\begin{equation}
-\log \frac{
    \exp{\left(s(\mathbf{i_q}, \mathbf{t_p}^{(+)},\mathbf{i_p}^{(+)})e^\tau\right)}}
    {\exp{\left(s(\mathbf{i_q}, \mathbf{t_p}^{(+)},\mathbf{i_p}^{(+)})e^\tau\right)} + \sum_{j} 
        \exp{\left(s(\mathbf{i_q}, \mathbf{t_p}^{(j)},\mathbf{i_p}^{(j)})e^\tau\right)}
    }
\label{eq:batch_contrastive}
\end{equation}
