Online Optimization for Large-Scale Max-Norm Regularization

Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner, which prevents it from processing big data due to possible memory budget. In this paper, hence, we propose an online algorithm that is scalable to large-scale setting. Particularly, we consider the matrix decomposition problem as an example, although a simple variant of the algorithm and analysis can be adapted to other important problems such as matrix completion. The crucial technique in our implementation is to reformulating the max-norm to an equivalent matrix factorization form, where the factors consist of a (possibly overcomplete) basis component and a coefficients one. In this way, we may maintain the basis component in the memory and optimize over it and the coefficients for each sample alternatively. Since the memory footprint of the basis component is independent of the sample size, our algorithm is appealing when manipulating a large collection of samples. We prove that the sequence of the solutions (i.e., the basis component) produced by our algorithm converges to a stationary point of the expected loss function asymptotically. Numerical study demonstrates encouraging results for the efficacy and robustness of our algorithm compared to the widely used nuclear norm solvers.Comment: A conference version appears in NIPS 201

Social Trust Prediction via Max-norm Constrained 1-bit Matrix Completion

Social trust prediction addresses the significant problem of exploring interactions among users in social networks. Naturally, this problem can be formulated in the matrix completion framework, with each entry indicating the trustness or distrustness. However, there are two challenges for the social trust problem: 1) the observed data are with sign (1-bit) measurements; 2) they are typically sampled non-uniformly. Most of the previous matrix completion methods do not well handle the two issues. Motivated by the recent progress of max-norm, we propose to solve the problem with a 1-bit max-norm constrained formulation. Since max-norm is not easy to optimize, we utilize a reformulation of max-norm which facilitates an efficient projected gradient decent algorithm. We demonstrate the superiority of our formulation on two benchmark datasets

Degeneracy and Discreteness in Cosmological Model Fitting

We explore the degeneracy and discreteness problems in the standard cosmological model (\Lambda CDM). We use the Observational Hubble Data (OHD) and the type Ia supernova (SNe Ia) data to study this issue. In order to describe the discreteness in fitting of data, we define a factor G to test the influence from each single data point and analyze the goodness of G. Our results indicate that a higher absolute value of G shows a better capability of distinguishing models, which means the parameters are restricted into smaller confidence intervals with a larger figure of merit evaluation. Consequently, we claim that the factor G is an effective way in model differentiation when using different models to fit the observational data.Comment: 12 pages, 4 figures, 1 table, accepted by RA

Adversarial Training for Code Retrieval with Question-Description Relevance Regularization

Code retrieval is a key task aiming to match natural and programming languages. In this work, we propose adversarial learning for code retrieval, that is regularized by question-description relevance. First, we adapt a simple adversarial learning technique to generate difficult code snippets given the input question, which can help the learning of code retrieval that faces bi-modal and data-scarce challenges. Second, we propose to leverage question-description relevance to regularize adversarial learning, such that a generated code snippet should contribute more to the code retrieval training loss, only if its paired natural language description is predicted to be less relevant to the user given question. Experiments on large-scale code retrieval datasets of two programming languages show that our adversarial learning method is able to improve the performance of state-of-the-art models. Moreover, using an additional duplicate question prediction model to regularize adversarial learning further improves the performance, and this is more effective than using the duplicated questions in strong multi-task learning baselinesComment: Accepted to Findings of EMNLP 2020. 11 pages, 2 figure

Perfect charge compensation in extremely large magnetoresistance materials LaSb and LaBi revealed by the first-principles calculations

By the first-principles electronic structure calculations, we have systematically studied the electronic structures of recently discovered extremely large magnetoresistance (XMR) materials LaSb and LaBi. We find that both LaSb and LaBi are semimetals with the electron and hole carriers in perfect balance. The calculated carrier densities in the order of $10^{20}$ cm$^{-3}$ are in good agreement with the experimental values, implying long mean free time of carriers and thus high carrier mobilities. With a semiclassical two-band model, the perfect charge compensation and high carrier mobilities naturally explain (i) the XMR observed in LaSb and LaBi; (ii) the non-saturating quadratic dependence of XMR on external magnetic field; and (iii) the resistivity plateau in the turn-on temperature behavior at very low temperatures. The explanation of these features without resorting to the topological effect indicates that they should be the common characteristics of all perfectly electron-hole compensated semimetals.Comment: 7 pages, 7 figures, 1 tabl

