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Trained using only image class label, deep weakly supervised methods allow image classification and ROI segmentation for interpretability. Despite their success on natural images, they face several challenges over histology data where ROI are visually similar to background making models vulnerable to high pixel-wise false positives. These methods lack mechanisms for modeling explicitly non-discriminative regions which raises false-positive rates. We propose novel regularization terms, which enable the model to seek both non-discriminative and discriminative regions, while discouraging unbalanced segmentations and using only image class label. Our method is composed of two networks: a localizer that yields segmentation mask, followed by a classifier. The training loss pushes the localizer to build a segmentation mask that holds most discrimiantive regions while simultaneously modeling background regions. Comprehensive experiments over two histology datasets showed the merits of our method in reducing false positives and accurately segmenting ROI.