Formal verification of neural networks is critical for their safe adoption in real-world applications. However, designing a precise and scalable verifier which can handle different activation functions, realistic network architectures and relevant specifications remains an open and difficult challenge.
In this paper, we take a major step forward in addressing this challenge and present a new verification framework, called PRIMA. PRIMA is both (i) general: it handles any non-linear activation function, and (ii) precise: it computes precise convex abstractions involving
multiple
neurons via novel convex hull approximation algorithms that leverage concepts from computational geometry. The algorithms have polynomial complexity, yield fewer constraints, and minimize precision loss.
We evaluate the effectiveness of PRIMA on a variety of challenging tasks from prior work. Our results show that PRIMA is significantly more precise than the state-of-the-art, verifying robustness to input perturbations for up to 20%, 30%, and 34% more images than existing work on ReLU-, Sigmoid-, and Tanh-based networks, respectively. Further, PRIMA enables, for the first time, the precise verification of a realistic neural network for autonomous driving within a few minutes.
Deep learning methods are actively used for brain lesion segmentation. One of the most popular models is DeepMedic, which was developed for segmentation of relatively large lesions like glioma and ischemic stroke. In our work, we consider segmentation of brain tumors appropriate to stereotactic radiosurgery which limits typical lesion sizes. These differences in target volumes lead to a large number of false negatives (especially for small lesions) as well as to an increased number of false positives for DeepMedic. We propose a new patch-sampling procedure to increase network performance for small lesions. We used a 6-year dataset from a stereotactic radiosurgery center. To evaluate our approach, we conducted experiments with the three most frequent brain tumors: metastasis, meningioma, schwannoma. In addition to cross-validation, we estimated quality on a hold-out test set which was collected several years later than the train one. The experimental results show solid improvements in both cases.
In the last years, neural networks have proven to be a powerful framework for various image analysis problems. However, some application domains have specific limitations. Notably, digital pathology is an example of such fields due to tremendous image sizes and quite limited number of training examples available. In this paper, we adopt state-of-the-art convolutional neural networks (CNN) architectures for digital pathology images analysis. We propose to classify image patches to increase effective sample size and then to apply an ensembling technique to build prediction for the original images. To validate the developed approaches, we conducted experiments with Breast Cancer Histology Challenge dataset and obtained 90% accuracy for the 4-class tissue classification task.
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