MMP.11:4.3 - Choose the representation and its range

Choose a representation whose operations fit the required use and available resources. A table can represent a finite function. A basis expansion or program can retain a useful structure. A neural representation can supply a flexible adjustable function. The meaning of its inputs and outputs, and the retained relations, remain part of the model.

Check two different questions. Does every admitted parameter setting produce a relation allowed by the construction? Does the construction cover all relations needed for the present conclusion? A witness may need only one candidate; an impossibility claim over all admissible models needs coverage of that whole family or another sufficient argument.

State restrictions introduced by knots, basis functions, regularity, network architecture or domain truncation when they can change the answer. A numerical fit inside the restricted family answers for that family. If its consequence is sufficient, a more flexible family may add only cost. If the missing case matters, change the representation.

Different parameters can denote the same function. Recover the function or consequence needed by the receiving use rather than demanding unique parameters by default. Section :5.3 gives a normalization redundancy. Use MATH.7 when a change of representation has constructed inverse maps; use C.29.1 when correspondence is more general.