arXiv subjects

Lihan Wang

Publications and source records attributed to Lihan Wang.

28 records · Page 2Linked to original sources

arXiv2022

S$^2$SQL: Injecting Syntax to Question-Schema Interaction Graph Encoder for Text-to-SQL Parsers

The task of converting a natural language question into an executable SQL query, known as text-to-SQL, is an important branch of semantic parsing. The state-of-the-art graph-based encoder has been successfully used in this task but does not model the question syntax well. In this paper, we propose S$^2$SQL, injecting Syntax to question-Schema graph encoder for Text-to-SQL parsers, which effectively leverages the syntactic dependency information of questions in text-to-SQL to improve the performance. We also employ the decoupling constraint to induce diverse relational edge embedding, which further improves the network's performance. Experiments on the Spider and robustness setting Spider-Syn demonstrate that the proposed approach outperforms all existing methods when pre-training models are used, resulting in a performance ranks first on the Spider leaderboard.

cs.CL↗

arXiv2022

Linking-Enhanced Pre-Training for Table Semantic Parsing

Recently pre-training models have significantly improved the performance of various NLP tasks by leveraging large-scale text corpora to improve the contextual representation ability of the neural network. The large pre-training language model has also been applied in the area of table semantic parsing. However, existing pre-training approaches have not carefully explored explicit interaction relationships between a question and the corresponding database schema, which is a key ingredient for uncovering their semantic and structural correspondence. Furthermore, the question-aware representation learning in the schema grounding context has received less attention in pre-training objective.To alleviate these issues, this paper designs two novel pre-training objectives to impose the desired inductive bias into the learned representations for table pre-training. We further propose a schema-aware curriculum learning approach to mitigate the impact of noise and learn effectively from the pre-training data in an easy-to-hard manner. We evaluate our pre-trained framework by fine-tuning it on two benchmarks, Spider and SQUALL. The results demonstrate the effectiveness of our pre-training objective and curriculum compared to a variety of baselines.

cs.CL↗

arXiv2022

Complexity of zigzag sampling algorithm for strongly log-concave distributions

We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each proposed bouncing event requires only one evaluation of partial derivative of the potential, while its convergence rate is dimension independent. Using these properties, we prove that the zigzag sampling algorithm achieves $\varepsilon$ error in chi-square divergence with a computational cost equivalent to $O\bigl(κ^2 d^\frac{1}{2}(\log\frac{1}{\varepsilon})^{\frac{3}{2}}\bigr)$ gradient evaluations in the regime $κ\ll \frac{d}{\log d}$ under a warm start assumption, where $κ$ is the condition number and $d$ is the dimension.

stat.ML↗

arXiv2021

Symplectic Boundary Conditions and Cohomology

We introduce new boundary conditions for differential forms on symplectic manifolds with boundary. These boundary conditions, dependent on the symplectic structure, allows us to write down elliptic boundary value problems for both second-order and fourth-order symplectic Laplacians and establish Hodge theories for the cohomologies of primitive forms on manifolds with boundary. We further use these boundary conditions to define a relative version of the primitive cohomologies and to relate primitive cohomologies with Lefschetz maps on manifolds with boundary. As we show, these cohomologies of primitive forms can distinguish certain Kähler structures of Kähler manifolds with boundary.

math.SG↗

arXiv2021

On explicit $L^2$-convergence rate estimate for piecewise deterministic Markov processes in MCMC algorithms

We establish $L^2$-exponential convergence rate for three popular piecewise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process, and the bouncy particle sampler. Our analysis is based on a variational framework for hypocoercivity, which combines a Poincaré-type inequality in time-augmented state space and a standard $L^2$ energy estimate. Our analysis provides explicit convergence rate estimates, which are more quantitative than existing results.

math.PR↗

arXiv2021

Numerical methods for stochastic differential equations based on Gaussian mixture

We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher order schemes for SDEs based on Itô-Taylor expansion and iterated Itô integrals, the proposed scheme approximates the probability measure $μ(X^{n+1}|X^n=x_n)$ by a mixture of Gaussians. The solution at next time step $X^{n+1}$ is then drawn from the Gaussian mixture with complexity linear in the dimension $d$. This provides a new general strategy to construct efficient high weak order numerical schemes for SDEs.

math.NA↗

arXiv2021

Complexity of randomized algorithms for underdamped Langevin dynamics

We establish an information complexity lower bound of randomized algorithms for simulating underdamped Langevin dynamics. More specifically, we prove that the worst $L^2$ strong error is of order $Ω(\sqrt{d}\, N^{-3/2})$, for solving a family of $d$-dimensional underdamped Langevin dynamics, by any randomized algorithm with only $N$ queries to $\nabla U$, the driving Brownian motion and its weighted integration, respectively. The lower bound we establish matches the upper bound for the randomized midpoint method recently proposed by Shen and Lee [NIPS 2019], in terms of both parameters $N$ and $d$.

math.NA↗

arXiv2020

Dual-comb delay spectroscopy with attometer resolution

Spectroscopy has attracted much attention in molecular detection, biomolecular identification, and chemical analysis for providing accurate measurement. However, it is almost unable to distinguish different sources with overlapped resonances in mixed analytes. Here, we present dual-comb delay spectroscopy to overcome this problem. The introduction of group delay spectroscopy provides a new tool to identify sources that would lead to overlapped resonances in intensity or phase spectroscopy. To obtain sufficiently high spectral resolution and signal-to-noise ratio for achieving reliable group delay spectrum, a probe comb with the wavelengths precisely scaned by a microwave source is applied, leading to attometer-level resolution and million-level signal-to-noise ratio. In an experiment, spectroscopy with an optional resolution up to 1 kHz (8 attometer), an average signal-to-noise ratio surpassing 2,000,000, and a span exceeding 33 nm is demonstrated. Two overlapped resonances from two different sources are clearly differentiated. Our work offers a new perspective for exploring the interaction between matter and light.

physics.ins-det↗

arXiv2019

Gradient estimate for harmonic functions on Kähler manifolds

We prove a sharp integral gradient estimate for harmonic functions on noncompact Kähler manifolds. As application, we obtain a sharp estimate for the bottom of spectrum of the p-Laplacian and prove a splitting theorem for manifolds achieving this estimate.

math.DG↗

arXiv2014

Hodge Theory and Symplectic Boundary Conditions

We study symplectic Laplacians on compact symplectic manifolds with boundary. These Laplacians are associated with symplectic cohomologies of differential forms and can be of fourth-order. We introduce several natural boundary conditions on differential forms and use them to establish Hodge theory by proving various form decomposition and also isomorphisms between the symplectic cohomologies and the spaces of harmonic fields. These novel boundary conditions can be applied in certain cases to study relative symplectic cohomologies and Lefschetz maps between relative de Rham cohomologies. As an application, our results are used to solve boundary value problems of differential forms.

math.SG↗