On a group of invariances in a class of functions

A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this family, nontrivial parametric invariances are identified and characterized, i.e., distinct parameter settings that induce identical input-output maps. A constructive description of the invariance structure is provided, enabling sparse function representations, parameter obfuscation, and potential dimensionality reduction for optimization.