LDMNet: Low Dimensional Manifold Regularized Neural Networks

Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing overfitting are data-independent, and their efficacy is often limited when the training set is very small. Data-dependent regularizations are mostly motivated by the observation that data of interest lie close to a manifold, which is typically hard to parametrize explicitly and often requires human input of tangent vectors. These methods typically only focus on the geometry of the input data, and do not necessarily encourage the networks to produce geometrically meaningful features. To resolve this, we propose a new framework, the Low-Dimensional-Manifold-regularized neural Network (LDMNet), which incorporates a feature regularization method that focuses on the geometry of both the input data and the output features. In LDMNet, we regularize the network by encouraging the combination of the input data and the output features to sample a collection of low dimensional manifolds, which are searched efficiently without explicit parametrization. To achieve this, we directly use the manifold dimension as a regularization term in a variational functional. The resulting Euler-Lagrange equation is a Laplace-Beltrami equation over a point cloud, which is solved by the point integral method without increasing the computational complexity. We demonstrate two benefits of LDMNet in the experiments. First, we show that LDMNet significantly outperforms widely-used network regularizers such as weight decay and DropOut. Second, we show that LDMNet can be designed to extract common features of an object imaged via different modalities, which proves to be very useful in real-world applications such as cross-spectral face recognition

Nuclear enhanced power corrections to DIS structure functions

We calculate nuclear enhanced power corrections to structure functions measured in deeply inelastic lepton-nucleus scattering in Quantum Chromodynamics (QCD). We find that the nuclear medium enhanced power corrections at order of $O(\alpha_s/Q^2)$ enhance the longitudinal structure function $F_L$, and suppress the transverse structure function $F_1$. We demonstrate that strong nuclear effects in $\sigma_A/\sigma_D$ and $R_A/R_D$, recently observed by HERMES Collaboration, can be explained in terms of the nuclear enhanced power corrections.Comment: Latex, 10 pages including 3 figure

A new approach to parton recombination in a QCD evolution equation

Parton recombination is reconsidered in perturbation theory without using the AGK cutting rules in the leading order of the recombination. We use time-ordered perturbation theory to sum the cut diagrams, which are neglected in the GLR evolution equation. We present a set of new evolution equations including parton recombination.Comment: 25 pages, LaTex, 10 PS figures, submmitted to Nucl. Phys.

Shear viscosity coefficient of magnetized QCD medium with anomalous magnetic moments near chiral phase transition

We study the properties of the shear viscosity coefficient of quark matter near the chiral phase transition at finite temperature and chemical potential, and the kinds of high temperature, high density and strong magnetic field background might be generated by high-energy heavy ion collisions. The strong magnetic field induces anisotropy, that is, the quantization of Landau energy levels in phase space. If the magnetic field is strong enough, it will interfere with significant QCD phenomena, such as the generation of dynamic quark mass, which may affect the transport properties of quark matter. The inclusion of the anomalous magnetic moments (AMM) of the quarks at finite density into the NJL model gives rise to additional spin polarization magnetic effects. As the inclusion of AMM of the quarks leads to inverse magnetic catalysis around the transition temperature, we will systematically study the thermodynamic phase transition characteristics of shear viscosity coefficient in QCD media near the phase boundary. The shear viscosity coefficient of the dissipative fluid system can be decomposed into five different components as the strong magnetic field exists. The influences of the order of chiral phase transition and the critical endpoint on dissipative phenomena in such a magnetized medium are quantitatively investigated. It is found that ${\eta}_{1}$, ${\eta}_{2}$, ${\eta}_{3}$, and ${\eta}_{4}$ all increase with temperature. For first-order phase transitions, ${\eta}_{1}$, ${\eta}_{2}$, ${\eta}_{3}$, and ${\eta}_{4}$ exhibit discontinuous characteristics.Comment: 22 pages, 10 figure