three layers. Note a smaller ${\gamma}_m$ value leads to larger gap between the weights of pedestrian instances from different layers.

Furthermore, our multi-task loss function $l^m( y_i, \hat{y}_i|\mathcal{W})$ on the $i$-th example at layer $m$ is defined as: $$\begin{aligned}
\label{eq_lm}
l^{m} \left( y_i, \hat{y}_i|\mathcal{W} \right) = l_{\mathrm{cls}} \left( p_i,\hat{p}_i \right) + \lambda p_i l_{\mathrm{loc}} \left(\vec{b}_i,\hat{b}_i \right),\end{aligned}$$ where $p_i$ is 1 if the anchor is labeled positive, and 0 otherwise. $\hat{p}_i$ denotes the predicted probability of the anchor being a pedestrian proposal. $\vec{b}_i=(b_i^x,b_i^y,b_i^w,b_i^h)$ represents the ground-truth bbox associated with a positive anchor, and $\hat{\vec{b}}_i=(\hat{b}_i^x,\hat{b}_i^y,\hat{b}_i^w,\hat{b}_i^h)$ denotes the predicted bbox. The second loss term is defined on the regression task, for which we adopt the same smooth-L1 loss function of Faster R-CNN [@RenEtAl:nips15], that is, $l_{\mathrm{loc}}=R \left(\vec{b}_i-\hat{\vec{b}}_i \right)$. Here $R(\vec{b})=0.5 \|\vec{b}\|^2$ if $\|\vec{b}\|<1$, and $R(\vec{b})=\|\vec{b}\|-0.5$ otherwise. The term $p_i l_{\mathrm{loc}}$ is to activate the regression loss only for positive anchors ($p_i=1$), which is disabled otherwise ($p_i=0$). $\lambda$ is a trade-off parameter (empirically set to 10) for which a larger value places a stronger emphasis on good bbox locations. In terms of the first loss, i.e. the classification loss, it takes the form of log-loss $l_{\mathrm{cls}}=-\sum_i \log \hat{p}_i$. In practice a variation of this 