prior at training phase. For each mini-batch at feed-forward time, the network runs both the objectness prior and class-specific detection. But at the back-propagation phase, the network firstly generates the objectness prior, then for detection, samples whose objectness scores are high than threshold $o_p$ are selected (Figure \[mapppp\]). The extra computation only comes from the selection of samples for back-propagation. With suitable $o_p$ (we use $o_p$ = 0.03 for all models), only a small number of samples is selected for updating the detection branch, thus the complexity of backward pass has been significantly reduced.

![Mapping the objectness prior with object detection. We first binarize the objectness prior maps according to $o_p$, then project the binary masks to the detection domain of the last convolutional feature maps. The locations within the masks are collected for detecting objects.[]{data-label="mapping"}](prior_det.pdf){width="0.6\linewidth"}

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Training and Testing
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In this section, we firstly introduce the multi-task loss function for optimizing the networks. Then we explain how to optimize the network jointly and perform inference directly.

Loss Function
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For each location, our network has three sibling output branches. The first outputs the objectness confidence score $p^{obj} = \{p_{0}^{obj}, p_{1}^{obj}\}$, computed by a Softmax 