MMP.11:10 - Architectural Rationale

Constructing the free part through the retained relations makes the reason for a property inspectable. A shared transfer preserves a total because the same quantity enters with opposite signs. A shape-constrained response preserves monotonicity because its increments are integrals of nonnegative values. Those reasons remain available when coefficients or learned functions change.

Separating function, representation and receiving consequence also permits economical inference. Many representations of the same function need not be distinguished. Functions that agree on the needed consequence may remain as alternatives. A new intervention can make a formerly irrelevant difference decisive.

The insertion point is therefore an architectural choice in the model. It determines what the adjustable contribution can change, which relations constrain it and which results still have the interpretation the work needs. A symbolic expression and a trained network can each participate in this construction when their mathematical role is recoverable.