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 a stateless functional interaction base class 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 (KG2ESimilarity) – 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