instruction:
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.
question:
Knowledge graph embedding research has overlooked the problem of probability calibration. We show popular embedding models are indeed uncalibrated. That means probability estimates associated to predicted triples are unreliable. We present a novel method to calibrate a model when ground truth negatives are not available, which is the usual case in knowledge graphs. We propose to use Platt scaling and isotonic regression alongside our method. Experiments on three datasets with ground truth negatives show our contribution leads to well calibrated models when compared to the gold standard of using negatives. We get significantly better results than the uncalibrated models from all calibration methods. We show isotonic regression offers the best the performance overall, not without trade-offs. We also show that calibrated models reach state-of-the-art accuracy without the need to define relation-specific decision thresholds.
answer:
We propose a novel method to calibrate knowledge graph embedding models without the need of negative examples.


question:
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.
answer:
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.


question:
Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax problem to global optimality, but in practice, are successfully trained with stochastic gradient descent-ascent. In this paper, we show that, when the generator is a one-layer network, stochastic gradient descent-ascent converges to a global solution in polynomial time and sample complexity.
answer:

We show that stochastic gradient descent ascent converges to a global optimum for WGAN with one-layer generator network.