Bowen E, Granger R, Rodriguez A (2023) A logical re-conception of neural networks: Hamiltonian bitwise part-whole architecture. Amer Assoc Art Intell (AAAI)

We introduce a simple initial working system in which rela- tions (such as part-whole) are directly represented via an ar- chitecture with operating and learning rules fundamentally distinct from standard artificial neural network methods. Ar- bitrary data are straightforwardly encoded as graphs whose edges correspond to codes from a small fixed primitive set of elemental pairwise relations, such that simple relational en- coding is not an add-on, but occurs intrinsically within the most basic components of the system. A novel graph-Hamil- tonian operator calculates energies among these encodings, with ground states denoting simultaneous satisfaction of all relation constraints among graph vertices. The method solely uses radically low-precision arithmetic; computational cost is correspondingly low, and scales linearly with the number of edges in the data. The resulting unconventional architecture can process standard ANN examples, but also produces rep- resentations that exhibit characteristics of symbolic compu- tation. Specifically, the method identifies simple logical re- lational structures in these data (part-of; next-to), building hi- erarchical representations that enable abductive inferential steps generating relational position-based encodings, rather than solely statistical representations. Notably, an equivalent set of ANN operations are derived, identifying a special case of embedded vector encodings that may constitute a useful approach to current work in higher-level semantic represen- tation. The very simple current state of the implemented sys- tem invites additional tools and improvements.