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Tian Liang

Publications and source records attributed to Tian Liang.

At least 55 records · Page 3Linked to original sources
arXiv2024

CriticBench: Benchmarking LLMs for Critique-Correct Reasoning

The ability of Large Language Models (LLMs) to critique and refine their reasoning is crucial for their application in evaluation, feedback provision, and self-improvement. This paper introduces CriticBench, a comprehensive benchmark designed to assess LLMs' abilities to critique and rectify their reasoning across a variety of tasks. CriticBench encompasses five reasoning domains: mathematical, commonsense, symbolic, coding, and algorithmic. It compiles 15 datasets and incorporates responses from three LLM families. Utilizing CriticBench, we evaluate and dissect the performance of 17 LLMs in generation, critique, and correction reasoning, i.e., GQC reasoning. Our findings reveal: (1) a linear relationship in GQC capabilities, with critique-focused training markedly enhancing performance; (2) a task-dependent variation in correction effectiveness, with logic-oriented tasks being more amenable to correction; (3) GQC knowledge inconsistencies that decrease as model size increases; and (4) an intriguing inter-model critiquing dynamic, where stronger models are better at critiquing weaker ones, while weaker models can surprisingly surpass stronger ones in their self-critique. We hope these insights into the nuanced critique-correct reasoning of LLMs will foster further research in LLM critique and self-improvement.

cs.CL↗
arXiv2024

Local Sobolev-Poincare imbedding domains

In this article, we study local Sobolev-Poincaré imbedding domains. The main result reads as below. \begin{enumerate} \item for $1\leq p\leq n$, a bounded uniform domain is also a local Sobolev-Poincaré imbedding domain of order $p$; conversely a local Sobolev-Poincaré imbedding domain of order $p$ is locally linearly connected $(LLC)$. A uniform domain is $(LLC)$. Conversely, with some very weak connecting assumption, a $(LLC)$ domain is uniform. \item for $n<p<\fz$, a bounded domain is a local Sobolev-Poincaré imbedding domain of order $p$ if and only if it is an $α$-cigar domain for $α=(p-n)/(p-1)$. Hence, a domain is a local Sobolev-Poincaré imbedding domain of oder $p$ if and only if it is a (global) Sobolev-Poincaré imbedding domain. \end{enumerate}

math.FA↗
arXiv2024

A $(ϕ_n, ϕ)$-Poincaré inequality on John domain

Given a bounded domain $Ω\subset {\mathbb R}^{n}$ with $n\ge2$, let $ϕ$ is a Young function satisfying the doubling condition with the constant $K_ϕ<2^{n}$. If $Ω$ is a John domain, we show that $Ω$ supports a $(ϕ_{n}, ϕ)$-Poincaré inequality. Conversely, assume additionally that $Ω$ is simply connected domain when $n=2$ or a bounded domain which is quasiconformally equivalent to some uniform domain when $n\ge3$. If $Ω$ supports a $(ϕ_n, ϕ)$-Poincaré inequality, we show that it is a John domain.

math.FA↗
arXiv2023

Exploring Human-Like Translation Strategy with Large Language Models

Large language models (LLMs) have demonstrated impressive capabilities in general scenarios, exhibiting a level of aptitude that approaches, in some aspects even surpasses, human-level intelligence. Among their numerous skills, the translation abilities of LLMs have received considerable attention. Compared to typical machine translation that focuses solely on source-to-target mapping, LLM-based translation can potentially mimic the human translation process which might take preparatory steps to ensure high-quality translation. This work explores this possibility by proposing the MAPS framework, which stands for Multi-Aspect Prompting and Selection. Specifically, we enable LLMs first to analyze the given source sentence and induce three aspects of translation-related knowledge: keywords, topics, and relevant demonstrations to guide the final translation process. Moreover, we employ a selection mechanism based on quality estimation to filter out noisy and unhelpful knowledge. Both automatic (3 LLMs x 11 directions x 2 automatic metrics) and human evaluation (preference study and MQM) demonstrate the effectiveness of MAPS. Further analysis shows that by mimicking the human translation process, MAPS reduces various translation errors such as hallucination, ambiguity, mistranslation, awkward style, untranslated text, and omission. Source code is available at https://github.com/zwhe99/MAPS-mt.

