Knowledge Graph Completion

The dominant paradigm for KGC, where entities and relations are mapped to low-dimensional vector representations in a continuous latent space. A scoring function evaluates the plausibility of any given triple. Key architectures include:

• Translational models (TransE, RotatE): Model relations as geometric translations or rotations in the embedding space.
• Bilinear models (RESCAL, ComplEx, TuckER): Use tensor factorization to capture multi-relational interactions.
• Neural models (ConvE, InteractE): Employ convolutional or fully connected layers to learn complex feature interactions. These models are trained to rank true triples higher than corrupted ones using a margin-based or cross-entropy loss.

GNN-based methods treat KGC as a node classification or edge prediction problem on the graph structure itself. A message-passing framework aggregates features from a node's local neighborhood to generate expressive embeddings.

• R-GCN (Relational Graph Convolutional Network): Extends GCNs to multi-relational data by using relation-specific weight matrices during neighbor aggregation.
• CompGCN: A composition-based GCN that jointly embeds entities and relations, reducing parameter explosion in highly relational graphs.
• SEAL (Subgraph Extraction and Link prediction): Frames link prediction as a binary classification task on an enclosing subgraph around the target link, capturing local structural heuristics like common neighbors.

These approaches mine logical rules from the existing graph and apply them to deduce new facts, offering explicit interpretability. Key techniques include:

• Inductive Logic Programming (ILP): Learns first-order Horn clauses from positive and negative examples.
• AMIE+ (Association Rule Mining under Incomplete Evidence): Efficiently mines closed Horn rules from large, incomplete knowledge graphs by pruning the search space with support and confidence thresholds.
• Neural Theorem Provers (NTPs): Differentiable implementations of backward-chaining reasoning that unify symbolic rule application with neural network learning, allowing for soft unification and end-to-end gradient-based optimization. These methods excel in low-data regimes and provide human-readable justifications for predictions.

Leveraging external text corpora or other modalities to infer missing facts that are not structurally encoded in the graph. This bridges the gap between unstructured knowledge and structured triples.

• Description-based models (DKRL): Learn entity embeddings from both graph structure and entity descriptions using a convolutional neural network encoder on the text.
• Pre-trained Language Model (PLM) integration (KG-BERT): Fine-tunes BERT on triple classification by serializing a triple as a text sequence, treating KGC as a sentence-pair classification task.
• Multimodal fusion (MMKG): Combines visual features from entity images with structural and textual embeddings to resolve ambiguities where entities share names but have distinct visual representations.

Extends static KGC to graphs where facts are associated with timestamps or time intervals, predicting facts that hold at a specific time or forecasting future events.

• RE-NET (Recurrent Event Network): Uses a recurrent neural network to model the temporal sequence of graph events, predicting future interactions based on historical neighborhood dynamics.
• TComplEx: A temporal extension of the ComplEx tensor factorization that incorporates a fourth-order tensor to model time, enabling the scoring of quadruples (subject, relation, object, timestamp).
• CyGNet (Cycle Graph Network): Models the repetitive patterns of historical facts to predict future links, explicitly capturing the cyclical nature of many real-world temporal events.