arXiv subjects

Huajie Li

Publications and source records attributed to Huajie Li.

7 recordsLinked to original sources

arXiv2026

DataArc-SynData-Toolkit: A Unified Closed-Loop Framework for Multi-Path, Multimodal, and Multilingual Data Synthesis

Synthetic data has emerged as a crucial solution to the data scarcity bottleneck in large language models (LLMs), particularly for specialized domains and low-resource languages. However, the broader adoption of existing synthetic data tools is severely hindered by convoluted workflows, fragmented data standards, and limited scalability across modalities. To address these limitations, we develop DataArc-SynData-Toolkit, an open-source framework featuring: (1) a configuration-driven, end-to-end pipeline equipped with an intuitive visual interface and simplified CLI for exceptional usability; (2) a unified, quality-controllable synthesis paradigm that standardizes multi-source data generation to ensure high reusability; and (3) a highly modular architecture designed for seamless multimodal, multilingual, and multi-task adaptation. We apply the toolkit in multiple application scenarios. Experimental results demonstrate that our toolkit achieves an optimal balance between generation efficiency and data quality. By offering an end-to-end and visually interactive pipeline, DataArc-SynData-Toolkit significantly lowers the technical barrier to synthetic data generation and subsequent model training, accelerating its practical deployment in real-world applications.

cs.LG↗

arXiv2026

Une formule des traces pour les espaces symétriques. Le cas de Guo-Jacquet

In the spirit of Arthur's trace formula, we establish a general trace formula for symmetric spaces associated with the variety of involutions of a finite $D$-module where $D$ is a division algebra central over a number field $F$. Such a formula should be useful for studying the automorphic spectrum of these symmetric spaces and the deep links between linear periods and special values of standard $L$-functions at their center of symmetry. Indeed, our formula yields an identity between spectral distributions, which generalize relative characters built on linear periods, and geometric distributions, which are an extension of relative orbital integrals. We show that the spectral distributions are, in a certain sense, asymptotic to truncated integrals of the components of the automorphic kernel associated with a cuspidal datum: this provides a handle on these distributions and has allowed, in a companion paper, to express some of these distributions in the form of a weighted relative character. The geometric distributions attached to "regular semi-simple" geometric data are expressed as weighted relative orbital integrals. In general, for non-regular geometric data, we introduce a procedure of descent to the centralizer, which allows us to express any geometric distribution in terms of the nilpotent contribution of infinitesimal trace formulas studied in previous papers.

math.NT↗

arXiv2024

On certain identities between Fourier transforms of weighted orbital integrals on infinitesimal symmetric spaces of Guo-Jacquet

In an infinitesimal variant of Guo-Jacquet trace formulae, the regular semi-simple terms are expressed as noninvariant weighted orbital integrals on two global infinitesimal symmetric spaces. We prove some relations between the Fourier transforms of invariant weighted orbital integrals on the corresponding local infinitesimal symmetric spaces. These relations should be useful in the noninvariant comparison of the infinitesimal variant of Guo-Jacquet trace formulae.

math.RT↗

arXiv2024

A nonabelian circle method

We count integral quaternion zeros of $γ_1^2 \pm \dots \pm γ_n^2$, giving an asymptotic when $n\ge 9$, and a likely near-optimal bound when $n=8$. To do so, we introduce a new, nonabelian delta symbol method, which is of independent interest. Our asymptotic at height $X$ takes the form $cX^{4n-8} + O(X^{3n+\varepsilon})$ for suitable $c \in \mathbb{C}$ and any $\varepsilon>0.$ We construct special subvarieties implying that, in general, $3n+\varepsilon$ can be at best improved to $3n-2.$

math.NT↗

arXiv2022

A local trace formula for $p$-adic infinitesimal symmetric spaces: the case of Guo-Jacquet

We establish an invariant local trace formula for the tangent space of some symmetric spaces over a non-archimedean local field of characteristic zero. These symmetric spaces are studied in Guo-Jacquet trace formulae and our methods are inspired by works of Waldspurger and Arthur. Some other results are given during the proof including a noninvariant local trace formula, Howe's finiteness for weighted orbital integrals and the representability of the Fourier transform of weighted orbital integrals. These local results are prepared for the comparison of regular semi-simple terms, which are weighted orbital integrals, of an infinitesimal variant of Guo-Jacquet trace formulae.

math.RT↗

arXiv2021

An infinitesimal variant of Guo-Jacquet trace formula I: the case of $(GL_{2n,D}, GL_{n,D}\times GL_{n,D})$

We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of $(GL_{2n,D}, GL_{n,D}\times GL_{n,D})$. It is a kind of Poisson summation formula obtained by an analogue of Arthur's truncation process. It consists in the equality of the sums of two types of distributions which are non-equivariant in general: one type is associated to rational points in the categorical quotient, while the other type is the Fourier transform of the first type. For regular semi-simple points in the categorical quotient, we obtain weighted orbital integrals.

math.NT↗

arXiv2021

An infinitesimal variant of Guo-Jacquet trace formula II

We establish an infinitesimal variant of Guo-Jacquet trace formula for the case of a central simple algebra over a number field $F$ containing a quadratic field extension $E/F$. It is an equality between a sum of geometric distributions on the tangent space of some symmetric space and its Fourier transform. To prove this, we need to define an analogue of Arthur's truncation and then use the Poisson summation formula. We describe the terms attached to regular semi-simple orbits as explicit weighted orbital integrals. To compare them to those for another case studied in our previous work, we state and prove the weighted fundamental lemma at the infinitesimal level by using Labesse's work on the base change for $GL_n$.

math.NT↗