Pressure-induced topological phase transition in LaSb: First-principles study

By using first-principles electronic structure calculations, we predict that the extreme magnetoresistance (XMR) material LaSb takes a topological phase transition without breaking any symmetry under a hydrostatic pressure applied between 3 and 4 GPa, meanwhile the electron-hole compensation remains in its electronic band structure. Thus LaSb provides an ideal platform for studying the individual role of topological property playing in the XMR phenomenon, in addition to the electron-hole compensation. This has general implication to the relationship of XMR effect and topological property in topological materials.Comment: 6 pages, 4 figures, 2 table

Robust superconductivity and transport properties in (Li1-xFex)OHFeSe single crystals

The recently discovered (Li${_{1-x}}$Fe${_x}$)OHFeSe superconductor with $T_c$ about 40K provides a good platform for investigating the magnetization and electrical transport properties of FeSe-based superconductors. By using a hydrothermal ion-exchange method, we have successfully grown crystals of (Li${_{1-x}}$Fe${_x}$)OHFeSe. X-ray diffraction on the sample shows the single crystalline PbO-type structure with the c-axis preferential orientation. Magnetic susceptibility and resistive measurements show an onset superconducting transition at around ${T_c}$=38.3K. Using the magnetization hysteresis loops and Bean critical state model, a large critical current ${J_s}$ is observed in low temperature region. The critical current density is suppressed exponentially with increasing magnetic field. Temperature dependencies of resistivity under various currents and fields are measured, revealing a robust superconducting current density and bulk superconductivity.Comment: 5 pages, 5 figure

Anisotropic Electronic Mobilities in the Nematic State of the Parent Phase NaFeAs

Hall effect and magnetoresistance have been measured on single crystals of the parent phase NaFeAs under a uniaxial pressure. Although significant difference of the in-plane resistivity $\rho_{xx}(I\parallel a)$ and $\rho_{xx}(I\parallel b)$ with the uniaxial pressure along $b$-axis was observed, the transverse resistivity $\rho_{xy}$ shows a surprisingly isotropic behavior. Detailed analysis reveals that the Hall coefficient $R_\mathrm{H}$ measured in the two orthogonal configurations ($I\parallel a$-axis and $I\parallel b$-axis) coincide very well and exhibit a deviation from the high temperature background at around the structural transition temperature $T_{\mathrm{s}}$. Furthermore, the magnitude of $R_\mathrm{H}$ increases remarkably below the structural transition temperature. This enhanced Hall coefficient is accompanied by the non-linear transverse resistivity versus magnetic field and enhanced magnetoresistance, which can be explained very well by the two band model with anisotropic mobilities of each band. Our results together with the two band model analysis clearly show that the anisotropic in-plane resistivity in the nematic state is closely related to the distinct quasiparticle mobilities when they are moving parallel or perpendicular to the direction of the uniaxial pressure.Comment: 9 pages, 8 figure

Simultaneous Vanishing of the Nematic Electronic State and the Structural Orthorhombicity in NaFe1−x_{1-x}Cox_xAs Single Crystals

We have carried out in-plane resistivity measurements under a uniaxial pressure in NaFe$_{1-x}$Co$_x$As single crystals. A clear distinction of the in-plane resistivity $\rho_a$ and $\rho_b$ with the uniaxial pressure along $b$-axis was discovered in the parent and underdoped regime with the doping level up to about x=0.025$\pm$0.002. From the deviating point of $\rho_a$ and $\rho_b$, and the unique kinky structure of resistivity together with the published data we determined the temperatures for the nematic, structural and antiferromagnetic transitions. It is clearly shown that the nematic electronic state vanishes simultaneously with the structural transition. The antiferromagnetic state disappears however at a lower doping level. Our results, in combination with the data in BaFe$_{2-x}$Co$_x$As$_2$, indicate a close relationship between nematicity and superconductivity.Comment: 5 pages, 5 figure

Primordial Magnetic Field from Gravitationally Coupled Electrodynamics in Bouncing Scenario

We in this paper study the generation of primordial magnetic field (PMF) in the non-singular bouncing scenario, through the coupling of the electromagnetic field to gravity. We adopt an electrodynamic model with a coupling coefficient as a function of the scale factor $a$, i.e. $f=1+(a/a_\star)^{-n}$, with $a_\star$ and $n>0$ being constants. The result implies that in this mechanism, the power spectrum of PMF today is always blue tilted on large scales from $1$ Mpc to the Hubble length, and the observational constraints favor the ekpyrotic-bounce scenario. Furthermore, the back reaction of the energy density of PMF at the bouncing point yields theoretical constraints on the bouncing model