Apprendre Symbolic Versus Vector Representations | Foundations of Knowledge Graphs

When working with knowledge graphs, you will encounter two major approaches to representing information: symbolic and vector representations. Symbolic representations are the traditional way of structuring knowledge. They use discrete structures such as triples, which are statements of the form ("entity", "relation", "entity"). For example, you might have a triple like ("Paris", "isCapitalOf", "France"). These triples are then organized into a graph, where nodes represent entities and edges represent relations. This structure is highly interpretable and allows for precise, logical reasoning.

In contrast, vector representations — often called embeddings — translate entities and relations into continuous, high-dimensional numerical vectors. Instead of working with explicit symbols and their connections, you work with arrays of numbers. These embeddings are learned from data and capture patterns and similarities that may not be immediately obvious from the symbolic structure. For instance, the entities "Paris" and "London" might be represented as vectors that are close together in the embedding space because they share similar roles as capital cities.

Symbolic representations are powerful for tasks requiring explicit logical inference, such as checking if a specific relationship exists or following a chain of relations. However, they can struggle with noisy or incomplete data, and they do not naturally capture similarities between different entities unless those are explicitly encoded.

Vector representations excel in capturing approximate similarities and supporting tasks like clustering, classification, and link prediction. They can generalize from observed data, making it possible to infer new, plausible relationships even when the exact symbolic pattern has not been seen before. However, their interpretability is lower, and precise logical reasoning is more challenging.

Symbolic reasoning use cases

When you need precise, explainable answers;
When the task requires strict adherence to rules, such as validating data consistency or enforcing ontological constraints;
When interpretability and auditability of the reasoning process are critical.

Vector-space reasoning use cases

When you need to handle noisy, incomplete, or ambiguous data;
When discovering latent patterns or similarities is important, such as in recommendation systems or clustering;
When scalability and the ability to generalize from existing data to unseen cases are priorities.


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import numpy as np

# Suppose you have three entities: Paris, London, and France
# Each entity is represented as a 3-dimensional embedding vector

entity_embeddings = {
    "Paris": np.array([0.8, 0.1, 0.5]),
    "London": np.array([0.75, 0.12, 0.48]),
    "France": np.array([0.9, 0.05, 0.6])
}

for entity, embedding in entity_embeddings.items():
    print(f"{entity}: {embedding}")

1. What is a key advantage of vector representations over symbolic ones?

2. In which scenario would symbolic reasoning be preferred?

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