Data model

PBG operates on directed multi-relation multigraphs, whose vertices are called entities. Each edge connects a source to a destination entity, which are respectively called its left- and right-hand side (shortened to LHS and RHS). Multiple edges between the same pair of entities are allowed. Loops, i.e., edges whose left- and right- hand sides are the same, are allowed as well.

Each entity is of a certain entity type (one and only one type per entity). Thus, the types partition all the entities into disjoint groups. Similarly, each edge also belongs to exactly one relation type. All edges of a given relation type must have all their left-hand side entities of the same entity type and, similarly, all their right-hand side entities of the same entity type (possibly a different entity type than the left-hand side one). This property means that each relation type has a left-hand side entity type and a right-hand side entity type.

a graph with three entity types and three relation types

In this graph, there are 14 entities: 5 of the red entity type, 6 of the yellow entity type and 3 of the blue entity type; there are also 12 edges: 6 of the orange relation type (between red and yellow entities), 3 of the purple entity type (between red and blue entities) and 3 of the green entity type (between yellow and blue entities).

In order for PBG to operate on large-scale graphs, the graph is broken up into small pieces, on which training can happen in a distributed manner. This is first achieved by further splitting the entities of each type into a certain number of subsets, called partitions. Then, for each relation type, its edges are divided into buckets: for each pair of partitions (one from the left- and one from the right-hand side entity types for that relation type) a bucket is created, which contains the edges of that type whose left- and right-hand side entities are in those partitions.

the graph from before, partitioned and with only one bucket visible

This graph shows a possible partition of the entities, with red having 3 partitions, yellow having 3, and blue having only one (hence blue is unpartitioned). The edges displayed are those of the orange bucket between the partitions 2 of the red entities and the partition 1 of the yellow entities.

Note

For technical reasons, at the current state all entity types that appear on the left-hand side of some relation type must be divided into the same number of partitions (except unpartitioned entities). The same must hold for all entity types that appear on the right-hand side. In numpy-speak, it means that the number of partitions of all entities must be broadcastable to the same value.

An entity is identified by its type, its partition and its index within the partition (indices must be contiguous, meaning that if there are \(N\) entities in a type’s partition, their indices lie in the half-open interval \([0, N)\)). An edge is identified by its type, its bucket (i.e., the partitions of its left- and right-hand side entity types) and the indices of its left- and right-hand side entities in their respective partitions. An edge doesn’t have to specify its left- and right-hand side entity types, because they are implicit in the edge’s relation type.

Formally, each bucket can be identifies by a pair of integers \((i, j)\), where \(i\) and \(j\) are respectively the left- and right-hand side partitions. Inside that bucket, each edge can be identified by a triplet of integers \((x, r, y)\), with \(x\) and \(y\) representing respectively the left- and right-hand side entities and \(r\) representing the relation type. This edge is “interpreted” by first looking up relation type \(r\) in the configuration, and finding out that it can only have entities of type \(e_1\) on its left-hand side and of type \(e_2\) on its right-hand side. One can then determine the left-hand side entity, which is given by \((e_1, i, x)\) (its type, its partition and its index within the partition), and, similarly, the right-hand side one which is \((e_2, j, y)\).