Knowledge Base Completion (KBC)

Foundational models like TransE treat relationships as vector translations. For a true triple (h, r, t), the embedding of the head entity plus the relation vector should approximate the tail entity embedding: h + r ≈ t.

• Scoring Function: Uses L1 or L2 distance to measure plausibility.
• Limitation: Struggles with complex 1-to-N, N-to-1, and N-to-N relations.
• Variants: TransH and TransR project entities into relation-specific hyperplanes or spaces to handle complex cardinalities.

Unlike translational models, semantic matching approaches like RESCAL and DistMult use tensor factorization. They model the interaction between head and tail entities via a bilinear product defined by the relation.

• RESCAL: Uses a full rank matrix for each relation, capturing complex interactions but at high computational cost.
• DistMult: Restricts the relation matrix to a diagonal vector, drastically reducing parameters but limiting the model to symmetric relations.
• ComplEx: Extends DistMult into the complex-valued space to elegantly model antisymmetric relations using the Hermitian dot product.

Modern KBC systems leverage Graph Neural Networks (GNNs) like R-GCN and CompGCN as encoders. These models generate entity embeddings by aggregating information from a node's local neighborhood, capturing the multi-hop graph structure.

• Message Passing: Entities iteratively update their representations based on connected relations and neighboring entities.
• Compositional Operators: CompGCN defines specific entity-relation composition operations (e.g., subtraction, multiplication, circular-correlation) during aggregation.
• Inductive Capability: Unlike transductive models, GNN encoders can generate embeddings for unseen entities seen during inference.

Training KBC models requires generating negative samples (false triples) to contrast against true facts. The strategy for corrupting a true triple is critical for model convergence.

• Uniform Negative Sampling: Randomly replacing the head or tail entity, often producing trivially false negatives that don't challenge the model.
• Bernoulli Sampling: Adjusts the probability of corrupting the head vs. tail based on the relation's cardinality mapping properties.
• Adversarial Sampling: Dynamically selects high-scoring negative triples that the current model is most likely to confuse, providing a harder training signal.

Beyond direct triples, KBC can be framed as a logical inference task using path-ranking algorithms. These methods find relational paths between two entities to predict a direct link.

• Path-Ranking Algorithm (PRA): Uses random walks to find sequences of relations connecting a head to a tail, treating these paths as features for a binary classifier.
• Neural Theorem Provers (NTPs): Learn differentiable first-order logic rules to prove a query triple by chaining relations.
• Reinforcement Learning: Frameworks like DeepPath train an RL agent to find the most informative reasoning paths in the graph to predict missing links.

Standard KBC assumes a static graph, but facts often have a temporal scope. Temporal KBC incorporates timestamps or time intervals into the scoring function.

• Time-Aware Embeddings: Models like TTransE concatenate a time vector to the entity or relation embedding.
• HyTE: Projects entities onto a time-specific hyperplane before applying the translational scoring function.
• Temporal GNNs: Use recurrent mechanisms or time-encoding functions within a GNN framework to model the evolution of entity representations over time.

A binary classification task that determines whether a given subject-predicate-object triple represents a true fact. Unlike link prediction which ranks tail entities, triple classification validates a complete statement.

• Positive Triples: Facts explicitly present in the knowledge graph.
• Negative Triples: Corrupted facts generated by swapping entities, used for training.
• Negative Sampling: The strategy for generating false triples is critical; random swapping often creates trivially false negatives.

A low-dimensional vector representation of a relationship, learned to capture its semantic properties. These embeddings encode the latent behavior of a predicate, such as transitivity or symmetry.

• Semantic Similarity: Relations like bornIn and hometown should have similar embeddings.
• Relational Patterns: Embeddings must capture logical rules like marriedTo being symmetric.
• Use Case: Used directly in scoring functions for link prediction and for clustering similar relation types.

The application of Graph Neural Networks (GNNs) to reason over the local neighborhood structure of a knowledge graph. Unlike shallow embeddings, GNNs can leverage node attributes and multi-hop paths.

• R-GCN: A relational graph convolutional network that aggregates messages from neighboring nodes based on relation type.
• CompGCN: A composition-based GCN that jointly embeds entities and relations in a unified framework.
• Advantage: Naturally handles the inductive setting where new entities arrive with initial connections.

The task of automatically assessing the truthfulness of a textual claim, often by grounding it against a structured knowledge base. This is the downstream application that validates the utility of a completed graph.

• FEVER Dataset: A standard benchmark for fact verification against Wikipedia.
• Retrieval Step: Involves finding relevant evidence documents or triples before classification.
• Contrast with KBC: KBC predicts missing facts; fact verification confirms or refutes existing claims.