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Interpreting the decision logic behind effective deep convolutional neural networks (CNN) on images complements the success of deep learning models. However, the existing methods can only interpret some specific decision logic on individual or a small number of images. To facilitate human understandability and generalization ability, it is important to develop representative interpretations that interpret common decision logics of a CNN on a large group of similar images, which reveal the common semantics data contributes to many closely related predictions. In this paper, we develop a novel unsupervised approach to produce a highly representative interpretation for a large number of similar images. We formulate the problem of finding representative interpretations as a co-clustering problem, and convert it into a submodular cost submodular cover problem based on a sample of the linear decision boundaries of a CNN. We also present a visualization and similarity ranking method. Our extensive experiments demonstrate the excellent performance of our method., Comment: Accepted by ICCV 2021 (http://iccv2021.thecvf.com/home) | A python notebook of the proposed method can be found in https://marketplace.huaweicloud.com/markets/aihub/notebook/detail/?id=8e92ea6c-2f4a-4cff-a89f-bf2905bb7ac0

Massive deployment of Graph Neural Networks (GNNs) in high-stake applications generates a strong demand for explanations that are robust to noise and align well with human intuition. Most existing methods generate explanations by identifying a subgraph of an input graph that has a strong correlation with the prediction. These explanations are not robust to noise because independently optimizing the correlation for a single input can easily overfit noise. Moreover, they do not align well with human intuition because removing an identified subgraph from an input graph does not necessarily change the prediction result. In this paper, we propose a novel method to generate robust counterfactual explanations on GNNs by explicitly modelling the common decision logic of GNNs on similar input graphs. Our explanations are naturally robust to noise because they are produced from the common decision boundaries of a GNN that govern the predictions of many similar input graphs. The explanations also align well with human intuition because removing the set of edges identified by an explanation from the input graph changes the prediction significantly. Exhaustive experiments on many public datasets demonstrate the superior performance of our method.

In this paper we establish a generalization of Bombieri-Vinogradov theorem for primes represented by a fixed positive definite binary quadratic form. Then we apply this theorem to generalize a result of Vatwani on bounded gap between Gaussian primes., Comment: 8 pages; comments welcome!

In this paper we generalize the result of Fouvry and Iwaniec dealing with prime values of the quadratic form $x^2 + y^2$ with one input restricted to a thin subset of the integers. We prove the same result with an arbitrary primitive positive definite binary quadratic form. In particular, for any positive definite binary quadratic form $F$ and binary linear form $G$, there exist infinitely many $\ell, m\in\mathbb{Z}$ such that both $F(\ell, m)$ and $G(\ell, m)$ are primes as long as there are no local obstructions., Comment: 26 pages; comments welcome!

Passive microwave sounders provide the highest-impact observations ingested by major numerical weather prediction (NWP) forecast models. The Advanced Technology Microwave Sounder (ATMS), built by Northrop Grumman, Azusa, CA, USA, is the latest operational microwave sounder series being launched by the United States to provide both temperature and water vapor soundings of the atmosphere. The first ATMS was launched on the Suomi National Polarorbiting Partnership (SNPP) satellite in 2011. This article focuses on the details of the on-orbit performance characterization of the second ATMS, which launched on November 18, 2017, on the Joint Polar Satellite System-1 (JPSS-1) satellite. After successful commissioning, JPSS-1 was renamed National Oceanic and Atmospheric Administration (NOAA)-20 (N-20). We present performance characterizations from prelaunch and postlaunch tests, including the thermal vacuum (TVAC) campaign, and postlaunch activities that contribute to the radiance data products. Significant improvements were found for reflector emissivity, 1/ f noise performance, antenna beam efficiency, inter-channel noise correlation, and scan drive bearing design. New geolocation and pointing algorithms were evaluated. The N-20 ATMS has the same channel set, polarizations, scan geometry, and calibration approach as the SNPP ATMS. The N-20 ATMS meets all performance requirements with margin.