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Nonlinear monotone transformations are used extensively in normalizing flows to construct invertible triangular mappings from simple distributions to complex ones. In existing literature, monotonicity is usually enforced by restricting function classes or model parameters and the inverse transformation is often approximated by root-finding algorithms as a closed-form inverse is unavailable. In this paper, we introduce a new integral-based approach termed: Atomic Unrestricted Time Machine (AUTM), equipped with unrestricted integrands and easy-to-compute explicit inverse. AUTM offers a versatile and efficient way to the design of normalizing flows with explicit inverse and unrestricted function classes or parameters. Theoretically, we present a constructive proof that AUTM is universal: all monotonic normalizing flows can be viewed as limits of AUTM flows. We provide a concrete example to show how to approximate any given monotonic normalizing flow using AUTM flows with guaranteed convergence. Our result implies that AUTM can be used to transform an existing flow into a new one equipped with explicit inverse and unrestricted parameters. The performance of the new approach is evaluated on high dimensional density estimation, variational inference and image generation. 

Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world applications. However, for large-scale problems involving a huge number of samples and extremely high-dimensional features, solving sparse SVMs remains challenging. By noting that sparse SVMs induce sparsities in both feature and sample spaces, we propose a novel approach, which is based on accurate estimations of the primal and dual optima of sparse SVMs, to simultaneously identify the features and samples that are guaranteed to be irrelevant to the outputs. Thus, we can remove the identified inactive samples and features from the training phase, leading to substantial savings in both the memory usage and computational cost without sacrificing accuracy. To the best of our knowledge, the proposed method is the first static feature and sample reduction method for sparse SVMs. Experiments on both synthetic and real datasets (e.g., the kddb dataset with about 20 million samples and 30 million features) demonstrate that our approach significantly outperforms state-of-the-art methods and the speedup gained by our approach can be orders of magnitude. 

The nature of dark matter and properties of neutrinos are among the most pressing issues in contemporary particle physics. The dual-phase xenon time-projection chamber is the leading technology to cover the available parameter space for weakly interacting massive particles, while featuring extensive sensitivity to many alternative dark matter candidates. These detectors can also study neutrinos through neutrinoless double-beta decay and through a variety of astrophysical sources. A next-generation xenon-based detector will therefore be a true multi-purpose observatory to significantly advance particle physics, nuclear physics, astrophysics, solar physics, and cosmology. This review article presents the science cases for such a detector.