Fundamental Limits of Transferability and Equivariance in Algebraic Signal Models I: Finite Dimensions

תקציר מקורי באנגליתarXiv:2609.36106v1 Announce Type: cross Abstract: We study the fundamental limits of transferability in algebraic signal processing through homomorphisms between algebraic signal models. Homomorphisms are linear maps between the signal spaces of two models that commute with filtering, so filtering a signal and transferring it across domains can be done in either order. The existence of such maps is governed entirely by coincidences among the filtered eigenvalues of the two models' shift operators, but existence alone is insufficient: the space of homomorphisms always contains trivial elements that destroy all information. We introduce the spectral transfer efficiency $\eta(\theta)\in[0,1]$ to quantify information-preserving quality, prove that every homomorphism decomposes into unconstrain