In Section 1 of Structural identifiability of generalized constraint neural network models for nonlinear regression by Yang et al, the authors have defined structural identifiability on the second page as follows.
The structural identifiability (s.i.) is concerned with the uniqueness of the parameters determined from the in- put–output data. The term ‘structural’ means independent of the parameter values [12]. If different parameter values lead to different output throughout the parameter space, the model is said to be structurally global identifiable (s.g.i.); if all different parameter values that lead to identical output are isolated from each other, the model is structurally local identifiable (s.l.i.), otherwise, it is structurally nonidentifiable (s.n.i.).
My question: What does it mean when the authors say
all different parameter values that lead to identical output are isolated from each other ?