Tensorizing Generative Adversarial Nets

Generative Adversarial Network (GAN) and its variants exhibit state-of-the-art performance in the class of generative models. To capture higher-dimensional distributions, the common learning procedure requires high computational complexity and a large number of parameters. The problem of employing such massive framework arises when deploying it on a platform with limited computational power such as mobile phones. In this paper, we present a new generative adversarial framework by representing each layer as a tensor structure connected by multilinear operations, aiming to reduce the number of model parameters by a large factor while preserving the generative performance and sample quality. To learn the model, we employ an efficient algorithm which alternatively optimizes both discriminator and generator. Experimental outcomes demonstrate that our model can achieve high compression rate for model parameters up to $35$ times when compared to the original GAN for MNIST dataset.Comment: 4 pages, 3 figure

On the topological pressure of the saturated set with non-uniform structure

We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1605.07283; text overlap with arXiv:1304.5497 by other author

The impact of SS-wave thresholds Ds1Dˉs+c.c.D_{s1}\bar{D}_{s}+c.c. and Ds0Dˉs∗+c.c.D_{s0}\bar{D}^*_{s}+c.c. on vector charmonium spectrum

By investigating the very closely lied $D_{s1}\bar{D}_{s}+c.c.$ and $D_{s0}\bar{D}^*_{s}+c.c.$ thresholds at about 4.43 GeV we propose that the $\psi(4415)$ and $\psi(4160)$ can be mixing states between the dynamic generated states of the strong $S$-wave $D_{s1}\bar{D}_{s}+c.c.$ and $D_{s0}\bar{D}^*_{s}+c.c.$ interactions and the quark model states $\psi(4S)$ and $\psi(2D)$. We investigate the $J/\psi K\bar{K}$ final states and invariant mass spectrum of $J/\psi K$ to demonstrate that nontrivial lineshapes can arise from such a mechanism. This process, which goes through triangle loop transitions, is located in the vicinity of the so-called "triangle singularity (TS)" kinematics. As a result, it provides a special mechanism for the production of exotic states $Z_{cs}$, which is the strange partner of $Z_c(3900)$, but with flavor contents of $c\bar{c}q\bar{s}$ (or $c\bar{c}s\bar{q}$) with $q$ denoting $u/d$ quarks. The lineshapes of the $e^+e^-\to J/\psi K\bar{K}$ cross sections and $J/\psi K \ (J/\psi \bar{K})$ spectrum are sensitive to the dynamically generated state, and we demonstrate that a pole structure can be easily distinguished from open threshold CUSP effects if an exotic state is created. A precise measurement of the cross section lineshapes can test such a mixing mechanism and provide navel information for the exotic partners of the $Z_c(3900)$ in the charmonium spectrum.Comment: 10 pages, 8 figures. Revised version including discussions on the new data from BESIII; version to appear in Phys. Rev.

Quantitative recurrence properties for systems with non-uniform structure

Let X be a subshift satisfy non-uniform structure. In this paper, we give quantitative estimate of the recurrence sets. These results can be applied to a large class of symbolic systems, including beta-shifts, S-gap shifts and their factors.Comment: 21 page

Host galaxy properties of mergers of stellar binary black holes and their implications for advanced LIGO gravitational wave sources

Understanding the host galaxy properties of stellar binary black hole (SBBH) mergers is important for revealing the origin of the SBBH gravitational-wave sources detected by advanced LIGO and helpful for identifying their electromagnetic counterparts. Here we present a comprehensive analysis of the host galaxy properties of SBBHs by implementing semi-analytical recipes for SBBH formation and merger into cosmological galaxy formation model. If the time delay between SBBH formation and merger ranges from \la\,Gyr to the Hubble time, SBBH mergers at redshift z\la0.3 occur preferentially in big galaxies with stellar mass M_*\ga2\times10^{10}\msun and metallicities $Z$ peaking at $\sim0.6Z_\odot$. However, the host galaxy stellar mass distribution of heavy SBBH mergers (M_{\bullet\bullet}\ga50\msun) is bimodal with one peak at \sim10^9\msun and the other peak at \sim2\times10^{10}\msun. The contribution fraction from host galaxies with Z\la0.2Z_\odot to heavy mergers is much larger than that to less heavy mergers. If SBBHs were formed in the early universe (e.g., $z>6$), their mergers detected at z\la0.3 occur preferentially in even more massive galaxies with M_*>3\times10^{10}\msun and in galaxies with metallicities mostly \ga0.2Z_\odot and peaking at $Z\sim0.6Z_\odot$, due to later cosmic assembly and enrichment of their host galaxies. SBBH mergers at z\la0.3 mainly occur in spiral galaxies, but the fraction of SBBH mergers occur in elliptical galaxies can be significant if those SBBHs were formed in the early universe; and about two thirds of those mergers occur in the central galaxies of dark matter halos. We also present results on the host galaxy properties of SBBH mergers at higher redshift.Comment: 12 pages, 9 figures, MNRAS accepte

