Introduced in [SDNT19].

$\mathcal{L} = -log\, \sigma(\gamma + f_{model} (\mathbf{s},\mathbf{o})) - \sum_{i=1}^{n} p(h_{i}^{'}, r, t_{i}^{'} ) \ log \ \sigma(-f_{model}(\mathbf{s}_{i}^{'},\mathbf{o}_{i}^{'}) - \gamma)$

where $$\mathbf{s}, \mathbf{o} \in \mathcal{R}^k$$ are the embeddings of the subject and object of a triple $$t=(s,r,o)$$, $$\gamma$$ is the margin, $$\sigma$$ the sigmoid function, and $$p(s_{i}^{'}, r, o_{i}^{'} )$$ is the negatives sampling distribution which is defined as:

$p(s'_j, r, o'_j | \{(s_i, r_i, o_i)\}) = \frac{\exp \alpha \, f_{model}(\mathbf{s'_j}, \mathbf{o'_j})} {\sum_i \exp \alpha \, f_{model}(\mathbf{s'_i}, \mathbf{o'_i})}$

where $$\alpha$$ is the temperature of sampling, $$f_{model}$$ is the scoring function of the desired embeddings model.

Methods

 __init__(eta[, loss_params, verbose]) Initialize Loss
__init__(eta, loss_params=None, verbose=False)

Initialize Loss

Parameters: eta (int) – number of negatives loss_params (dict) – Dictionary of loss-specific hyperparams: ’margin’: (float). Margin to be used for loss computation (default: 1) ’alpha’ : (float). Temperature of sampling (default:0.5) Example: loss_params={'margin': 1, 'alpha': 0.5}