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.

Input: Consider Input: We present a new approach to assessing the robustness of neural networks based on estimating the proportion of inputs for which a property is violated. Specifically, we estimate the probability of the event that the property is violated under an input model. Our approach critically varies from the formal verification framework in that when the property can be violated, it provides an informative notion of how robust the network is, rather than just the conventional assertion that the network is not verifiable. Furthermore, it provides an ability to scale to larger networks than formal verification approaches. Though the framework still provides a formal guarantee of satisfiability whenever it successfully finds one or more violations, these advantages do come at the cost of only providing a statistical estimate of unsatisfiability whenever no violation is found. Key to the practical success of our approach is an adaptation of multi-level splitting, a Monte Carlo approach for estimating the probability of rare events, to our statistical robustness framework. We demonstrate that our approach is able to emulate formal verification procedures on benchmark problems, while scaling to larger networks and providing reliable additional information in the form of accurate estimates of the violation probability.

Output: We introduce a statistical approach to assessing neural network robustness that provides an informative notion of how robust a network is, rather than just the conventional binary assertion of whether or not of property is violated.


Input: Consider Input: We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of M data points on the nondifferentiability of the ReLU divides the parameter space into at most 2^M regions, which makes analysis difficult. By exploiting polyhedral geometry, we reduce the total computation down to one convex quadratic program (QP) for each hidden node, O(M) (in)equality tests, and one (or a few) nonconvex QP. For the last QP, we show that our specific problem can be solved efficiently, in spite of nonconvexity. In the benign case, we solve one equality constrained QP, and we prove that projected gradient descent solves it exponentially fast. In the bad case, we have to solve a few more inequality constrained QPs, but we prove that the time complexity is exponential only in the number of inequality constraints. Our experiments show that either benign case or bad case with very few inequality constraints occurs, implying that our algorithm is efficient in most cases.

Output: A theoretical algorithm for testing local optimality and extracting descent directions at nondifferentiable points of empirical risks of one-hidden-layer ReLU networks.


Input: Consider Input: Disentangling underlying generative factors of a data distribution is important for interpretability and generalizable representations. In this paper,  we introduce two novel disentangling methods. Our first method, Unlabeled Disentangling GAN (UD-GAN, unsupervised), decomposes the latent noise by generating similar/dissimilar image pairs and it learns a distance metric on these pairs with siamese networks and a contrastive loss. This pairwise approach provides consistent representations for similar data points. Our second method (UD-GAN-G, weakly supervised) modifies the UD-GAN with user-defined guidance functions, which restrict the information that goes into the siamese networks. This constraint helps UD-GAN-G to focus on the desired semantic variations in the data. We  show  that  both  our  methods  outperform  existing  unsupervised approaches in quantitative metrics that measure semantic accuracy of the learned representations. In addition, we illustrate that simple guidance functions we use in UD-GAN-G allow us to directly capture the desired variations in the data.


Output: We use Siamese Networks to guide and disentangle the generation process in GANs without labeled data.