text: # -*- coding: utf-8 -*-
  
  """Implementation of UM."""
  
  from typing import Any, ClassVar, Mapping
  
  from ..nbase import ERModel
  from ...constants import DEFAULT_EMBEDDING_HPO_EMBEDDING_DIM_RANGE
  from ...nn.emb import EmbeddingSpecification
  from ...nn.init import xavier_normal_
  from ...nn.modules import UMInteraction
  from ...typing import Hint, Initializer
  
  __all__ = [
      "UM",
  ]
  
  
  class UM(ERModel):
      r"""An implementation of the Unstructured Model (UM) published by [bordes2014]_.
  
      UM computes the distance between head and tail entities then applies the $l_p$ norm.
  
      .. math::
  
          f(h, r, t) = - \|\textbf{e}_h  - \textbf{e}_t\|_p^2
  
      A small distance between the embeddings for the head and tail entity indicates a plausible triple. It is
      appropriate for networks with a single relationship type that is undirected.
  
      .. warning::
  
          In UM, neither the relations nor the directionality are considered, so it can't distinguish between them.
          However, it may serve as a baseline for comparison against relation-aware models.
      ---
      name: Unstructured Model
      citation:
          author: Bordes
          year: 2014
          link: https://link.springer.com/content/pdf/10.1007%2Fs10994-013-5363-6.pdf
      """
  
      #: 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,
          scoring_fct_norm=dict(type=int, low=1, high=2),
      )
  
      def __init__(
          self,
          *,
          embedding_dim: int = 50,
          scoring_fct_norm: int = 1,
          entity_initializer: Hint[Initializer] = xavier_normal_,
          **kwargs,
      ) -> None:
          r"""Initialize UM.
  
          :param embedding_dim: The entity embedding dimension $d$. Is usually $d \in [50, 300]$.
          :param scoring_fct_norm: The $l_p$ norm. Usually 1 for UM.
          :param entity_initializer: The initializer for the entity embeddings.
              Defaults to the xavier normal distribution.
          :param kwargs: Remaining keyword arguments passed through to :class:`pykeen.models.ERModel`.
          """
          super().__init__(
              interaction=UMInteraction,
              interaction_kwargs=dict(p=scoring_fct_norm),
              entity_representations=EmbeddingSpecification(
                  embedding_dim=embedding_dim,
                  initializer=entity_initializer,
              ),
              **kwargs,
          )
  