Invariants for neural automata

Abstract Computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. One particular way for combining these approaches within a framework called vector architectures leads to automata. Specifically, automata result from the assignment symbols symbol strings numbers, known as Gödel encoding. Under this assignment, computation becomes represented by trajectories state vectors in real phase space, that allows statistical correlation analyses with real-world measurements experimental data. However, assignments are usually completely arbitrary. Hence, it makes sense address problem which aspects dynamics observed under representation is intrinsic not. In study, we develop formally rigorous mathematical investigation symmetries invariants different encodings. As central concept define patterns equality such systems. We consider macroscopic observables, mean activation level network, ask their invariance properties. Our main shows only step functions defined over those invariant recodings, while activation, e.g., work could be substantial importance related regression studies neurosymbolic processors avoiding confounding results dependant on encoding not