Convergence of the conformal Ward identity in the derivative expansion approximation

What the math gives to ML

The paper provides a constructive convergence diagnostic for truncated functional renormalization-group calculations: regulator parameters that minimize conformal Ward-identity breaking also show reduced sensitivity of universal critical exponents. The transferable asset is a computable symmetry-breaking residual for selecting approximation hyperparameters, rather than conformal symmetry by itself. This can be adapted to neural approximations of effective actions, fields, or scale-dependent operators by penalizing violations of known transformation identities and testing whether the residual decreases as model capacity or truncation order increases.