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In convolutional networks designed to serve the purpose of object detection, following the output of the final activations in the network, said activations are processed in accordance with the theory of non-max suppression. Of course, we may include this process on the computation graph corresponding to the given convolutional network, and in this sense it makes sense that, when training our network, we'd back propagate through this non-max suppression layer, but is this necessary?

Thank you in advance for any responses.

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Generally no this isn't done, since NMS isn't a very differentiable operation by it's discrete nature. There has been work on Learning NMS, which replaces NMS with a backpropable trained component.

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