An improved algorithm based on finite difference schemes for fractional boundary value problems with non-smooth solution

In this paper, an efficient algorithm is presented by the extrapolation technique to improve the accuracy of finite difference schemes for solving the fractional boundary value problems with non-smooth solution. Two popular finite difference schemes, the weighted shifted Gr\"{u}nwald difference (WSGD) scheme and the fractional centered difference (FCD) scheme, are revisited and the error estimate of the schemes is provided in maximum norm. Based on the analysis of leading singularity of exact solution for the underlying problem, it is demonstrated that, with the use of the proposed algorithm, the improved WSGD and FCD schemes can recover the second-order accuracy for non-smooth solution. Several numerical examples are given to validate our theoretical prediction. It is shown that both accuracy and convergence rate of numerical solutions can be significantly improved by using the proposed algorithm.Comment: the Riesz fractional derivatives, extrapolation technique, error estimate in maximum norm, weak singularity, convergence rat

Completion of High Order Tensor Data with Missing Entries via Tensor-train Decomposition

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this problem, we propose an efficient algorithm called TT-WOPT (Tensor-train Weighted OPTimization) to find the latent core tensors of tensor data and recover the missing entries. Tensor-train decomposition, which has the powerful representation ability with linear scalability to tensor order, is employed in our algorithm. The experimental results on synthetic data and natural image completion demonstrate that our method significantly outperforms the other related methods. Especially when the missing rate of data is very high, e.g., 85% to 99%, our algorithm can achieve much better performance than other state-of-the-art algorithms.Comment: 8 pages, ICONIP 201

Capsule-Transformer for Neural Machine Translation

Transformer hugely benefits from its key design of the multi-head self-attention network (SAN), which extracts information from various perspectives through transforming the given input into different subspaces. However, its simple linear transformation aggregation strategy may still potentially fail to fully capture deeper contextualized information. In this paper, we thus propose the capsule-Transformer, which extends the linear transformation into a more general capsule routing algorithm by taking SAN as a special case of capsule network. So that the resulted capsule-Transformer is capable of obtaining a better attention distribution representation of the input sequence via information aggregation among different heads and words. Specifically, we see groups of attention weights in SAN as low layer capsules. By applying the iterative capsule routing algorithm they can be further aggregated into high layer capsules which contain deeper contextualized information. Experimental results on the widely-used machine translation datasets show our proposed capsule-Transformer outperforms strong Transformer baseline significantly

Asymptotics of the partition function of a Laguerre-type random matrix model

We study asymptotics of the partition function $Z_N$ of a Laguerre-type random matrix model when the matrix order $N$ tends to infinity. By using the Deift-Zhou steepest descent method for Riemann-Hilbert problems, we obtain an asymptotic expansion of $\log Z_N$ in powers of $N^{-2}$.Comment: 29 pages with 4 figure

High-order Tensor Completion for Data Recovery via Sparse Tensor-train Optimization

In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train Optimization (STTO) which considers incomplete data as sparse tensor and uses first-order optimization method to find the factors of tensor-train decomposition. Our algorithm is shown to perform well in simulation experiments at both low-order cases and high-order cases. We also employ a tensorization method to transform data to a higher-order form to enhance the performance of our algorithm. The results of image recovery experiments in various cases manifest that our method outperforms other completion algorithms. Especially when the missing rate is very high, e.g., 90\% to 99\%, our method is significantly better than the state-of-the-art methods.Comment: 5 pages (include 1 page of reference) ICASSP 201