We present an approach to learn a dense pixel-wise labeling from image-level
tags. Each image-level tag imposes constraints on the output labeling of a
Convolutional Neural Network (CNN) classifier. We propose Constrained CNN
(CCNN), a method which uses a novel loss function to optimize for any set of
linear constraints on the output space (i.e. predicted label distribution) of a
CNN. Our loss formulation is easy to optimize and can be incorporated directly
into standard stochastic gradient descent optimization. The key idea is to
phrase the training objective as a biconvex optimization for linear models,
which we then relax to nonlinear deep networks. Extensive experiments
demonstrate the generality of our new learning framework. The constrained loss
yields state-of-the-art results on weakly supervised semantic image
segmentation. We further demonstrate that adding slightly more supervision can
greatly improve the performance of the learning algorithm.

我们提出了一个名为约束卷积神经网络的方法，它使用一种新的损失函数来优化 CNN 模型输出空间上任何一组线性约束条件，并且通过大量实验得出该方法在弱监督语义图像分割任务中表现出卓越的效果。