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Automatic histopathological Whole Slide Image (WSI) analysis for cancer classification has been highlighted along with the advancements in microscopic imaging techniques, since manual examination and diagnosis with WSIs are time- and cost-consuming. Recently, deep convolutional neural networks have succeeded in histopathological image analysis. However, despite the success of the development, there are still opportunities for further enhancements. In this paper, we propose a novel cancer texture-based deep neural network (CAT-Net) that learns scalable morphological features from histopathological WSIs. The innovation of CAT-Net is twofold: (1) capturing invariant spatial patterns by dilated convolutional layers and (2) improving predictive performance while reducing model complexity. Moreover, CAT-Net can provide discriminative morphological (texture) patterns formed on cancerous regions of histopathological images comparing to normal regions. We elucidated how our proposed method, CAT-Net, captures morphological patterns of interest in hierarchical levels in the model. The proposed method out-performed the current state-of-the-art benchmark methods on accuracy, precision, recall, and F1 score.