  Large receptive field and dense prediction are both important for achieving
high accuracy in pixel labeling tasks such as semantic segmentation. These two
properties, however, contradict with each other. A pooling layer (with stride
2) quadruples the receptive field size but reduces the number of predictions to
25\%. Some existing methods lead to dense predictions using computations that
are not equivalent to the original model. In this paper, we propose the
equivalent convolution (eConv) and equivalent pooling (ePool) layers, leading
to predictions that are both dense and equivalent to the baseline CNN model.
Dense prediction models learned using eConv and ePool can transfer the baseline
CNN's parameters as a starting point, and can inverse transfer the learned
parameters in a dense model back to the original one, which has both fast
testing speed and high accuracy. The proposed eConv and ePool layers have
achieved higher accuracy than baseline CNN in various tasks, including semantic
segmentation, object localization, image categorization and apparent age
estimation, not only in those tasks requiring dense pixel labeling.