cs.CL↗
arXiv2023

Leveraging Word Guessing Games to Assess the Intelligence of Large Language Models

The automatic evaluation of LLM-based agent intelligence is critical in developing advanced LLM-based agents. Although considerable effort has been devoted to developing human-annotated evaluation datasets, such as AlpacaEval, existing techniques are costly, time-consuming, and lack adaptability. In this paper, inspired by the popular language game ``Who is Spy'', we propose to use the word guessing game to assess the intelligence performance of LLMs. Given a word, the LLM is asked to describe the word and determine its identity (spy or not) based on its and other players' descriptions. Ideally, an advanced agent should possess the ability to accurately describe a given word using an aggressive description while concurrently maximizing confusion in the conservative description, enhancing its participation in the game. To this end, we first develop DEEP to evaluate LLMs' expression and disguising abilities. DEEP requires LLM to describe a word in aggressive and conservative modes. We then introduce SpyGame, an interactive multi-agent framework designed to assess LLMs' intelligence through participation in a competitive language-based board game. Incorporating multi-agent interaction, SpyGame requires the target LLM to possess linguistic skills and strategic thinking, providing a more comprehensive evaluation of LLMs' human-like cognitive abilities and adaptability in complex communication situations. The proposed evaluation framework is very easy to implement. We collected words from multiple sources, domains, and languages and used the proposed evaluation framework to conduct experiments. Extensive experiments demonstrate that the proposed DEEP and SpyGame effectively evaluate the capabilities of various LLMs, capturing their ability to adapt to novel situations and engage in strategic communication.

cs.CL↗
arXiv2023

ParroT: Translating during Chat using Large Language Models tuned with Human Translation and Feedback

Large language models (LLMs) like ChatGPT have exhibited remarkable abilities on a wide range of natural language processing~(NLP) tasks, including various machine translation abilities accomplished during chat. However, these models are only accessible through restricted APIs, which creates barriers to new research and advancements in the field. Therefore, we propose ParroT, a framework to enhance and regulate the translation abilities during chat based on open-source LLMs (e.g., LLaMA), human-written translation and feedback data. Specifically, ParroT reformulates translation data into the instruction-following style, and introduces a "$\mathbf{Hint}$" field for incorporating extra requirements to regulate the translation process. Accordingly, we propose three instruction types for finetuning ParroT models, including translation instruction, contrastive instruction, and error-guided instruction. Experiments on Flores subsets and WMT22 test sets suggest that translation instruction improves the translation performance of vanilla LLMs significantly while error-guided instruction can lead to further improvement, which demonstrates the importance of learning from low-quality translations annotated by humans. We also demonstrate the potential of automatic evaluation tools in providing quality information of translations, when constructing error-guided instructions for directions that lack human annotation data. Please refer to our Github project for more implementation details: https://github.com/wxjiao/ParroT

cs.CL↗
arXiv2023

A resolvent-based prediction framework for incompressible turbulent channel flow with limited measurements

