KG2EInteraction

class KG2EInteraction(similarity: str | KG2ESimilarity | type[KG2ESimilarity] | None = None, similarity_kwargs: Mapping[str, Any] | None = None)

Bases: Interaction[tuple[Tensor, Tensor], tuple[Tensor, Tensor], tuple[Tensor, Tensor]]

The stateless KG2E interaction function.

Inspired by TransEInteraction, relations are modeled as transformations from head to tail entities \(\mathcal{H} - \mathcal{T} \approx \mathcal{R}\), where

\[\begin{split}\mathcal{H} \sim \mathcal{N}(\mu_h, \Sigma_h)\\ \mathcal{T} \sim \mathcal{N}(\mu_t, \Sigma_t)\\ \mathcal{R} \sim \mathcal{N}(\mu_r, \Sigma_r)\end{split}\]

and thus, since head and tail entities are considered independent with respect to the relations,

\[\mathcal{P}_e = \mathcal{H} - \mathcal{T} \sim \mathcal{N}(\mu_h - \mu_t, \Sigma_h + \Sigma_t)\]

To obtain scores, the interaction measures the similarity between \(\mathcal{P}_e\) and \(\mathcal{P}_r = \mathcal{N}(\mu_r, \Sigma_r)\), either by means of the (asymmetric) NegativeKullbackLeiblerDivergence, or a symmetric variant with ExpectedLikelihood.

Note

This interaction module does not sub-class from FunctionalInteraction just for the technical reason that the choice of the similarity represents some “state”. However, it does not contain any trainable parameters.

Initialize the interaction module.

Parameters:

• similarity (HintOrType[KG2ESimilarity] | None) – The similarity measures for gaussian distributions. Defaults to NegativeKullbackLeiblerDivergence.

• similarity_kwargs (OptionalKwargs) – Additional keyword-based parameters used to instantiate the similarity.

Note

The parameter pair (similarity, similarity_kwargs) is used for pykeen.nn.sim.kg2e_similarity_resolver

An explanation of resolvers and how to use them is given in https://class-resolver.readthedocs.io/en/latest/.

Attributes Summary

entity_shape	The symbolic shapes for entity representations
relation_shape	The symbolic shapes for relation representations

Methods Summary

forward(h, r, t)

Evaluate the interaction function.

Attributes Documentation

entity_shape: Sequence[str] = ('d', 'd')

The symbolic shapes for entity representations

relation_shape: Sequence[str] = ('d', 'd')

The symbolic shapes for relation representations

Methods Documentation

forward(h: tuple[Tensor, Tensor], r: tuple[Tensor, Tensor], t: tuple[Tensor, Tensor]) → Tensor

Evaluate the interaction function.

Parameters:

• h (tuple[Tensor, Tensor]) – both shape: (*batch_dims, d) The head representations, mean and (diagonal) variance.

• r (tuple[Tensor, Tensor]) – shape: (*batch_dims, d) The relation representations, mean and (diagonal) variance.

• t (tuple[Tensor, Tensor]) – shape: (*batch_dims, d) The tail representations, mean and (diagonal) variance.

Returns:

shape: batch_dims The scores.

Return type:

Tensor