ComplEx¶
- class ComplEx(*, embedding_dim=200, entity_initializer=<function normal_>, relation_initializer=<function normal_>, **kwargs)[source]¶
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
embedding_dim (
int
) – The embedding dimensionality of the entity embeddings.entity_initializer (
Union
[str
,Callable
[[FloatTensor
],FloatTensor
],None
]) – Entity initializer function. Defaults totorch.nn.init.normal_()
relation_initializer (
Union
[str
,Callable
[[FloatTensor
],FloatTensor
],None
]) – Relation initializer function. Defaults totorch.nn.init.normal_()
kwargs – Remaining keyword arguments to forward to
pykeen.models.EntityRelationEmbeddingModel
Attributes Summary
The default strategy for optimizing the model’s hyper-parameters
The default parameters for the default loss function class
The LP settings used by [trouillon2016] for ComplEx.
Methods Summary
forward
(h_indices, r_indices, t_indices)Unified score function.
interaction_function
(h, r, t)Evaluate the interaction function of ComplEx for given embeddings.
score_h
(rt_batch)Forward pass using left side (head) prediction.
score_hrt
(hrt_batch)Forward pass.
score_r
(ht_batch)Forward pass using middle (relation) prediction.
score_t
(hr_batch)Forward pass using right side (tail) prediction.
Attributes Documentation
- hpo_default: ClassVar[Mapping[str, Any]] = {'embedding_dim': {'high': 256, 'low': 16, 'q': 16, 'type': <class 'int'>}}¶
The default strategy for optimizing the model’s hyper-parameters
- loss_default_kwargs: ClassVar[Mapping[str, Any]] = {'reduction': 'mean'}¶
The default parameters for the default loss function class
- regularizer_default_kwargs: ClassVar[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)[source]¶
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_h(rt_batch)[source]¶
Forward pass using left side (head) prediction.
This method calculates the score for all possible heads for each (relation, tail) pair.
- Parameters
rt_batch (
LongTensor
) – shape: (batch_size, 2), dtype: long The indices of (relation, tail) pairs.- Return type
FloatTensor
- Returns
shape: (batch_size, num_entities), dtype: float For each r-t pair, the scores for all possible heads.
- score_hrt(hrt_batch)[source]¶
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.
- score_r(ht_batch)[source]¶
Forward pass using middle (relation) prediction.
This method calculates the score for all possible relations for each (head, tail) pair.
- Parameters
ht_batch (
LongTensor
) – shape: (batch_size, 2), dtype: long The indices of (head, tail) pairs.- Return type
FloatTensor
- Returns
shape: (batch_size, num_relations), dtype: float For each h-t pair, the scores for all possible relations.
- score_t(hr_batch)[source]¶
Forward pass using right side (tail) prediction.
This method calculates the score for all possible tails for each (head, relation) pair.
- Parameters
hr_batch (
LongTensor
) – shape: (batch_size, 2), dtype: long The indices of (head, relation) pairs.- Return type
FloatTensor
- Returns
shape: (batch_size, num_entities), dtype: float For each h-r pair, the scores for all possible tails.