Common use of Graph Embeddings Clause in Contracts

Graph Embeddings. We base the training of our entity embeddings on Wikipedia2Vec [25, 26]. Taking a knowledge graph as the input, Wikipedia2Vec extends the skip-gram variant of Word2Vec [18, 19] and learns word and entity embeddings jointly. The objective function of this model is composed of three components. The first component infers optimal embeddings for words W in the corpus. Given a sequence of words w1w2...wT and a context window of size c, the word-based objective function is: Lw = Σ exp(VT U ) Σ T Σ w log wt t+j exp(V Uw) t=1 —c≤j≤c,j=0 w∈W wt where matrices U and V represent the input and output vector representations, deriving the final embeddings from matrix V. The two other components of the objective function take the knowledge graph into account. One addition considers a link-based measure estimated from the knowledge graph (i.e., Wikipedia). This measure captures the relatedness between entities in the knowledge base, based on the similarity between their incoming links: = Σ Σ log exp(VT Ue )

Graph Embeddings. We base the training of our entity embeddings on Wikipedia2Vec [25, 26]. Taking a knowledge graph as the input, Wikipedia2Vec extends the skip-gram variant of Word2Vec [18, 19] and learns word and entity embeddings jointly. The objective function of this model is composed of three components. The first first component infers optimal embeddings for words W in the corpus. Given a sequence of words w1w2...wT and a context window of size c, the word-based objective function is: Lw = Σ exp(VT U ) Σ T Σ w log wt t+j exp(V Uw) t=1 —c≤j≤c−c≤j≤c,j=0 w∈W wt where matrices U and V represent the input and output vector representations, deriving the final final embeddings from matrix V. ei The two other components of the objective function take the knowledge graph into account. One addition considers a link-based measure estimated from the knowledge graph (i.e., Wikipedia). This measure captures the relatedness between entities in the knowledge base, based on the similarity between their incoming links: ei∈E eo∈Cei ,ei = Σ Σ log exp(VT Ue )) ei ei