TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: Empirical risk minimization (ERM), with proper loss function and regularization, is the common practice of supervised classification. In this paper, we study training arbitrary (from linear to deep) binary classifier from only unlabeled (U) data by ERM. We prove that it is impossible to estimate the risk of an arbitrary binary classifier in an unbiased manner given a single set of U data, but it becomes possible given two sets of U data with different class priors. These two facts answer a fundamental question---what the minimal supervision is for training any binary classifier from only U data. Following these findings, we propose an ERM-based learning method from two sets of U data, and then prove it is consistent. Experiments demonstrate the proposed method could train deep models and outperform state-of-the-art methods for learning from two sets of U data.

SOLUTION: Three class priors are all you need to train deep models from only U data, while any two should not be enough.

PROBLEM: Now GANs can generate more and more realistic face images that can easily fool human beings. In contrast, a common convolutional neural network(CNN), e.g. ResNet-18, can achieve more than 99.9% accuracy in discerning fake/real faces if training and testing faces are from the same source. In this paper, we performed both human studies and CNN experiments, which led us to two important findings. One finding is that the textures of fake faces are substantially different from real ones. CNNs can capture local image texture information for recognizing fake/real face, while such cues are easily overlooked by humans. The other finding is that global image texture information is more robust to image editing and generalizable to fake faces from different GANs and datasets. Based on the above findings, we propose a novel architecture coined as Gram-Net, which incorporates "Gram Block" in multiple semantic levels to extract global image texture representations. Experimental results demonstrate that our Gram-Net performs better than existing approaches for fake face detection. Especially, our Gram-Net is more robust to image editing, e.g. downsampling, JPEG compression, blur, and noise. More importantly, our Gram-Net generalizes significantly better in detecting fake faces from GAN models not seen in the training phase.

SOLUTION: An empirical study on fake images reveals that texture is an important cue that current fake images differ from real images. Our improved model capturing global texture statistics shows better cross-GAN fake image detection performance.

PROBLEM: We present a novel approach for the certification of neural networks against adversarial perturbations which combines scalable overapproximation methods with precise (mixed integer) linear programming. This results in significantly better precision than state-of-the-art verifiers on challenging feedforward and convolutional neural networks with piecewise linear activation functions.

SOLUTION:
We refine the over-approximation results from incomplete verifiers using MILP solvers to prove more robustness properties than state-of-the-art.