Decomposition of Binary Relationships (in Superposition Multi-graphs)

The diagram below is part of the paper we’re working on “The Immersion of Directed Multigraphs in Embedding Fields“. This part is about generalizing the concept of “edge” in a graph from a deterministic object to a richer object, defined by direction, type and identity superposition.

While Node A, on the lefthand side, is deterministic, the virtual node X (which is a super-position of B,C,D,E), with bounded probabilities.

The same principle of superposition can further be continuated to representing the “direction” of the relationship. While in deterministic graphs, the direction is either A->B, B->A or A<->B. In the case of an edge direction in superposition, only a normalizing quadratic constraint (similar to softmax) is placed on “directions” manifested.

Anthropocentric languages, both spoken languages and programming languages, are too poor in their individual constructs to have coverage or quorum on the topics of intelligence. One of the reasons for this is that anthropocentric languages are rather biased and overconfident towards poor, human-centric view of the world. This need to change, as we invent new languages, such as the most promising of Wolfram’s proposals so far (which itself is not without its criticisms)

The context of this topic is covered in more depth in our recently published paper “The Immersion of Directed Multi-graphs in Embedding Fields. Generalisations.

Don’t hesitate to reach out for questions, suggestions and details.

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