Dimension reduction in recurrent networks by canonicalization

<p style='text-indent:20px;'>Many recurrent neural network machine learning paradigms can be formulated using state-space representations. The classical notion of canonical realization is adapted in this paper to accommodate semi-infinite inputs so that it used as a dimension reduction tool the networks setup. so-called input forgetting property identified key hypothesis guarantees existence and uniqueness (up system isomorphisms) realizations for causal time-invariant input/output systems with inputs. Additionally, optimal coming from theory symmetric Hamiltonian implemented our setup construct out but not necessarily ones. These two procedures are studied detail framework linear fading memory systems. {Finally, implicit reproducing kernel Hilbert spaces (RKHS) introduced which allows, readouts, achieve without need actually compute reduced first part paper.</p>