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Zhongyang Li

Publications and source records attributed to Zhongyang Li.

At least 55 records · Page 3Linked to original sources

ReCo: Reliable Causal Chain Reasoning via Structural Causal Recurrent Neural Networks

Causal chain reasoning (CCR) is an essential ability for many decision-making AI systems, which requires the model to build reliable causal chains by connecting causal pairs. However, CCR suffers from two main transitive problems: threshold effect and scene drift. In other words, the causal pairs to be spliced may have a conflicting threshold boundary or scenario. To address these issues, we propose a novel Reliable Causal chain reasoning framework~(ReCo), which introduces exogenous variables to represent the threshold and scene factors of each causal pair within the causal chain, and estimates the threshold and scene contradictions across exogenous variables via structural causal recurrent neural networks~(SRNN). Experiments show that ReCo outperforms a series of strong baselines on both Chinese and English CCR datasets. Moreover, by injecting reliable causal chain knowledge distilled by ReCo, BERT can achieve better performances on four downstream causal-related tasks than BERT models enhanced by other kinds of knowledge.

cs.AI↗

Asymptotics of pure dimer coverings on rail-yard graphs

We study asymptotic limit of random pure dimer coverings on rail yardgraphs when the mesh sizes of the graphs go to 0. Each pure dimer covering correspondsto a sequence of interlacing partitions starting with an empty partition and ending inan empty partition. Under the assumption that the probability of each dimer covering isproportional to the product of weights of present edges, we obtain the limit shape (Law ofLarge Numbers) of the rescaled height function and the convergence of unrescaled heightfluctuation to a diffeomorphic image of Gaussian Free Field (Central Limit Theorem); an-swering a question in [6]. Applications include the limit shape and height fluctuations forpure steep tilings ([8]) and pyramid partitions ([20, 35, 36, 37]). The technique to obtainthese results is to analyze a class of Mcdonald processes which involve dual partitions as well.

math.PR↗

Brownian snails with removal: epidemics in diffusing populations

Two stochastic models of susceptible/infected/removed (SIR) type are introduced for the spread of infection through a spatially-distributed population. Individuals are initially distributed at random in space, and they move continuously according to independent diffusion processes. The disease may pass from an infected individual to an uninfected individual when they are sufficiently close. Infected individuals are permanently removed at some given rate $α$. Such processes are reminiscent of so-called frog models, but differ through the action of removal, as well as the fact that frogs jump whereas snails slither. Two models are studied here, termed the `delayed diffusion' and the `diffusion' models. In the first, individuals are stationary until they are infected, at which time they begin to move; in the second, all individuals start to move at the initial time $0$. Using a perturbative argument, conditions are established under which the disease infects a.s. only finitely many individuals. It is proved for the delayed diffusion model that there exists a critical value $α_c\in(0,\infty)$ for the survival of the epidemic.

math.PR↗

Limit shape of perfect matchings on rail-yard graphs

We obtain limit shape of perfect matchings on a large class of rail-yard graphs with right boundary condition given by the empty partition, and left boundary condition given by either by a staircase partition with constant density or a piecewise partition with densities either 1 or 0. We prove the parametric equations for the frozen boundary, and find conditions under which the frozen boundary is a cloud curve, or a union of disjoint cloud curves.

math.CO↗

Site Percolation on Planar Graphs

We prove that for a non-amenable, locally finite, connected, transitive, planar graph with one end, any automorphism invariant site percolation on the graph does not have exactly 1 infinite 1-cluster and exactly 1 infinite 0-cluster a.s. If we further assume that the site percolation is insertion-tolerant and a.s.~there exists a unique infinite 0-cluster, then a.s.~there are no infinite 1-clusters. The proof is based on the analysis of a class of delicately constructed interfaces between clusters and contours. Applied to the case of i.i.d.~Bernoulli site percolation on infinite, connected, locally finite, transitive, planar graphs, these results solve two conjectures of Benjamini and Schramm (Conjectures 7 and 8 in \cite{bs96}) in 1996.

math.PR↗

Pressure-induced superconductivity reentrant in transition metal dichalcogenide TiSe2

Through either elements intercalation or application of pressure, transition metal dichalcogenide 1T-TiSe2 exhibits superconductivity in proximity to a charge density wave (CDW) quantum critical point (QCP), thus providing an ideal avenue to study the correlation between the two symmetry-breaking exotic quantum electronic states. We report herein that, in addition to the well-known superconducting dome that emerges within the low pressure range of 2 - 4 GPa and peaks with the maximal Tc of about 1.8 K, the pressure induces another separate superconducting transition starting around 15 GPa with a substantially higher Tc that reaches 5.6 K at about 21.5 GPa. The high-pressure X-ray diffraction and Raman spectroscopy measurements unveil that the superconductivity reentrant is caused by a first-order structural phase transition (from P-3m1 space group to Pnma space group), which is also supported by the density functional theory calculation. A comparative theoretical calculation also reveals that the conventional phonon-mediated mechanism can account for the superconductivity of 1T-TiSe2 under low pressure, while the electron-phonon coupling of 4O-TiSe2 under high pressure is too weak to induce the superconductivity with a Tc as high as 5.6 K. This implies that the emergent superconductivity in the 4O-TiSe2 may have an unconventional origin. Our finding would open a new window toward the discovery of more exotic quantum states in transition metal dichalcogenides via high pressure.

