Parameterin

Parameterin is a proposed intrinsic parameter of a mathematical or physical model that remains invariant under a specified group of transformations. Unlike ordinary parameters, which may change under reparameterization or coordinate changes, a parameterin aims to encode a core structural property of the system that is preserved across equivalent representations.

Origin and terminology: The term is a neologism formed from parameter with a common -in suffix used in mathematical language. It is not widely standardized and appears mainly in speculative or tutorial discussions about model invariants rather than in established literature.

Characteristics: A parameterin is defined with respect to a transformation class, such as coordinate changes, scaling, or reparameterization. It is often scalar but can be tensorial, and it is intended to be identifiable from data as an invariant quantity across representations that are mathematically equivalent.

Applications: In dynamical systems, parameterin can aid model comparison by focusing on invariant structure rather than chosen parametrizations. In machine learning, it can serve as a regularization target or a criterion for identifiability, helping to reduce degeneracy caused by reparameterizations.

Examples: Suppose a model has parameters p and q that transform under a change of variables x -> s x. A parameterin might be defined as a product pq or the spectrum of an associated operator, which remains unchanged under the transformation. The exact form is context-dependent and not uniquely prescribed.

Status and see also: The concept is not part of standard terminology in core textbooks. It appears in occasional theoretical notes and should be treated as a heuristic notion. See also parameter, parameterization, invariants, model identifiability.