methodological rather than ontological: a minimal experimental framework for detecting, testing, or rejecting the presence of structured divergence behavior in representation stability.