Inhomogeneous Boundary Value Problem for Hartree Type Equation

In this paper, we settle the problem for time-dependent Hartree equation with inhomogeneous boundary condition in a bounded Lipschitz domain in $\mathbb{R}^{N}$. A global existence result is derived.Comment: 10 page

Towards Practical Verification of Machine Learning: The Case of Computer Vision Systems

Due to the increasing usage of machine learning (ML) techniques in security- and safety-critical domains, such as autonomous systems and medical diagnosis, ensuring correct behavior of ML systems, especially for different corner cases, is of growing importance. In this paper, we propose a generic framework for evaluating security and robustness of ML systems using different real-world safety properties. We further design, implement and evaluate VeriVis, a scalable methodology that can verify a diverse set of safety properties for state-of-the-art computer vision systems with only blackbox access. VeriVis leverage different input space reduction techniques for efficient verification of different safety properties. VeriVis is able to find thousands of safety violations in fifteen state-of-the-art computer vision systems including ten Deep Neural Networks (DNNs) such as Inception-v3 and Nvidia's Dave self-driving system with thousands of neurons as well as five commercial third-party vision APIs including Google vision and Clarifai for twelve different safety properties. Furthermore, VeriVis can successfully verify local safety properties, on average, for around 31.7% of the test images. VeriVis finds up to 64.8x more violations than existing gradient-based methods that, unlike VeriVis, cannot ensure non-existence of any violations. Finally, we show that retraining using the safety violations detected by VeriVis can reduce the average number of violations up to 60.2%.Comment: 16 pages, 11 tables, 11 figure

Multi-Adversarial Domain Adaptation

Recent advances in deep domain adaptation reveal that adversarial learning can be embedded into deep networks to learn transferable features that reduce distribution discrepancy between the source and target domains. Existing domain adversarial adaptation methods based on single domain discriminator only align the source and target data distributions without exploiting the complex multimode structures. In this paper, we present a multi-adversarial domain adaptation (MADA) approach, which captures multimode structures to enable fine-grained alignment of different data distributions based on multiple domain discriminators. The adaptation can be achieved by stochastic gradient descent with the gradients computed by back-propagation in linear-time. Empirical evidence demonstrates that the proposed model outperforms state of the art methods on standard domain adaptation datasets.Comment: AAAI 2018 Oral. arXiv admin note: substantial text overlap with arXiv:1705.10667, arXiv:1707.0790