# AutoSFInteraction¶

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

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:

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]. 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:

ForwardRef

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:

ForwardRef

Returns:

An AutoSF interaction module

static func(h, r, t, coefficients)[source]

Evaluate an AutoSF-style interaction function as described by [zhang2020].

Parameters:
Return type:

FloatTensor

Returns:

shape: batch_dims The scores

latex_visualize()[source]

Create the LaTeX + tikz visualization as shown in the paper.

Return type:

str