Dieu, Patrick-Olivier: 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 projection