Bring Your Own Interaction
This is a tutorial about how to implement your own interaction modules (also known as scoring functions) as subclasses
of pykeen.nn.modules.Interaction
for use in PyKEEN.
Implementing your first Interaction Module
Imagine you’ve taken a time machine back to 2013 and you have just invented TransE, defined as:
where \(\mathbf{e}_i\) is the \(d\)-dimensional representation for entity \(i\), \(\mathbf{r}_j\) is the \(d\)-dimensional representation for relation \(j\), and \(\|...\|_2\) is the \(L_2\) norm.
To implement TransE in PyKEEN, you need to subclass the pykeen.nn.modules.Interaction
. This class it itself a
subclass of torch.nn.Module
, which means that you need to provide an implementation of
torch.nn.Module.forward()
. However, the arguments are predefined as h
, r
, and t
, which correspond to
the representations of the head, relation, and tail, respectively.
from pykeen.nn.modules import Interaction
class TransEInteraction(Interaction):
def forward(self, h, r, t):
return -(h + r - t).norm(p=2, dim=-1)
Note the dim=-1
because this operation is actually defined over an entire batch of head, relation, and tail
representations.
See also
A reference implementation is provided in pykeen.nn.modules.TransEInteraction
As a researcher who just invented TransE, you might wonder what would happen if you replaced the addition +
with
multiplication *
. You might then end up with a new interaction like this (which just happens to be DistMult, which
was published just a year after TransE):
where \(\mathbf{e}_i\) is the \(d\)-dimensional representation for entity \(i\), \(\mathbf{r}_j\) is the \(d\)-dimensional representation for relation \(j\).
from pykeen.nn.modules import Interaction
class DistMultInteraction(Interaction):
def forward(self, h, r, t):
return (h * r * t).sum(dim=-1)
See also
A reference implementation is provided in pykeen.nn.modules.DistMultInteraction
Interactions with Hyper-Parameters
While we previously defined TransE with the \(L_2\) norm, it could be calculated with a different value for \(p\):
This could be incorporated into the interaction definition by using the __init__()
, storing the value for \(p\) in the
instance, then accessing it in forward()
.
from pykeen.nn.modules import Interaction
class TransEInteraction(Interaction):
def __init__(self, p: int):
super().__init__()
self.p = p
def forward(self, h, r, t):
return -(h + r - t).norm(p=self.p, dim=-1)
In general, you can put whatever you want in __init__()
to support the calculation of scores.
Interactions with Trainable Parameters
In ER-MLP, the multi-layer perceptron consists of an input layer with \(3 \times d\) neurons, a hidden layer with \(d\) neurons and output layer with one neuron. The input is represented by the concatenation embeddings of the heads, relations and tail embeddings. It is defined as:
with hidden dimension \(y\), \(W_1 \in \mathcal{R}^{3d \times y}\), \(W_2\in \mathcal{R}^y\), and biases \(b_1 \in \mathcal{R}^y\) and \(b_2 \in \mathcal{R}\).
\(W_1\), \(W_1\), \(b_1\), and \(b_2\) are global parameters, meaning that they are trainable, but are neither attached to the
entities nor relations. Unlike the \(p\) in TransE, these global trainable parameters are not considered hyper-parameters.
However, like hyper-parameters, they can also be defined in the __init__ function of your
pykeen.nn.modules.Interaction
class. They are trained jointly with the entity and relation embeddings during
training.
import torch.nn
from pykeen.nn.modules import Interaction
from pykeen.utils import broadcast_cat
class ERMLPInteraction(Interaction):
def __init__(self, embedding_dim: int, hidden_dim: int):
super().__init__()
# The weights of this MLP will be learned.
self.mlp = torch.nn.Sequential(
torch.nn.Linear(in_features=3 * embedding_dim, out_features=hidden_dim, bias=True),
torch.nn.ReLU(),
torch.nn.Linear(in_features=hidden_dim, out_features=1, bias=True),
)
def forward(self, h, r, t):
x = broadcast_cat([h, r, t], dim=-1)
return self.mlp(x)
Note that pykeen.utils.broadcast_cat()
was used instead of the standard torch.cat()
because of the
standardization of shapes of head, relation, and tail vectors.
