ComplEx

class ComplEx(triples_factory, embedding_dim=200, automatic_memory_optimization=None, loss=None, preferred_device=None, random_seed=None, regularizer=None)

Bases: pykeen.models.base.EntityRelationEmbeddingModel

An implementation of ComplEx [trouillon2016].

ComplEx is an extension of pykeen.models.DistMult that uses complex valued representations for the entities and relations. Entities and relations are represented as vectors \(\textbf{e}_i, \textbf{r}_i \in \mathbb{C}^d\), and the plausibility score is computed using the Hadamard product:

\[f(h,r,t) = Re(\mathbf{e}_h\odot\mathbf{r}_r\odot\mathbf{e}_t)\]

Which expands to:

\[f(h,r,t) = \left\langle Re(\mathbf{e}_h),Re(\mathbf{r}_r),Re(\mathbf{e}_t)\right\rangle + \left\langle Im(\mathbf{e}_h),Re(\mathbf{r}_r),Im(\mathbf{e}_t)\right\rangle + \left\langle Re(\mathbf{e}_h),Re(\mathbf{r}_r),Im(\mathbf{e}_t)\right\rangle - \left\langle Im(\mathbf{e}_h),Im(\mathbf{r}_r),Im(\mathbf{e}_t)\right\rangle\]

where \(Re(\textbf{x})\) and \(Im(\textbf{x})\) denote the real and imaginary parts of the complex valued vector \(\textbf{x}\). Because the Hadamard product is not commutative in the complex space, ComplEx can model anti-symmetric relations in contrast to DistMult.

See also

Official implementation: https://github.com/ttrouill/complex/

Initialize ComplEx.

Parameters

• triples_factory (TriplesFactory) – TriplesFactory The triple factory connected to the model.

• embedding_dim (int) – The embedding dimensionality of the entity embeddings.

• automatic_memory_optimization (Optional[bool]) – bool Whether to automatically optimize the sub-batch size during training and batch size during evaluation with regards to the hardware at hand.

• loss (Optional[Loss]) – OptionalLoss (optional) The loss to use. Defaults to SoftplusLoss.

• preferred_device (Optional[str]) – str (optional) The default device where to model is located.

• random_seed (Optional[int]) – int (optional) An optional random seed to set before the initialization of weights.

• regularizer (Optional[Regularizer]) – BaseRegularizer The regularizer to use.

Attributes Summary

hpo_default	The default strategy for optimizing the model’s hyper-parameters
loss_default_kwargs	The default parameters for the default loss function class
regularizer_default_kwargs	The LP settings used by [trouillon2016] for ComplEx.

Methods Summary

interaction_function(h, r, t)	Evaluate the interaction function of ComplEx for given embeddings.
score_hrt(hrt_batch)	Forward pass.

Attributes Documentation

hpo_default: ClassVar[Mapping[str, Any]] = {'embedding_dim': {'high': 300, 'low': 50, 'q': 50, 'type': <class 'int'>}}

The default strategy for optimizing the model’s hyper-parameters

loss_default_kwargs: ClassVar[Optional[Mapping[str, Any]]] = {'reduction': 'mean'}

The default parameters for the default loss function class

regularizer_default_kwargs: ClassVar[Optional[Mapping[str, Any]]] = {'normalize': True, 'p': 2.0, 'weight': 0.01}

The LP settings used by [trouillon2016] for ComplEx.

Methods Documentation

static interaction_function(h, r, t)

Evaluate the interaction function of ComplEx for given embeddings.

The embeddings have to be in a broadcastable shape.

Parameters

• h (FloatTensor) – Head embeddings.

• r (FloatTensor) – Relation embeddings.

• t (FloatTensor) – Tail embeddings.

Return type

FloatTensor

Returns

shape: (…) The scores.

score_hrt(hrt_batch)

Forward pass.

This method takes head, relation and tail of each triple and calculates the corresponding score.

Parameters

hrt_batch (LongTensor) – shape: (batch_size, 3), dtype: long The indices of (head, relation, tail) triples.

Raises

NotImplementedError – If the method was not implemented for this class.

Return type

FloatTensor

Returns

shape: (batch_size, 1), dtype: float The score for each triple.