Shapes and Norms of Random Pairs

What the math gives to ML

The paper introduces a two-parameter information profile that optimizes a weighted sum of conditional entropies against residual conditional mutual information over auxiliary variables. Its transferable asset is the full convex surface over $(\alpha,\beta)$, including a theoretically distinguished affine upper-right triangle and an information-rich lower-left triangle. A neural implementation can use this surface as a dependence-sensitive regularizer or representation diagnostic, with an adversarial auxiliary encoder searching for the extension $W$ that maximizes the profile. The approach is experimentally plausible for learning paired representations, although estimating the supremum and conditional mutual information accurately will be the main bottleneck.