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The size of the inputs and the depth of\ntypical CNN architectures in computer vision only compound this problem.\nUncertainty in neural networks has thus been largely ignored in practice,\ndespite the fact that it may provide important information about the\nreliability of predictions and the inner workings of the network. In this\npaper, we introduce two lightweight approaches to making supervised learning\nwith probabilistic deep networks practical: First, we suggest probabilistic\noutput layers for classification and regression that require only minimal\nchanges to existing networks. Second, we employ assumed density filtering and\nshow that activation uncertainties can be propagated in a practical fashion\nthrough the entire network, again with minor changes. Both probabilistic\nnetworks retain the predictive power of the deterministic counterpart, but\nyield uncertainties that correlate well with the empirical error induced by\ntheir predictions. 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