cond-mat.supr-con↗

Pressure-induced ideal Weyl semimetal state in the layered antiferromagnet EuCd2As2

The rich nontrivial topological phases rooted in the interplay between magnetism and topology in the layered antiferromagnet EuCd2As2 have captured vast attention, especially the ideal Weyl semimetal state realized in the spin-polarized ferromagnetic (FM) structure driven by a moderate external magnetic field. In this work, combining high-pressure magnetotransport measurements, structure chracterizations and first principles calculations, we find that application of pressure can also realize the ideal Weyl state in EuCd2As2 through driving the in-plane antiferromagnetic state across an intermediate in-plane FM state then into the out-of-plane FM state. Our high-pressure angle dispersive X-ray diffraction and X-ray absorption near-edge spectroscopy measurements excluded structure transition and/or change of Eu2+ valence state as the sources for the magnetic phase transitions. Alternatively, the apparently reduced axial ratio (c/a) and compressed Eu-layer space distance should play important roles. Our result provides an alternative way to realize the ideal Weyl semimetal state in EuCd2As2 and would be instructive for the exploration of exotic topological properties in such layered magnetic topological phase with strongly competing magnetic exchanges by using high pressure.

cond-mat.mtrl-sci↗

On the coercivity condition in the learning of interacting particle systems

In the learning of systems of interacting particles or agents, coercivity condition ensures identifiability of the interaction functions, providing the foundation of learning by nonparametric regression. The coercivity condition is equivalent to the strictly positive definiteness of an integral kernel arising in the learning. We show that for a class of interaction functions such that the system is ergodic, the integral kernel is strictly positive definite, and hence the coercivity condition holds true.

stat.ML↗

Schur function at generic points and limit shape of perfect matchings on contracting square hexagon lattices with piecewise boundary conditions

We obtain a new formula to relate the value of a Schur polynomial with variables $(x_1,\ldots,x_N)$ with values of Schur polynomials at $(1,\ldots,1)$. This allows to study the limit shape of perfect matchings on a square hexagon lattice with periodic weights and piecewise boundary conditions. In particular, when the edge weights satisfy certain conditions, asymptotics of the Schur function imply that the liquid region of the model in the scaling limit has multiple connected components, while the frozen boundary consists of disjoint cloud curves.

math.PR↗

CausalBERT: Injecting Causal Knowledge Into Pre-trained Models with Minimal Supervision

Recent work has shown success in incorporating pre-trained models like BERT to improve NLP systems. However, existing pre-trained models lack of causal knowledge which prevents today's NLP systems from thinking like humans. In this paper, we investigate the problem of injecting causal knowledge into pre-trained models. There are two fundamental problems: 1) how to collect various granularities of causal pairs from unstructured texts; 2) how to effectively inject causal knowledge into pre-trained models. To address these issues, we extend the idea of CausalBERT from previous studies, and conduct experiments on various datasets to evaluate its effectiveness. In addition, we adopt a regularization-based method to preserve the already learned knowledge with an extra regularization term while injecting causal knowledge. Extensive experiments on 7 datasets, including four causal pair classification tasks, two causal QA tasks and a causal inference task, demonstrate that CausalBERT captures rich causal knowledge and outperforms all pre-trained models-based state-of-the-art methods, achieving a new causal inference benchmark.

cs.CL↗

Guided Generation of Cause and Effect

We present a conditional text generation framework that posits sentential expressions of possible causes and effects. This framework depends on two novel resources we develop in the course of this work: a very large-scale collection of English sentences expressing causal patterns CausalBank; and a refinement over previous work on constructing large lexical causal knowledge graphs Cause Effect Graph. Further, we extend prior work in lexically-constrained decoding to support disjunctive positive constraints. Human assessment confirms that our approach gives high-quality and diverse outputs. Finally, we use CausalBank to perform continued training of an encoder supporting a recent state-of-the-art model for causal reasoning, leading to a 3-point improvement on the COPA challenge set, with no change in model architecture.

cs.CL↗

Limit shape of perfect matchings on contracting bipartite graphs

We consider random perfect matchings on a general class of contracting bipartite graphs by letting certain edge weights be 0 on the contracting square-hexagon lattice in a periodic way. We obtain a deterministic limit shape in the scaling limit. The results can also be applied to prove the existence of multiple disconnected liquid regions for all the contracting square-hexagon lattices with certain edge weights, extending the results proved in [13] for contracting square-hexagon lattices where the number of square rows in each period is either 0 or 1.