A new resolvent-based method is developed to predict the space-time properties of the flow field. To overcome the deterioration of the prediction accuracy with the increasing distance between the measurements and predictions in the Resolvent-Based Estimation (RBE), the newly proposed method utilizes the RBE to estimate the relative energy distribution near the wall rather than the absolute energy directly estimated from the measurements. Using this extra information from RBE, the new method modifies the energy distribution of the spatially uniform and uncorrelated forcing that drives the flow system by minimizing the norm of the cross-spectral density (CSD) tensor of the error matrix in the near-wall region in comparison with the RBE-estimated one, and therefore it is named as the Resolvent-informed White-noise-based Estimation (RWE) method. For validation, three time-resolved direct numerical simulation (DNS) datasets with the friction Reynolds numbers $Re_τ= 180$, 550, and 950 are generated, with various locations of measurements ranging from the near-wall region ($y^+ = 40$) to the upper bound of the logarithmic region ($y/h \approx 0.2$) for the predictions. Besides the RWE, three existing methods, i.e., the RBE, the $λ$-model, and the White-noise-Based Estimation (WBE), are also included for the validation. The performance of the RBE and $λ$-model in predicting the energy spectra shows a strong dependence on the measurement locations. The newly proposed RWE shows a low sensitivity on $Re_τ$ and the measurement locations, which may range from the near-wall region to the upper bound of the logarithmic region, and has a high accuracy in predicting the energy spectra.

physics.flu-dyn↗
arXiv2023

A new smoothed particle hydrodynamics method based on high-order moving-least-square targeted essentially non-oscillatory scheme for compressible flows

In this study, we establish a hybrid high-order smoothed particle hydrodynamics (SPH) framework (MLS-TENO-SPH) for compressible flows with discontinuities, which is able to achieve genuine high-order convergence in smooth regions and also capture discontinuities well in non-smooth regions. The framework can be either fully Lagrangian, Eulerian or realizing arbitary-Lagrangian-Eulerian (ALE) feature enforcing the isotropic particle distribution in specific cases. In the proposed framework, the computational domain is divided into smooth regions and non-smooth regions, and these two regions are determined by a strong scale separation strategy in the targeted essentially non-oscillatory (TENO) scheme. In smooth regions, the moving-least-square (MLS) approximation is used for evaluating high-order derivative operator, which is able to realize genuine high-order construction; in non-smooth regions, the new TENO scheme based on Vila's framework with several new improvements will be deployed to capture discontinuities and high-wavenumber flow scales with low numerical dissipation. The present MLS-TENO-SPH method is validated with a set of challenging cases based on the Eulerian, Lagrangian or ALE framework. Numerical results demonstrate that the MLS-TENO-SPH method features lower numerical dissipation and higher efficiency than the conventional method, and can restore genuine high-order accuracy in smooth regions. Overall, the proposed framework serves as a new exploration in high-order SPH methods, which are potential for compressible flow simulations with shockwaves.

physics.flu-dyn↗
arXiv2023

A $(ϕ_\frac{n}{s}, ϕ)$-Poincaré inequality in John domain

Let $Ω$ be a bounded domain in $\mathbb{R}^n$ with $n\ge2$ and $s\in(0,1)$. Assume that $ϕ: [0, \infty) \to [0, \infty)$ be a Young function obeying the doubling condition with the constant $K_ϕ<2^{\frac{n}{s}}$. We demonstrate that $Ω$ supports a $(ϕ_\frac{n}{s}, ϕ)$-Poincaré inequality if it is is a John domain. Alternately, assume further that $Ω$ is a bounded domain that is quasiconformally equivalent to some uniform domain when $n\ge3$ or a simply connected domain when $n=2$. We demonstrate $Ω$ is a John domain if a $(ϕ_\frac{n}{s}, ϕ)$-Poincaré inequality holds.

math.FA↗
arXiv2023

A five-point TENO scheme with adaptive dissipation based on a new scale sensor

In this paper, a new five-point targeted essentially non-oscillatory (TENO) scheme with adaptive dissipation is proposed. With the standard TENO weighting strategy, the cut-off parameter $C_T$ determines the nonlinear numerical dissipation of the resultant TENO scheme. Moreover, according to the dissipation-adaptive TENO5-A scheme, the choice of the cut-off parameter $C_T$ highly depends on the effective scale sensor. However, the scale sensor in TENO5-A can only roughly detect the discontinuity locations instead of evaluating the local flow wavenumber as desired. In this work, a new five-point scale sensor, which can estimate the local flow wavenumber accurately, is proposed to further improve the performance of TENO5-A. In combination with a hyperbolic tangent function, the new scale sensor is deployed to the TENO5-A framework for adapting the cut-off parameter $C_T$, i.e., the local nonlinear dissipation, according to the local flow wavenumber. Overall, sufficient numerical dissipation is generated to capture discontinuities, whereas a minimum amount of dissipation is delivered for better resolving the smooth flows. A set of benchmark cases is simulated to demonstrate the performance of the new TENO5-A scheme.

