Dynamical similarity analysis (DSA)

DSA is a recent method for comparing two systems by the structure of their dynamics rather than by the geometry of their representations. Where representational similarity analysis compares the arrangement of activity patterns, DSA (Ostrow et al.) first fits a linear operator to each system's trajectories in a delay-embedded space (a Koopman/DMD-style approximation) and then measures how similar those operators are in a way invariant to a change of basis — comparing intrinsic dynamical features (eigenvalues, recurrent structure) rather than arbitrary coordinates. Two networks that solve a task with the same underlying dynamics but different representational geometry are judged similar; two with matching geometry but different flow are judged different.

The motivation is precisely the identifiability problem: because latent coordinates are meaningful only up to transformation, comparisons of neural computation across brains, subjects, and models should be built on transformation-invariant dynamical quantities. DSA is young, and its verdicts depend on the delay-embedding and linear-operator approximation it uses, but it exemplifies the field's shift toward invariant, dynamics-first ways of asking whether two systems compute alike.