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Jinhua Cheng

Publications and source records attributed to Jinhua Cheng.

5 recordsLinked to original sources

Benchmarking Multi-Step Legal Reasoning and Analyzing Chain-of-Thought Effects in Large Language Models

Large language models (LLMs) have demonstrated strong reasoning abilities across specialized domains, motivating research into their application to legal reasoning. However, existing legal benchmarks often conflate factual recall with genuine inference, fragment the reasoning process, and overlook the quality of reasoning. To address these limitations, we introduce MSLR, the first Chinese multi-step legal reasoning dataset grounded in real-world judicial decision making. MSLR adopts the IRAC framework (Issue, Rule, Application, Conclusion) to model structured expert reasoning from official legal documents. In addition, we design a scalable Human-LLM collaborative annotation pipeline that efficiently produces fine-grained step-level reasoning annotations and provides a reusable methodological framework for multi-step reasoning datasets. Evaluation of multiple LLMs on MSLR shows only moderate performance, highlighting the challenges of adapting to complex legal reasoning. Further experiments demonstrate that Self-Initiated Chain-of-Thought prompts generated by models autonomously improve reasoning coherence and quality, outperforming human-designed prompts. MSLR contributes to advancing LLM reasoning and Chain-of-Thought strategies and offers open resources for future research. The dataset and code are available at https://github.com/yuwenhan07/MSLR-Bench and https://law.sjtu.edu.cn/flszyjzx/index.html.

cs.AI

On Some Multipliers Related to Discrete Fractional Integrals

This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler's identity, and Dedekind zeta functions of quadratic imaginary fields. Employing Fourier transform techniques, the Hardy--Littlewood circle method, and a discrete analogue of the Stein--Weiss inequality on product space through implication methods, we establish $\ell^p\rightarrow\ell^q$ bounds for these operators. Our results contribute to a deeper understanding of the intricate relationship between number theory and harmonic analysis in discrete domains, offering insights into the convergence behavior of these operators.

math.CA

$L^p$-boundedness of multi-parameter Fourier integral operators

We study a specific class of Fourier integral operators characterized by symbols belonging to the multi-parameter Hörmander class $\mathbf{S}^m(\R^{ n_1} \times \R^{ n_2} \times \cdots \times \R^{n_d} )$, where $n= n_1 + n_2 +\cdots + n_d$. Our investigation focuses on cases where the phase function $Φ(x,ξ)$ can be decomposed into a sum of individual components $Φ_i(x_i,ξ_i)$, with each component satisfying a non-degeneracy condition. We extend the Seeger-Sogge-Stein theorem under the condition that the dimension $ n_i \ge 2$ for each $1\le i \le d$. As a corollary, we obtain the boundedness of multi-parameter Fourier integral operators on local Hardy spaces, Lipschitz spaces, and Sobolev spaces.

math.CA

$L^p$-Boundedness of a Class of Bi-Parameter Pseudo-Differential Operators

In this paper, we explore a specific class of bi-parameter pseudo-differential operators characterized by symbols $σ(x_1,x_2,ξ_1,ξ_2)$ falling within the product-type Hörmander {class} $\mathbf{S}^m_{ρ, δ}$. This classification imposes constraints on the behavior of partial derivatives of $σ$ with respect to both spatial and frequency variables. Specifically, we demonstrate that for each multi-index $α, β$, the inequality $| \partial_ξ^α\partial_x^βσ(x_1,x_2,ξ_1,ξ_2)| \le C_{α, β}(1+|ξ|)^m\prod_{i=1}^2 (1+|ξ_i|)^{-ρ|α_i|+δ|β_i|} $ is satisfied. Our investigation culminates in a rigorous analysis of the $L^p$-boundedness of such pseudo-differential operators, thereby extending the seminal findings of C. Fefferman from 1973 concerning pseudo-differential operators within the Hörmander class.

math.CA

A class of multi-parameter Fourier integral operators: endpoint Hardy space bounds

In this paper we study a class of Fourier integral operators, whose symbols lie in the multi-parameter Hörmander class $S^{\vec m}( \mathbb{R}^\vn)$, where ~$\vec m=(m_1,m_2,\dots,m_d)$ is the order. We show that if in addition the phase function $Φ(x,ξ)$ can be written as $Φ(x,ξ)=\sum_{i=1}^dΦ_i(x_i,ξ_i)$, and each $Φ_i(x_i,ξ_i)$ satisfies the non-degeneracy condition, then such Fourier integral operators with order ~$\vec m=(-(n_1-1)/2, -(n_2-1)/2,\dots, -(n_d-1)/2)$ are actually bounded from rectangular Hardy space $H_{rect}^1(\mathbb{R}^\vn)$ to $L^1( \mathbb{R}^n )$.

math.CA