physics.flu-dyn↗
arXiv2022

A novel buckling pattern in periodically porous elastomers with applications to elastic wave regulations

This paper proposes a new metamaterial structure consisting of a periodically porous elastomer with pore coatings. This design enables us to engender finite deformation by a contactless load. As a case study, we apply thermal load to the pore coating and carry out a finite element analysis to probe instabilities and the associated phononic properties. It turns out that a novel buckling mode, preserving the nature of surface wrinkling in tubular structures, can be induced under a plane-strain setup, and a smaller size of the unit cell is attained compared to the counterpart of traditional buckled profile in soft porous elastomers. In particular, this buckling pattern is able to produce several bandgaps in different frequency ranges as the macroscopic mean strain increases. We further introduce a metallic core as local resonator, and the updated metamaterial allows a low-frequency bandgap, the bandgap width of which can be estimated by a simplified theoretical model. As more free parameters are involved in the structure, we perform a detailed parametric study to elucidate the influences of the modulus ratio between coating and matrix, the porosity, the core radius, and the macroscopic mean strain on the buckling initiation and the evolution of bandgap. Remarkably, a stiffer surface coating is prone to enhance the stability of the structure, which is contrary to existing results in film/substrate bilayers. It is expected that the current study could shed light on new insight into pattern formation and wave manipulation in porous elastomers.

cond-mat.soft↗
arXiv2022

A class of new high-order finite-volume TENO schemes for hyperbolic conservation laws with unstructured meshes

The recently proposed high-order TENO scheme [Fu et al., Journal of Computational Physics, 305, pp.333-359] has shown great potential in predicting complex fluids owing to the novel weighting strategy, which ensures the high-order accuracy, the low numerical dissipation, and the sharp shock-capturing capability. However, the applications are still restricted to simple geometries with Cartesian or curvilinear meshes. In this work, a new class of high-order shock-capturing TENO schemes for unstructured meshes are proposed. Similar to the standard TENO schemes and some variants of WENO schemes, the candidate stencils include one large stencil and several small third-order stencils. Following a strong scale-separation procedure, a tailored novel ENO-like stencil selection strategy is proposed such that the high-order accuracy is restored in smooth regions by selecting the candidate reconstruction on the large stencil while the ENO property is enforced near discontinuities by adopting the candidate reconstruction from smooth small stencils. The nonsmooth stencils containing genuine discontinuities are explicitly excluded from the final reconstruction, leading to excellent numerical stability. Different from the WENO concept, such unique sharp stencil selection retains the low numerical dissipation without sacrificing the shock-capturing capability. The newly proposed framework enables arbitrarily high-order TENO reconstructions on unstructured meshes. For conceptual verification, the TENO schemes with third- to sixth-order accuracy are constructed. Without parameter tuning case by case, the performance of the proposed TENO schemes is demonstrated by examining a set of benchmark cases with broadband flow length scales.

math.NA↗
arXiv2021

Berry curvature generation detected by Nernst responses in ferroelectric Weyl semimetal

