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What is the fully-convolutional model?

Is fully-convolutional model a model that has only convolutional layers (with Batch-norm and Activation) and has not any: max-pool, fully-connected, and other layers?

If it is true, then why Yolo v2 neural network for object detection is named Fully-Convolutional model if it uses Max-pool layers: https://arxiv.org/pdf/1612.08242v1.pdf

Table 2: The path from YOLO to YOLOv2. Most of the listed design decisions lead to significant increases in mAP. Two exceptions are switching to a fully convolutional network with anchor boxes and using the new network.

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Also why Fully Convolutional Networks for Semantic Segmentation is named Fully Convolutional if it has Max-pool layers: https://people.eecs.berkeley.edu/~jonlong/long_shelhamer_fcn.pdf

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In general, a network with CNN with no Fully connected layers is termed as Fully Convolutional Network(FCN). It can include any type of pooling layers, batch norm, dropouts etc.

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