$(x^g, y^g, z^g)$ represents the coordinates of the front left top corner of the box and $(w^g, h^g, l^g)$ represents width, height and length. We define the residual vector as $\textbf{u} \in \mathbb{R}^3$, which contains the 3 regression targets corresponding to center location $\Delta x, \Delta y$ and $\Delta z$, and define the residual vector as $\textbf{v} \in \mathbb{R}^3$ containing 3 dimensions ($\Delta w, \Delta h$, $\Delta l$). The residuals are computed as: $\Delta x = (x^g - x^a)/w_a, \Delta y = (y^g - y^a)/h_a$, $\Delta z =(z^g - z^a)/l_a, \Delta w = \log ((w^g-w^c)/w_a)$, $\Delta h = \log ((h^g-h^c)/h_a), \Delta l =\log ((l^g-l^c)/l_a)$.

The proposed loss function is defined as: $$\begin{aligned}
\begin{split}
    Loss &= \frac{1}{N_{cls}} \sum_i^{N_{cls}}  L_{neighbor}(p_i, p_i^*) +\\ 
     \beta  \frac{1}{N_{reg}} \sum_j^{N_{reg}} &p_j^* (L_{c-reg}(\textbf{u}_j, \textbf{u}_j^*)+ L_{s-reg}(\textbf{v}_j, \textbf{v}_j^*)),
\end{split}
\label{eqn:2}\end{aligned}$$ where $p_i, p_i^*$ are respectively the predicted probability of anchor $i$ and its label, $u_j, u_j^*$ are the box center regression output and ground truth for anchor $j$, $v_j, v_j^*$ are the box size residual regression output and ground truth. $L_{neighbor}$ is the classification loss reweighted by the guiding sequence, which will be introduced in the next section. $L_{c-reg}$, $L_{s-reg}$ are the center coordinates and residual box size regression loss 