Representations

In PyKEEN, a Representation is used to map integer indices to numeric representations. A simple example is an Embedding, where the mapping is a simple lookup. However, more advanced representation modules are available, too.

This tutorial is intended to provide a comprehensive overview of possible components. Feel free to visit the pages of the individual representations for detailed technical information.

Base

The Representation class defines a common interface for all representation modules. Each representation defines a max_id attribute. We can pass any integer index \(i \in [0, \text{max_id})\) to a representation module to get a numeric representation of a fixed shape shape.

Note

To support efficient training and inference, all representations accept batches of indices of arbitrary shape, and return batches of corresponding numeric representations. The batch dimensions always precede the actual shape of the returned numerical representations.

Combinations & Adapters

PyKEEN provides a rich set of generic tools to combine and adapt representations to form new representations.

Transformed Representations

A TransformedRepresentation adds a (learnable) transformation to an existing representation. It can be particularly useful when we have some fixed features for entities or relations, e.g. from a pre-trained model, or encodings of other modalities like text or images, and want to learn a transformation on them to make them suitable for simple interaction functions like DistMultInteraction.

Subset Representations

A SubsetRepresentation allows to “hide” some indices. This can be useful e.g. if we want to share some representations between modules, while others should be exclusive, e.g. we want to use inverse relations for a message passing phase, but no inverses in scoring triples.

Partitioned Representations

A PartitionRepresentation uses multiple base representations and chooses exactly one of them for each index based on a fixed mapping. BackfillRepresentation implements a frequently used special case, where we have two base representations, where one is the “main” representation and the other is used as a backup whenever the first one fails to provide a representation. This is useful when we want to use features or pre-trained embeddings whenever possible, and learn new embeddings for any entities or relations for which we have no features.

Combined Representations

CombinedRepresentation can be used when we have multiple sources of representations and want to combine those into a single one. Use cases are multi-modal models, or NodePieceRepresentation.

Embedding

An Embedding is the simplest representation, where the an index is mapped to a numerical representation by a simple lookup in a table. Despite its simplicity, almost all publications on transductive link prediction rely on embeddings to represent entities or relations.

Decomposition

Since knowledge graphs can contain a large number of entities, having independent trainable embeddings for each of them can lead to an excessive number of trainable parameters. Therefore, methods have been developed that do not learn independent representations, but rather have a set of base representations and create individual representations by combining them.

Low-Rank Factorization

A simple method to reduce the number of parameters is to use a low-rank decomposition of the embedding matrix, as implemented in LowRankRepresentation. Here, each representation is a linear combination of shared base representations. Typically, the number of bases is chosen to be smaller than the dimension of each base representation. Low-rank factorization can also be seen as a special case of CombinedRepresentation with a restricted (but very efficient) combination operation.

Tensor Train Factorization

TensorTrainRepresentation uses a tensor factorization method, which can also be interpreted as a hierarchical decomposition. The tensor train decomposition is also known as matrix product states.

Tokenization

In TokenizationRepresentation, each index is associated with a fixed number of tokens. The tokens have their own individual representations. They are concatenated to form the combined representation.

The representation itself does not provide any means to obtain the token mapping, but it usually carries some domain information. An example is NodePiece, which provides tokenization via anchor nodes, i.e. representative entities within the graph neighborhood, or relation tokenization using the set of occurring relation types.

NodePiece

The NodePieceRepresentation contains one or more TokenizationRepresentation and uses an additional aggregation. The aggregation can be simple non-parametric, e.g. the dimension-wise mean, but it can also have trainable parameters itself.

See also

Embedding Bag

An EmbeddingBagRepresentation represents each index by a bag of individual embeddings. Each index can have a variable number of associated embeddings. To obtain the representation, the individual embeddings are aggregated by a simple sum, mean, or max pooling operation.

This representation is less flexible than the tokenization representation and/or NodePiece, which allow more powerful aggregations as well as arbitrary base representations. However, it has built-in support in PyTorch, cf. EmbeddingBag.

Message Passing

Message passing representation modules enrich the representations of entities by aggregating the information from their graph neighborhood.

RGCN

The RGCNRepresentation uses RGCNLayer to pass messages between entities. These layers aggregate representations of neighboring entities, which are first transformed by a relation-specific linear transformation.

