\begin{equation}
\hat{\boldsymbol{n}}_{i}^{(l)} =
\begin{cases}
\frac{\widetilde{\boldsymbol{y}}_j - \displaystyle\sum_{\substack{t=1\\t\neq i}}^T \hat{w}_{tj}^{(l+1)} \boldsymbol{n}_{t}^{(l)}}{\hat{w}_{ij}^{(l+1)}}, & \text{if} \,\,\, l = L,\\
\\
\frac{\hat{\boldsymbol{n}}_{k}^{(l+1)} - \displaystyle\sum_{\substack{u=1\\u\neq i}}^{N_l} \hat{w}_{uk}^{(l+1)} \boldsymbol{n}_{u}^{(l)}}{\hat{w}_{ik}^{(l+1)}}, & \text{otherwise}
\end{cases},
\label{eq:neuron_upd}
\end{equation}
