Source code for pykeen.models.unimodal.rescal

# -*- coding: utf-8 -*-

"""Implementation of RESCAL."""

from typing import Any, ClassVar, Mapping, Type

import torch
from torch.nn.init import uniform_

from ..base import EntityRelationEmbeddingModel
from ...nn.emb import EmbeddingSpecification
from ...regularizers import LpRegularizer, Regularizer
from ...typing import Hint, Initializer

__all__ = [

[docs]class RESCAL(EntityRelationEmbeddingModel): r"""An implementation of RESCAL from [nickel2011]_. This model represents relations as matrices and models interactions between latent features. RESCAL is a bilinear model that models entities as vectors and relations as matrices. The relation matrices $\textbf{W}_{r} \in \mathbb{R}^{d \times d}$ contain weights $w_{i,j}$ that capture the amount of interaction between the $i$-th latent factor of $\textbf{e}_h \in \mathbb{R}^{d}$ and the $j$-th latent factor of $\textbf{e}_t \in \mathbb{R}^{d}$. Thus, the plausibility score of $(h,r,t) \in \mathbb{K}$ is given by: .. math:: f(h,r,t) = \textbf{e}_h^{T} \textbf{W}_{r} \textbf{e}_t = \sum_{i=1}^{d}\sum_{j=1}^{d} w_{ij}^{(r)} (\textbf{e}_h)_{i} (\textbf{e}_t)_{j} --- citation: author: Nickel year: 2011 link: """ #: The default strategy for optimizing the model's hyper-parameters hpo_default: ClassVar[Mapping[str, Any]] = dict( embedding_dim=DEFAULT_EMBEDDING_HPO_EMBEDDING_DIM_RANGE, ) #: The regularizer used by [nickel2011]_ for for RESCAL #: According to #: a normalized weight of 10 is used. regularizer_default: ClassVar[Type[Regularizer]] = LpRegularizer #: The LP settings used by [nickel2011]_ for for RESCAL regularizer_default_kwargs: ClassVar[Mapping[str, Any]] = dict( weight=10, p=2., normalize=True, ) def __init__( self, *, embedding_dim: int = 50, entity_initializer: Hint[Initializer] = uniform_, relation_initializer: Hint[Initializer] = uniform_, **kwargs, ) -> None: r"""Initialize RESCAL. :param embedding_dim: The entity embedding dimension $d$. Is usually $d \in [50, 300]$. :param entity_initializer: Entity initializer function. Defaults to :func:`torch.nn.init.uniform_` :param relation_initializer: Relation initializer function. Defaults to :func:`torch.nn.init.uniform_` :param kwargs: Remaining keyword arguments to forward to :class:`pykeen.models.EntityRelationEmbeddingModel` .. seealso:: - OpenKE `implementation of RESCAL <>`_ """ super().__init__( entity_representations=EmbeddingSpecification( embedding_dim=embedding_dim, initializer=entity_initializer, ), relation_representations=EmbeddingSpecification( shape=(embedding_dim, embedding_dim), # d x d matrices initializer=relation_initializer, ), **kwargs, )
[docs] def score_hrt(self, hrt_batch: torch.LongTensor) -> torch.FloatTensor: # noqa: D102 # Get embeddings # shape: (b, d) h = self.entity_embeddings(indices=hrt_batch[:, 0]).unsqueeze(dim=1) # shape: (b, d, d) r = self.relation_embeddings(indices=hrt_batch[:, 1]) # shape: (b, d) t = self.entity_embeddings(indices=hrt_batch[:, 2]).unsqueeze(dim=-1) # Compute scores scores = h @ r @ t # Regularization self.regularize_if_necessary(h, r, t) return scores[:, :, 0]
[docs] def score_t(self, hr_batch: torch.LongTensor) -> torch.FloatTensor: # noqa: D102 h = self.entity_embeddings(indices=hr_batch[:, 0]).unsqueeze(dim=1) r = self.relation_embeddings(indices=hr_batch[:, 1]) t = self.entity_embeddings(indices=None).unsqueeze(dim=0).transpose(-1, -2) # Compute scores scores = h @ r @ t # Regularization self.regularize_if_necessary(h, r, t) return scores[:, 0, :]
[docs] def score_h(self, rt_batch: torch.LongTensor) -> torch.FloatTensor: # noqa: D102 """Forward pass using left side (head) prediction.""" # Get embeddings h = self.entity_embeddings(indices=None).unsqueeze(dim=0) r = self.relation_embeddings(indices=rt_batch[:, 0]) t = self.entity_embeddings(indices=rt_batch[:, 1]).unsqueeze(dim=-1) # Compute scores scores = h @ r @ t # Regularization self.regularize_if_necessary(h, r, t) return scores[:, :, 0]