See also
A reference implementation is provided in pykeen.nn.modules.ERMLPInteraction
Interactions with Different Shaped Vectors
The Structured Embedding uses a 2-tensor for representing each relation, with an interaction defined as:
where \(\mathbf{e}_i\) is the \(d\)-dimensional representation for entity \(i\), \(\mathbf{M}^{head}_j\) is the \(d \times d\)-dimensional representation for relation \(j\) for head entities, \(\mathbf{M}^{tail}_j\) is the \(d \times d\)-dimensional representation for relation \(j\) for tail entities, and \(\|...\|_2\) is the \(L_p\) norm.
For the purposes of this tutorial, we will propose a simplification to Strucuterd Embedding (also similar to TransR) where the same relation 2-tensor is used to project both the head and tail entities as in:
where \(\mathbf{e}_i\) is the \(d\)-dimensional representation for entity \(i\), \(\mathbf{M}_j\) is the \(d \times d\)-dimensional representation for relation \(j\), and \(\|...\|_2\) is the \(L_2\) norm.
from pykeen.nn.modules import Interaction
class SimplifiedStructuredEmbeddingInteraction(Interaction):
relation_shape = ("dd",)
def forward(self, h, r, t):
h_proj = r @ h.unsqueeze(dim=-1)
t_proj = r @ t.unsqueeze(dim=-1)
return -(h_proj - t_proj).squeeze(dim=-1).norm(p=2, dim=-1)
Note the definition of the relation_shape
. By default, the entity_shape
and relation_shape
are both equal to
('d', )
, which uses eigen-notation to show that they both are 1-tensors with the same shape. In this simplified
version of Structured Embedding, we need to denote that the shape of the relation is \(d \times d\), so it’s written as
dd
.
See also
Reference implementations are provided in pykeen.nn.modules.StructuredEmbeddingInteraction
and in
pykeen.nn.modules.TransRInteraction
.
Interactions with Multiple Representations
Sometimes, like in the canonical version of Structured Embedding, you need more than one representation for entities
and/or relations. To specify this, you just need to extend the tuple for relation_shape
with more entries, each
corresponding to the sequence of representations.
from pykeen.nn.modules import Interaction
class StructuredEmbeddingInteraction(Interaction):
relation_shape = (
"dd", # Corresponds to $\mathbf{M}^{head}_j$
"dd", # Corresponds to $\mathbf{M}^{tail}_j$
)
def forward(self, h, r, t):
# Since the relation_shape is more than length 1, the r value is given as a sequence
# of the representations defined there. You can use tuple unpacking to get them out
r_h, r_t = r
h_proj = r_h @ h.unsqueeze(dim=-1)
t_proj = r_t @ t.unsqueeze(dim=-1)
return -(h_proj - t_proj).squeeze(dim=-1).norm(p=2, dim=-1)
Interactions with Different Dimension Vectors
TransD is an example of an interaction module that not only uses two different representations for each entity and two representations for each relation, but they are of different dimensions.
It can be implemented by choosing a different letter for use in the entity_shape
and/or relation_shape
dictionary. Ultimately, the letters used are arbitrary, but you need to remember what they are when using the
pykeen.models.make_model()
, pykeen.models.make_model_cls()
, or pykeen.pipeline.interaction_pipeline()
functions to instantiate a model, make a model class, or run the pipeline using your custom interaction module
(respectively).
from pykeen.nn.modules import Interaction
from pykeen.utils import project_entity
class TransDInteraction(Interaction):
entity_shape = ("d", "d")
relation_shape = ("e", "e")
def forward(self, h, r, t):
h, h_proj = h
r, r_proj = r
t, t_proj = t
h_bot = project_entity(
e=h,
e_p=h_p,
r_p=r_p,
)
t_bot = project_entity(
e=t,
e_p=t_p,
r_p=r_p,
)
return -(h_bot + r - t_bot).norm(p=2, dim=-1)
Note
The pykeen.utils.project_entity()
function was used in this implementation to reduce the complexity. So far,
it’s the case that all of the models using multiple different representation dimensions are quite complicated and
don’t fall into the paradigm of presenting simple examples.
