Representing graph edges using neural networks

A system comprising:

• one or more computers;
• and
• one or more storage devices communicatively coupled to the one or more computers, wherein the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations for training a manifold neural network and a learned edge function to determine trained values of parameters of the manifold neural network and the learned edge function, wherein:
• the manifold neural network is a deep neural network that is configured to receive input numeric embeddings representing input nodes in a graph and to process each input numeric embedding to generate manifold coordinates of the input node represented by the input numeric embedding, and
• the learned edge function is configured to receive manifold coordinates of a first node in the graph and manifold coordinates of a second node in the graph and to process the manifold coordinates of the first node and the manifold coordinates of the second node to generate an edge score that represents a likelihood that an entity represented by the first node and an entity represented by the second node have a particular relationship, the operations comprising:
• performing a plurality of random walks on the graph, wherein each random walk defines a sequence of nodes from the graph;
• generating a set of positive training examples based on the random walks on the graph, wherein each positive training example comprises a reference node and a positive node, wherein the reference node and the positive node are within a context window in a random walk on the graph;
• obtaining:
• (i) a positive training example from the set of positive training examples, wherein the positive training example comprises a reference node and a positive node that are separated by at least one intervening node in a random walk on the graph, and (ii) one or more negative nodes corresponding to the reference node;
• determining, using the manifold neural network and in accordance with current values of parameters of the manifold neural network, respective manifold coordinates of the reference node, the positive node, and the negative nodes;
• determining, using the learned edge function and in accordance with current values of parameters of the learned edge function, a respective edge score with the reference node for the positive node and each of the negative nodes from the respective manifold coordinates;
• determining gradients of an objective function that promotes generating a high edge score for the positive node and penalizes generating high edge scores for the negative nodes with respect to the parameters of the manifold neural network and the parameters of the learned edge function;
• and
• using the gradients to update the current values of the parameters of the manifold neural network and of the parameters of the learned edge function.

One or more non-transitory computer storage media storing instructions that when executed by one or more computers cause the one or more computers to perform operations for training a manifold neural network and a learned edge function to determine trained values of parameters of the manifold neural network and the learned edge function, wherein:

• the manifold neural network is a deep neural network that is configured to receive input numeric embeddings representing input nodes in a graph and to process each input numeric embedding to generate manifold coordinates of the input node represented by the input numeric embedding, and
• the learned edge function is configured to receive manifold coordinates of a first node in the graph and manifold coordinates of a second node in the graph and to process the manifold coordinates of the first node and the manifold coordinates of the second node to generate an edge score that represents a likelihood that an entity represented by the first node and an entity represented by the second node have a particular relationship, the operations comprising:
• performing a plurality of random walks on the graph, wherein each random walk defines a sequence of nodes from the graph;
• generating a set of positive training examples based on the random walks on the graph, wherein each positive training example comprises a reference node and a positive node, wherein the reference node and the positive node are within a context window in a random walk on the graph;
• obtaining:
• (i) a positive training example from the set of positive training examples, wherein the positive training example comprises a reference node and a positive node that are separated by at least one intervening node in a random walk on the graph, and (ii) one or more negative nodes corresponding to the reference node;
• determining, using the manifold neural network and in accordance with current values of parameters of the manifold neural network, respective manifold coordinates of the reference node, the positive node, and the negative nodes;
• determining, using the learned edge function and in accordance with current values of parameters of the learned edge function, a respective edge score with the reference node for the positive node and each of the negative nodes from the respective manifold coordinates;
• determining gradients of an objective function that promotes generating a high edge score for the positive node and penalizes generating high edge scores for the negative nodes with respect to the parameters of the manifold neural network and the parameters of the learned edge function;
• and
• using the gradients to update the current values of the parameters of the manifold neural network and of the parameters of the learned edge function.