[R] Measuring the Symmetry--Data Exchange Rate

The prediction that equivariance reduces sample complexity by a factor of |G| appears in roughly every paper on geometric deep learning and is measured as an actual scaling law in roughly none of them. This paper does the measurement. The methodology is the interesting part. Naive estimators conflate group order with task difficulty (larger groups induce harder symmetry structure, not just more constraint), so the authors derive a relative exchange rate that cancels the shared difficulty out, meaning roughl