# NTN¶

class NTN(triples_factory, embedding_dim=100, automatic_memory_optimization=None, num_slices=4, loss=None, preferred_device=None, random_seed=None, non_linearity=None, regularizer=None)[source]

An implementation of NTN from [socher2013].

NTN uses a bilinear tensor layer instead of a standard linear neural network layer:

$f(h,r,t) = \textbf{u}_{r}^{T} \cdot \tanh(\textbf{h} \mathfrak{W}_{r} \textbf{t} + \textbf{V}_r [\textbf{h};\textbf{t}] + \textbf{b}_r)$

where $$\mathfrak{W}_r \in \mathbb{R}^{d \times d \times k}$$ is the relation specific tensor, and the weight matrix $$\textbf{V}_r \in \mathbb{R}^{k \times 2d}$$, and the bias vector $$\textbf{b}_r$$ and the weight vector $$\textbf{u}_r \in \mathbb{R}^k$$ are the standard parameters of a neural network, which are also relation specific. The result of the tensor product $$\textbf{h} \mathfrak{W}_{r} \textbf{t}$$ is a vector $$\textbf{x} \in \mathbb{R}^k$$ where each entry $$x_i$$ is computed based on the slice $$i$$ of the tensor $$\mathfrak{W}_{r}$$: $$\textbf{x}_i = \textbf{h}\mathfrak{W}_{r}^{i} \textbf{t}$$. As indicated by the interaction model, NTN defines for each relation a separate neural network which makes the model very expressive, but at the same time computationally expensive.

Initialize NTN.

Parameters

Attributes Summary

 hpo_default The default strategy for optimizing the model’s hyper-parameters

Methods Summary

 score_h(rt_batch[, slice_size]) Forward pass using left side (head) prediction. score_hrt(hrt_batch) Forward pass. score_t(hr_batch[, slice_size]) Forward pass using right side (tail) prediction.

Attributes Documentation

hpo_default: ClassVar[Mapping[str, Any]] = {'embedding_dim': {'high': 350, 'low': 50, 'q': 25, 'type': <class 'int'>}, 'num_slices': {'high': 4, 'low': 2, 'type': <class 'int'>}}

The default strategy for optimizing the model’s hyper-parameters

Methods Documentation

score_h(rt_batch, slice_size=None)[source]

Forward pass using left side (head) prediction.

This method calculates the score for all possible heads for each (relation, tail) pair.

Parameters

rt_batch (LongTensor) – shape: (batch_size, 2), dtype: long The indices of (relation, tail) pairs.

Return type

FloatTensor

Returns

shape: (batch_size, num_entities), dtype: float For each r-t pair, the scores for all possible heads.

score_hrt(hrt_batch)[source]

Forward pass.

This method takes head, relation and tail of each triple and calculates the corresponding score.

Parameters

hrt_batch (LongTensor) – shape: (batch_size, 3), dtype: long The indices of (head, relation, tail) triples.

Raises

NotImplementedError – If the method was not implemented for this class.

Return type

FloatTensor

Returns

shape: (batch_size, 1), dtype: float The score for each triple.

score_t(hr_batch, slice_size=None)[source]

Forward pass using right side (tail) prediction.

This method calculates the score for all possible tails for each (head, relation) pair.

Parameters

hr_batch (LongTensor) – shape: (batch_size, 2), dtype: long The indices of (head, relation) pairs.

Return type

FloatTensor

Returns

shape: (batch_size, num_entities), dtype: float For each h-r pair, the scores for all possible tails.