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Non-small-cell lung cancer (NSCLC) represents approximately 80-85% of lung cancer diagnoses and is the leading cause of cancer-related death worldwide. Recent studies indicate that image-based radiomics features from positron emission tomography/computed tomography (PET/CT) images have predictive power for NSCLC outcomes. To this end, easily calculated functional features such as the maximum and the mean of standard uptake value (SUV) and total lesion glycolysis (TLG) are most commonly used for NSCLC prognostication, but their prognostic value remains controversial. Meanwhile, convolutional neural networks (CNN) are rapidly emerging as a new method for cancer image analysis, with significantly enhanced predictive power compared to hand-crafted radiomics features. Here we show that CNNs trained to perform the tumor segmentation task, with no other information than physician contours, identify a rich set of survival-related image features with remarkable prognostic value. In a retrospective study on pre-treatment PET-CT images of 96 NSCLC patients before stereotactic-body radiotherapy (SBRT), we found that the CNN segmentation algorithm (U-Net) trained for tumor segmentation in PET and CT images, contained features having strong correlation with 2- and 5-year overall and disease-specific survivals. The U-Net algorithm has not seen any other clinical information (e.g. survival, age, smoking history, etc.) than the images and the corresponding tumor contours provided by physicians. In addition, we observed the same trend by validating the U-Net features against an extramural data set provided by Stanford Cancer Institute. Furthermore, through visualization of the U-Net, we also found convincing evidence that the regions of metastasis and recurrence appear to match with the regions where the U-Net features identified patterns that predicted higher likelihoods of death. We anticipate our findings will be a starting point for more sophisticated non-intrusive patient specific cancer prognosis determination. For example, the deep learned PET/CT features can not only predict survival but also visualize high-risk regions within or adjacent to the primary tumor and hence potentially impact therapeutic outcomes by optimal selection of therapeutic strategy or first-line therapy adjustment.