On the Possible Structure of Coupling between Representation Similarity and Transformation Stability: A Hypothesis Based on Empirical Regimes

Recent empirical results suggest that the relationship between representation similarity and transformation-dependent stability in neural networks is structured and non-monotonic. In particular, this relationship appears to exhibit regime-dependent behavior across transformation strengths and architectures. In this paper, we do not propose a validated theory, but a candidate structural interpretation consistent with these observations. We introduce a minimal effective functional whose projections recover similarity and stability as observables, and whose curvature structure may induce regime transitions. We emphasize that this framework is not claimed to be necessary, complete, or uniquely determined. Rather, it is proposed as a possible organizing structure that could help interpret non-monotonic coupling patterns observed in representation–transformation systems.