🤖 AI Summary
Traditional neural networks struggle to explicitly model logical relationships such as part-whole hierarchies and lack symbolic reasoning capabilities. This work proposes a novel graph-structured neural architecture that encodes input data into a relational graph, where edges are drawn from a predefined set of primitive relations. The system employs a graph Hamiltonian operator to drive energy minimization, ensuring that the ground state satisfies all relational constraints. By embedding relational representations directly into fundamental components and integrating ultra-low-precision arithmetic with bit-level part-whole mechanisms, the approach achieves efficient symbolic reasoning and hierarchical structure construction while maintaining linear computational complexity. The model not only performs competitively on standard neural network tasks but also generates relation-aware positional encodings imbued with symbolic semantics, offering a new paradigm for vector-based representations.
📝 Abstract
We introduce a simple initial working system in which relations (such as part-whole) are directly represented via an architecture with operating and learning rules fundamentally distinct from standard artificial neural network methods. Arbitrary 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 encoding is not an add-on, but occurs intrinsically within the most basic components of the system. A novel graph-Hamiltonian 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 representations that exhibit characteristics of symbolic computation. Specifically, the method identifies simple logical relational structures in these data (part-of; next-to), building hierarchical 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 representation. The very simple current state of the implemented system invites additional tools and improvements.