The quest for nonmagnetic Weyl semimetals with high tunability of phase has remained a demanding challenge. As the symmetry breaking control parameter, the ferroelectric order can be steered to turn on/off the Weyl semimetals phase, adjust the band structures around the Fermi level, and enlarge/shrink the momentum separation of Weyl nodes which generate the Berry curvature as the emergent magnetic field. Here, we report the realization of a ferroelectric nonmagnetic Weyl semimetal based on indium doped Pb1 xSnxTe alloy where the underlying inversion symmetry as well as mirror symmetry is broken with the strength of ferroelectricity adjustable via tuning indium doping level and Sn/Pb ratio. The transverse thermoelectric effect, i.e., Nernst effect both for out of plane and in plane magnetic field geometry, is exploited as a Berry curvature sensitive experimental probe to manifest the generation of Berry curvature via the redistribution of Weyl nodes under magnetic fields. The results demonstrate a clean non-magnetic Weyl semimetal coupled with highly tunable ferroelectric order, providing an ideal platform for manipulating the Weyl fermions in nonmagnetic system.

cond-mat.mtrl-sci↗
arXiv2020

AIM 2020 Challenge on Learned Image Signal Processing Pipeline

This paper reviews the second AIM learned ISP challenge and provides the description of the proposed solutions and results. The participating teams were solving a real-world RAW-to-RGB mapping problem, where to goal was to map the original low-quality RAW images captured by the Huawei P20 device to the same photos obtained with the Canon 5D DSLR camera. The considered task embraced a number of complex computer vision subtasks, such as image demosaicing, denoising, white balancing, color and contrast correction, demoireing, etc. The target metric used in this challenge combined fidelity scores (PSNR and SSIM) with solutions' perceptual results measured in a user study. The proposed solutions significantly improved the baseline results, defining the state-of-the-art for practical image signal processing pipeline modeling.

cs.CV↗
arXiv2019

Formal Verification of Dynamic and Stochastic Behaviors for Automotive Systems

Formal analysis of functional and non-functional requirements is crucial in automotive systems. The behaviors of those systems often rely on complex dynamics as well as on stochastic behaviors. We have proposed a probabilistic extension of Clock Constraint Specification Language, called PrCCSL,for specification of (non)-functional requirements and proved the correctness of requirements by mapping the semantics of the specifications into UPPAAL models. Previous work is extended in this paper by including an extension of PrCCSL, called PrCCSL*, for specification of stochastic and dynamic system behaviors, as well as complex requirements related to multiple events. To formally analyze the system behaviors/requirements specified in PrCCSL*, the PrCCSL* specifications are translated into stochastic UPPAAL models for formal verification. We implement an automatic translation tool, namely ProTL, which can also perform formal analysis on PrCCSL* specifications using UPPAAL-SMC as an analysis backend. Our approach is demonstrated on two automotive systems case studies.

cs.SE↗
arXiv2019

Orlicz-Besov extension and Ahlfors $n$-regular domains

Let $n\ge2$ and $ϕ: [0,\fz) \to [0,\infty)$ be a Young's function satisfying $\sup_{x>0} \int_0^1\frac{ϕ( t x)}{ ϕ(x)}\frac{dt}{t^{n+1} }<\infty. $ We show that Ahlfors $n$-regular domains are Besov-Orlicz ${\dot {\bf B}}^ϕ$ extension domains, which is necessary to guarantee the nontrivially of ${\dot {\bf B}}^ϕ$. On the other hand, assume that $ϕ$ grows sub-exponentially at $\fz$ additionally. If $Ω$ is a Besov-Orlicz ${\dot {\bf B}}^ϕ$ extension domain, then it must be Ahlfors $n$-regular.

math.FA↗
arXiv2019

Platform of chiral Majorana edge modes and its quantum transport phenomena

We propose a method to create two-dimensional topological superconductors with a heterostructure of ferromagnet (FM), topological insulator (TI) thin film and superconductor, in which the two surfaces of the TI thin film are treated as a two-dimensional system. One of surfaces is superconducting due to proximity effect and the other feels an exchange field from the FM. We show that there is a topological phase with single chiral Majorana edge mode that exists in readily achievable parameter regions and does not require magnetization to be small. An experimental setup is proposed based on our model to uniquely determine the existence of Majorana chiral modes using a Josephson junction. Also, we show that multiple chiral Majorana edge modes may appear when unconventional superconductors are used.

cond-mat.supr-con↗