CompGCN

The SingleCompGCNRepresentation enriches representations using CompGCNLayer, which instead uses a more flexible composition of entity and relation representations along each edge. As a technical detail, since each CompGCNLayer transforms entity and relation representations, we must first construct a CombinedCompGCNRepresentations and then split its output into separate SingleCompGCNRepresentation for entities and relations, respectively.

PyTorch Geometric

Another way to utilize message passing is via the modules provided in pykeen.nn.pyg, which allow to use the message passing layers from PyTorch Geometric to enrich base representations via message passing. We include the following templates to easily create custom transformations:

Text-based

Text-based representations use the entities’ (or relations’) labels to derive representations. To this end, TextRepresentation uses a (pre-trained) transformer model from the transformers library to encode the labels. Since the transformer models have been trained on huge corpora of text, their text encodings often contain semantic information, i.e., labels with similar semantic meaning get similar representations. While we can also benefit from these strong features by just initializing an Embedding with the vectors, e.g., using LabelBasedInitializer, the TextRepresentation include the transformer model as part of the KGE model, and thus allow fine-tuning the language model for the KGE task. This is beneficial, e.g., since it allows a simple form of obtaining an inductive model, which can make predictions for entities not seen during training.

import torch

from pykeen.datasets import get_dataset
from pykeen.models import ERModel
from pykeen.nn import TextRepresentation
from pykeen.pipeline import pipeline

dataset = get_dataset(dataset="nations")
entity_representations = TextRepresentation.from_dataset(dataset=dataset, encoder="transformer")
result = pipeline(
    dataset=dataset,
    model=ERModel,
    model_kwargs=dict(
        interaction="ermlpe",
        interaction_kwargs=dict(
            embedding_dim=entity_representations.shape[0],
        ),
        entity_representations=entity_representations,
        relation_representations_kwargs=dict(
            shape=entity_representations.shape,
        ),
    ),
    training_kwargs=dict(num_epochs=1),
)
model = result.model

We can use the label-encoder part to generate representations for unknown entities with labels. For instance, “uk” is an entity in nations, but we can also put in “united kingdom”, and get a roughly equivalent vector representations

entity_representation = model.entity_representations[0]
label_encoder = entity_representation.encoder
uk, united_kingdom = label_encoder(labels=["uk", "united kingdom"])

Thus, if we would put the resulting representations into the interaction function, we would get similar scores

# true triple from train: ['brazil', 'exports3', 'uk']
relation_representation = model.relation_representations[0]
h_repr = entity_representation.get_in_more_canonical_shape(
    dim="h", indices=torch.as_tensor(dataset.entity_to_id["brazil"]).view(1)
)
r_repr = relation_representation.get_in_more_canonical_shape(
    dim="r", indices=torch.as_tensor(dataset.relation_to_id["exports3"]).view(1)
)
scores = model.interaction(h=h_repr, r=r_repr, t=torch.stack([uk, united_kingdom]))
print(scores)

As a downside, this will usually substantially increase the computational cost of computing triple scores.

Wikidata

Since quite a few benchmark datasets for link prediction on knowledge graphs use Wikidata as a source, e.g., CoDExSmall or WD50KT, we added a convenience class WikidataTextRepresentation that looks up labels based on Wikidata QIDs (e.g., Q42 for Douglas Adams).

Biomedical Entities

If your dataset is labeled with compact uniform resource identifiers (e.g., CURIEs) for biomedical entities like chemicals, proteins, diseases, and pathways, then the BiomedicalCURIERepresentation representation can make use of pyobo to look up names (via CURIE) via the pyobo.get_name() function, then encode them using the text encoder.

All biomedical knowledge graphs in PyKEEN (at the time of adding this representation), unfortunately do not use CURIEs for referencing biomedical entities. In the future, we hope this will change.

To learn more about CURIEs, please take a look at the Bioregistry and this blog post on CURIEs.

Visual

Sometimes, we also have visual information about entities, e.g., in the form of images. For these cases there is VisualRepresentation which uses an image encoder backbone to obtain representations.

Wikidata

As for textual representations, we provide a convenience class WikidataVisualRepresentation for Wikidata-based datasets that looks up labels based on Wikidata QIDs.