Structure of CPWL parameter variety constraints for ReLU networks

Determine the precise structure of the polynomial equations and inequalities (of degree at most L+1) defining the semi-algebraic feasible set of canonical continuous piecewise linear (CPWL) parameters that correspond to functions representable by a ReLU network of given architecture (n_0,\ldots,n_L), including how the structure depends on the architecture and the chosen representation sizes n and m.

Background

The authors discuss mapping ReLU network parameters to a canonical CPWL parameterization capturing gradients and intercepts of linear pieces. Prior work establishes existence of polynomial equations and inequalities of bounded degree describing the representable set.

However, the detailed architecture-dependent form of these constraints is not known; clarifying this would bridge the CPWL parameter perspective with the pattern and output varieties developed in the paper.