arXiv subjects

Jiahao Xu

Publications and source records attributed to Jiahao Xu.

76 records · Page 5Linked to original sources

arXiv2020

DisenE: Disentangling Knowledge Graph Embeddings

Knowledge graph embedding (KGE), aiming to embed entities and relations into low-dimensional vectors, has attracted wide attention recently. However, the existing research is mainly based on the black-box neural models, which makes it difficult to interpret the learned representation. In this paper, we introduce DisenE, an end-to-end framework to learn disentangled knowledge graph embeddings. Specially, we introduce an attention-based mechanism that enables the model to explicitly focus on relevant components of entity embeddings according to a given relation. Furthermore, we introduce two novel regularizers to encourage each component of the entity representation to independently reflect an isolated semantic aspect. Experimental results demonstrate that our proposed DisenE investigates a perspective to address the interpretability of KGE and is proved to be an effective way to improve the performance of link prediction tasks.

cs.CL↗

arXiv2020

High-resolution Monte Carlo study of the order-parameter distribution of the three-dimensional Ising model

We apply extensive Monte Carlo simulations to study the probability distribution $P(m)$ of the order parameter $m$ for the simple cubic Ising model with periodic boundary condition at the transition point. Sampling is performed with the Wolff cluster flipping algorithm, and histogram reweighting together with finite-size scaling analyses are then used to extract a precise functional form for the probability distribution of the magnetization, $P(m)$, in the thermodynamic limit. This form should serve as a benchmark for other models in the three-dimensional Ising Universality class.

physics.comp-ph↗

arXiv2019

Finite size scaling for a first order transition where a continuous symmetry is broken: The spin-flop transition in the 3D XXZ Heisenberg antiferromagnet

Finite size scaling for a first order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field in order to study the finite size behavior on a $L \times L \times L$ simple cubic lattice for the first order "spin-flop" transition between the Ising-like antiferromagnetic state and the canted, XY-like state. Our theory predicts that for large linear dimension $L$ the field dependence of all moments of the order parameters as well as the fourth-order cumulants exhibit universal intersections. Corrections to leading order should scale as the inverse volume. The values of these intersections at the spin-flop transition point can be expressed in terms of a factor $q$ that characterizes the relative degeneracy of the ordered phases. Our theory yields $q=π$, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality can be invoked for first order phase transitions.

physics.comp-ph↗

arXiv2018

Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model

While the 3d Ising model has defied analytic solution, various numerical methods like Monte Carlo, MCRG and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g. logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc = 0.221 654 626(5) and the critical exponent of the correlation length ν = 0.629 912(86) with precision that exceeds all previous Monte Carlo estimates.

physics.comp-ph↗