The Riemannian Geometry of Deep Generative Models

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to generate analogies, i.e., to transport a change in one data point into a semantically similar change of another data point. Our experiments on real image data show that the manifolds learned by deep generative models, while nonlinear, are surprisingly close to zero curvature. The practical implication is that linear paths in the latent space closely approximate geodesics on the generated manifold. However, further investigation into this phenomenon is warranted, to identify if there are other architectures or datasets where curvature plays a more prominent role. We believe that exploring the Riemannian geometry of deep generative models, using the tools developed in this paper, will be an important step in understanding the high-dimensional, nonlinear spaces these models learn.Comment: 9 page

The changing role of gold in the International Monetary System

Special issue on goldGold standard ; International finance ; Gold reserves

Central bank policy towards inflation

Inflation (Finance) ; Monetary theory ; Pacific Area ; Banks and banking, Central

Small molecule inhibitors against PD-1/PD-L1 immune checkpoints and current methodologies for their development: a review

Programmed death-1/programmed death ligand-1 (PD-1/PD-L1) based immunotherapy is a revolutionary cancer therapy with great clinical success. The majority of clinically used PD-1/PD-L1 inhibitors are monoclonal antibodies but their applications are limited due to their poor oral bioavailability and immune-related adverse effects (irAEs). In contrast, several small molecule inhibitors against PD-1/PD-L1 immune checkpoints show promising blockage effects on PD-1/PD-L1 interactions without irAEs. However, proper analytical methods and bioassays are required to effectively screen small molecule derived PD-1/PD-L1 inhibitors. Herein, we summarize the biophysical and biochemical assays currently employed for the measurements of binding capacities, molecular interactions, and blocking effects of small molecule inhibitors on PD-1/PD-L1. In addition, the discovery of natural products based PD-1/PD-L1 antagonists utilizing these screening assays are reviewed. Potential pitfalls for obtaining false leading compounds as PD-1/PD-L1 inhibitors by using certain binding bioassays are also discussed in this review

Dynamical invariants in non-Markovian quantum state diffusion equation

We find dynamical invariants for open quantum systems described by the non-Markovian quantum state diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with from bi-orthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamic invariants to reverse-engineering a Hamiltonian that is capable of driving the system to the target state, providing a novel way to design control strategy for open quantum systems.Comment: 6 pages, 2 figure

The Influence of in-medium NN cross-sections, symmetry potential and impact parameter on the isospin observables

We explore the influence of in-medium nucleon-nucleon cross section, symmetry potential and impact parameter on isospin sensitive observables in intermediate-energy heavy-ion collisions with the ImQMD05 code, a modified version of Quantum Molecular Dynamics model. At incident velocities above the Fermi velocity, we find that the density dependence of symmetry potential plays a more important role on the double neutron to proton ratio $DR(n/p)$ and the isospin transport ratio $R_i$ than the in-medium nucleon-nucleon cross sections, provided that the latter are constrained to a fixed total NN collision rate. We also explore both $DR(n/p)$ and $R_i$ as a function of the impact parameter. Since the copious production of intermediate mass fragments is a distinguishing feature of intermediate-energy heavy-ion collisions, we examine the isospin transport ratios constructed from different groups of fragments. We find that the values of the isospin transport ratios for projectile rapidity fragments with $Z\ge20$ are greater than those constructed from the entire projectile rapidity source. We believe experimental investigations of this phenomenon can be performed. These may provide significant tests of fragmentation time scales predicted by ImQMD calculations.Comment: 24 pages, 9 figures, to be published in Phys. Rev.

Octa: Omissions and Conflicts in Target-Aspect Sentiment Analysis

Sentiments in opinionated text are often determined by both aspects and target words (or targets). We observe that targets and aspects interrelate in subtle ways, often yielding conflicting sentiments. Thus, a naive aggregation of sentiments from aspects and targets treated separately, as in existing sentiment analysis models, impairs performance. We propose Octa, an approach that jointly considers aspects and targets when inferring sentiments. To capture and quantify relationships between targets and context words, Octa uses a selective self-attention mechanism that handles implicit or missing targets. Specifically, Octa involves two layers of attention mechanisms for, respectively, selective attention between targets and context words and attention over words based on aspects. On benchmark datasets, Octa outperforms leading models by a large margin, yielding (absolute) gains in accuracy of 1.6% to 4.3%.Comment: Accepted by Findings of EMNLP 202

Intraband and interband spin-orbit torques in non-centrosymmetric ferromagnets

Intraband and interband contributions to the current-driven spin-orbit torque in magnetic materials lacking inversion symmetry are theoretically studied using Kubo formula. In addition to the current-driven field-like torque ${\bf T}_{\rm FL}= \tau_{\rm FL}{\bf m}\times{\bf u}_{\rm so}$ (${\bf u}_{\rm so}$ being a unit vector determined by the symmetry of the spin-orbit coupling), we explore the intrinsic contribution arising from impurity-independent interband transitions and producing an anti-damping-like torque of the form ${\bf T}_{\rm DL}= \tau_{\rm DL}{\bf m}\times({\bf u}_{\rm so}\times{\bf m})$. Analytical expressions are obtained in the model case of a magnetic Rashba two-dimensional electron gas, while numerical calculations have been performed on a dilute magnetic semiconductor (Ga,Mn)As modeled by the Kohn-Luttinger Hamiltonian exchanged coupled to the Mn moments. Parametric dependences of the different torque components and similarities to the analytical results of the Rashba two-dimensional electron gas in the weak disorder limit are described.Comment: 10 pages, 5 figure