math.PR↗

On the identifiability of interaction functions in systems of interacting particles

We address a fundamental issue in the nonparametric inference for systems of interacting particles: the identifiability of the interaction functions. We prove that the interaction functions are identifiable for a class of first-order stochastic systems, including linear systems with general initial laws and nonlinear systems with stationary distributions. We show that a coercivity condition is sufficient for identifiability and becomes necessary when the number of particles approaches infinity. The coercivity is equivalent to the strict positivity of related integral operators, which we prove by showing that their integral kernels are strictly positive definite by using Müntz type theorems.

math.ST↗

Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices

We study asymptotics of perfect matchings on a large class of graphs called the contracting square-hexagon lattice, which is constructed row by row from either a row of a square grid or a row of a hexagonal lattice. We assign the graph periodic edge weights with period $1\times n$, and consider the probability measure of perfect matchings in which the probability of each configuration is proportional to the product of edge weights. We show that the partition function of perfect matchings on such a graph can be computed explicitly by a Schur function depending on the edge weights. By analyzing the asymptotics of the Schur function, we then prove the Law of Large Numbers (limit shape) and the Central Limit Theorem (convergence to the Gaussian free field) for the corresponding height functions. We also show that the distribution of certain type of dimers near the turning corner is the same as the eigenvalues of Gaussian Unitary Ensemble, and that in the scaling limit under the boundary condition that each segment of the bottom boundary grows linearly with respect the dimension of the graph, the frozen boundary is a cloud curve whose number of tangent points to the bottom boundary of the domain depends on the size of the period, as well as the number of segments along the bottom boundary.

math.PR↗

Asymptotics of Schur functions on almost staircase partitions

We study the asymptotics of Schur polynomials with partitions $λ$ which are almost staircase; more precisely, partitions that differ from $((m-1)(N-1),(m-1)(N-2),\ldots,(m-1),0)$ by at most one component at the beginning as $N\rightarrow \infty$, for a positive integer $m\ge 1$ independent of $N$. By applying either determinant formulas or integral representations for Schur functions, we show that $\frac{1}{N}\log \frac{s_λ(u_1,\ldots,u_k, x_{k+1},\ldots,x_N)}{s_λ(x_1,\ldots,x_N)}$ converges to a sum of $k$ single-variable holomorphic functions, each of which depends on the variable $u_i$ for $1\leq i\leq k$, when there are only finitely many distinct $x_i$'s and each $u_i$ is in a neighborhood of $x_i$, as $N\rightarrow\infty$. The results are related to the law of large numbers and central limit theorem for the dimer configurations on contracting square-hexagon lattices with certain boundary conditions.

math.PR↗

Exact Recovery of Community Detection in k-Community Gaussian Mixture Model

We study the community detection problem on a Gaussian mixture model, in which vertices are divided into $k\geq 2$ distinct communities. The major difference in our model is that the intensities for Gaussian perturbations are different for different entries in the observation matrix, and we do not assume that every community has the same number of vertices. We explicitly find the threshold for the exact recovery of the maximum likelihood estimation. Applications include the community detection on hypergraphs.

cs.SI↗

Event Representation Learning Enhanced with External Commonsense Knowledge

Prior work has proposed effective methods to learn event representations that can capture syntactic and semantic information over text corpus, demonstrating their effectiveness for downstream tasks such as script event prediction. On the other hand, events extracted from raw texts lacks of commonsense knowledge, such as the intents and emotions of the event participants, which are useful for distinguishing event pairs when there are only subtle differences in their surface realizations. To address this issue, this paper proposes to leverage external commonsense knowledge about the intent and sentiment of the event. Experiments on three event-related tasks, i.e., event similarity, script event prediction and stock market prediction, show that our model obtains much better event embeddings for the tasks, achieving 78% improvements on hard similarity task, yielding more precise inferences on subsequent events under given contexts, and better accuracies in predicting the volatilities of the stock market.

cs.AI↗

Ising Percolation on Nonamenable Planar Graphs

We study infinite ``$+$'' or ``$-$'' clusters for an Ising model on an connected, transitive, non-amenable, planar, one-ended graph $G$ with finite vertex degree. If the critical percolation probability $p_c^{site}$ for the i.i.d.~Bernoulli site percolation on $G$ is less than $\frac{1}{2}$, we find an explicit region for the coupling constant of the Ising model such that there are infinitely many infinite ``$+$''-clusters and infinitely many infinite ``$-$''-clusters, while the random cluster representation of the Ising model has no infinite 1-clusters. If $p_c^{site}>\frac{1}{2}$, we obtain a lower bound for the critical probability in the random cluster representation of the Ising model in terms of $p_c^{site}$.

math.PR↗