See also
A reference implementation is provided in pykeen.nn.modules.TransDInteraction
Differences between pykeen.nn.modules.Interaction
and pykeen.models.Model
The high-level pipeline()
function allows you to pass pre-defined subclasses of pykeen.models.Model
such
as pykeen.models.TransE
or pykeen.models.DistMult
. These classes are high-level wrappers around the
interaction functions pykeen.nn.modules.TransEInteraction
and nn.modules.DistMultInteraction
that are
more suited for running benchmarking experiments or practical applications of knowledge graph embeddings that include
lots of information about default hyper-parameters, recommended hyper-parameter optimization strategies, and more
complex applications of regularization schemas.
As a researcher, the pykeen.nn.modules.Interaction
is a way to quickly translate ideas into new models that can
be used without all of the overhead of defining a pykeen.models.Model
. These components are also completely
reusable throughout PyKEEN (e.g., in self-rolled training loops) and can be used as standalone components outside of
PyKEEN.
If you are happy with your interaction module and would like to go the next step to making it generally reusable, check the “Extending the Models” tutorial.
Ad hoc Models from Interactions
A pykeen.models.ERModel
can be constructed from pykeen.nn.modules.Interaction
.
The new style-class, pykeen.models.ERModel
abstracts the interaction away from the representations
such that different interactions can be used interchangably. A new model can be constructed directly from the
interaction module, given a dimensions
mapping. In each pykeen.nn.modules.Interaction
, there
is a field called entity_shape
and relation_shape
that allows for using eigen-notation for defining
the different dimensions of the model. Most models share the d
dimensionality for both the entity and relation
vectors. Some (but not all) exceptions are:
pykeen.nn.modules.RESCALInteraction
, which uses a square matrix for relations written asdd
pykeen.nn.modules.TransDInteraction
, which usesd
for entity shape ande
for a different relation shape.
With this in mind, you’ll have to investigate the dimensions of the vectors through the PyKEEN documentation.
If you’re implementing your own, you have control over this and will know which dimensions to specify (though
the d
for both entities and relations is standard). As a shorthand for {'d': value}
, you can directly
pass value
for the dimension and it will be automatically interpreted as the {'d': value}
.
Make a model class from lookup of an interaction module class:
>>> from pykeen.nn.modules import TransEInteraction
>>> from pykeen.models import make_model_cls
>>> embedding_dim = 3
>>> model_cls = make_model_cls(
... dimensions={"d": embedding_dim},
... interaction='TransE',
... interaction_kwargs={'p': 2},
... )
If there’s only one dimension in the entity_shapes
and relation_shapes
, it can
be directly given as an integer as a shortcut.
>>> # Implicitly can also be written as:
>>> model_cls_alt = make_model_cls(
... dimensions=embedding_dim,
... interaciton='TransE',
... interaction_kwargs={'p': 2},
... )
Make a model class from an interaction module class:
>>> from pykeen.nn.modules import TransEInteraction
>>> from pykeen.models import make_model_cls
>>> embedding_dim = 3
>>> model_cls = make_model_cls({"d": embedding_dim}, TransEInteraction, {'p': 2})
Make a model class from an instantiated interaction module:
>>> from pykeen.nn.modules import TransEInteraction
>>> from pykeen.models import make_model_cls
>>> embedding_dim = 3
>>> model_cls = make_model_cls({"d": embedding_dim}, TransEInteraction(p=2))
All of these model classes can be passed directly into the model
argument of pykeen.pipeline.pipeline()
.
Interaction Pipeline
The pykeen.pipeline.pipeline()
also allows passing of an interaction such that the following code block can be
compressed:
from pykeen.pipeline import pipeline
from pykeen.nn.modules import TransEInteraction
model = make_model_cls(
interaction=TransEInteraction,
interaction_kwargs={"p": 2},
dimensions={"d": 100},
)
results = pipeline(dataset="Nations", model=model, ...)
into:
from pykeen.pipeline import pipeline
from pykeen.nn.modules import TransEInteraction
results = pipeline(
dataset="Nations", interaction=TransEInteraction, interaction_kwargs={"p": 2}, dimensions={"d": 100}, ...
)
This can be used with any subclass of the pykeen.nn.modules.Interaction
, not only ones that are implemented in
the PyKEEN package.