AutoSFInteraction

class AutoSFInteraction(coefficients, *, num_blocks=None, num_entity_representations=None, num_relation_representations=None)[source]

Bases: FunctionalInteraction[HeadRepresentation, RelationRepresentation, TailRepresentation]

The AutoSF interaction as described by [zhang2020].

This interaction function is a parametrized way to express bi-linear models with block structure. It divides the entity and relation representations into blocks, and expresses the interaction as a sequence of 4-tuples \((i_h, i_r, i_t, s)\), where \(i_h, i_r, i_t\) index a _block_ of the head, relation, or tail representation, and \(s \in {-1, 1}\) is the sign.

The interaction function is then given as

\[\sum_{(i_h, i_r, i_t, s) \in \mathcal{C}} s \cdot \langle h[i_h], r[i_r], t[i_t] \rangle\]

where \(\langle \cdot, \cdot, \cdot \rangle\) denotes the tri-linear dot product.

This parametrization allows to express several well-known interaction functions, e.g.

pykeen.nn.DistMultInteraction:
one block, \(\mathcal{C} = \{(0, 0, 0, 1)\}\)
pykeen.nn.ComplExInteraction:
two blocks, \(\mathcal{C} = \{(0, 0, 0, 1), (0, 1, 1, 1), (1, 0, 1, -1), (1, 0, 1, 1)\}\)
pykeen.nn.SimplEInteraction:
two blocks: \(\mathcal{C} = \{(0, 0, 1, 1), (1, 1, 0, 1)\}\)

While in theory, we can have up to num_blocks**3 unique triples, usually, a smaller number is preferable to have some sparsity.

Initialize the interaction function.

Parameters:

coefficients (Iterable[Tuple[int, int, int, Literal[-1, 1]]]) – the coefficients for the individual blocks, cf. pykeen.nn.AutoSFInteraction
num_blocks (Optional[int]) – the number of blocks. If given, will be used for both, entity and relation representations.
num_entity_representations (Optional[int]) – an explicit number of entity representations / blocks. Only used if num_blocks is None. If num_entity_representations is None, too, this number if inferred from coefficients.
num_relation_representations (Optional[int]) – an explicit number of relation representations / blocks. Only used if num_blocks is None. If num_relation_representations is None, too, this number if inferred from coefficients.

Methods Summary

`extend`(*new_coefficients)	Extend AutoSF function, as described in the greedy search algorithm in the paper.
`from_searched_sf`(coefficients, **kwargs)	Instantiate AutoSF interaction from the "official" serialization format.
`func`(h, r, t, coefficients)	Evaluate an AutoSF-style interaction function as described by [zhang2020].
`latex_visualize`()	Create the LaTeX + tikz visualization as shown in the paper.

Methods Documentation

extend(*new_coefficients)[source]

Extend AutoSF function, as described in the greedy search algorithm in the paper.

Return type:: AutoSFInteraction
Parameters:: new_coefficients (Tuple[int, int, int, Literal[-1, 1]]) –

classmethod from_searched_sf(coefficients, **kwargs)[source]

Instantiate AutoSF interaction from the “official” serialization format.

> The first 4 values (a,b,c,d) represent h_1 * r_1 * t_a + h_2 * r_2 * t_b + h_3 * r_3 * t_c + h_4 * r_4 * t_d. > For the others, every 4 values represent one adding block: index of r, index of h, index of t, the sign s.

Parameters:

coefficients (Sequence[int]) – the coefficients in the “official” serialization format.
kwargs – additional keyword-based parameters passed to pykeen.nn.AutoSFInteraction.__init__()

Return type:

AutoSFInteraction

Returns:

An AutoSF interaction module