  We approach structured output prediction by optimizing a deep value network
(DVN) to precisely estimate the task loss on different output configurations
for a given input. Once the model is trained, we perform inference by gradient
descent on the continuous relaxations of the output variables to find outputs
with promising scores from the value network. When applied to image
segmentation, the value network takes an image and a segmentation mask as
inputs and predicts a scalar estimating the intersection over union between the
input and ground truth masks. For multi-label classification, the DVN's
objective is to correctly predict the F1 score for any potential label
configuration. The DVN framework achieves the state-of-the-art results on
multi-label prediction and image segmentation benchmarks.
