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Jinjia Li

Publications and source records attributed to Jinjia Li.

9 recordsLinked to original sources
arXiv2026

InfiCoEvalChain: A Blockchain-Based Decentralized Framework for Collaborative LLM Evaluation

The rapid advancement of large language models (LLMs) demands increasingly reliable evaluation, yet current centralized evaluation suffers from opacity, overfitting, and hardware-induced variance. Our empirical analysis reveals an alarming inconsistency in existing evaluations: the standard deviation across ten repeated runs of a single model on HumanEval (1.67) actually exceeds the performance gap among the top-10 models on the official leaderboard (0.91), rendering current rankings statistically precarious. To mitigate these instabilities, we propose a decentralized evaluation framework that enables hardware and parameter diversity through large-scale benchmarking across heterogeneous compute nodes. By leveraging the blockchain-based protocol, the framework incentivizes global contributors to act as independent validators, using a robust reward system to ensure evaluation integrity and discourage dishonest participation. This collective verification transforms evaluation from a "centralized black box" into a "decentralized endorsement" where multi-party consensus and diverse inference environments yield a more stable, representative metric. Experimental results demonstrate that the decentralized evaluation framework reduces the standard deviation across ten runs on the same model to 0.28. This significant improvement over conventional frameworks ensures higher statistical confidence in model rankings. We have completely implemented this platform and will soon release it to the community.

cs.AI↗
arXiv2025

InfiAgent: Self-Evolving Pyramid Agent Framework for Infinite Scenarios

Large Language Model (LLM) agents have demonstrated remarkable capabilities in organizing and executing complex tasks, and many such agents are now widely used in various application scenarios. However, developing these agents requires carefully designed workflows, carefully crafted prompts, and iterative tuning, which requires LLM techniques and domain-specific expertise. These hand-crafted limitations hinder the scalability and cost-effectiveness of LLM agents across a wide range of industries. To address these challenges, we propose \textbf{InfiAgent}, a Pyramid-like DAG-based Multi-Agent Framework that can be applied to \textbf{infi}nite scenarios, which introduces several key innovations: a generalized "agent-as-a-tool" mechanism that automatically decomposes complex agents into hierarchical multi-agent systems; a dual-audit mechanism that ensures the quality and stability of task completion; an agent routing function that enables efficient task-agent matching; and an agent self-evolution mechanism that autonomously restructures the agent DAG based on new tasks, poor performance, or optimization opportunities. Furthermore, InfiAgent's atomic task design supports agent parallelism, significantly improving execution efficiency. This framework evolves into a versatile pyramid-like multi-agent system capable of solving a wide range of problems. Evaluations on multiple benchmarks demonstrate that InfiAgent achieves 9.9\% higher performance compared to ADAS (similar auto-generated agent framework), while a case study of the AI research assistant InfiHelper shows that it generates scientific papers that have received recognition from human reviewers at top-tier IEEE conferences.

cs.AI↗
arXiv2012

A Direct Limit for Limit Hilbert-Kunz Multiplicity for Smooth Projective Curves

This paper concerns the question of whether a more direct limit can be used to obtain the limit Hilbert-Kunz multiplicity, a possible candidate for a characteristic zero Hilbert-Kunz multiplicity. The main goal is to establish an affirmative answer for one of the main cases for which the limit Hilbert-Kunz multiplicity is even known to exist, namely that of graded ideals in the homogeneous coordinate ring of smooth projective curves. The proof involves more careful estimates of bounds found independently by Brenner and Trivedi on the dimensions of the cohomologies of twists of the syzygy bundle as the characteristic p goes to infinity and uses asymptotic results of Trivedi on the slopes of Harder-Narasimham filtrations of Frobenius pullbacks of bundles. In view of unpublished results of Gessel and Monsky, the case of maximal ideals in diagonal hypersurfaces is also discussed in depth.

math.AC↗
arXiv2012

Asymptotic behavior of the socle of Frobenius powers

Let $(R, m)$ be a local ring of prime characteristic $p$ and $q$ a varying power of $p$. We study the asymptotic behavior of the socle of $R/I^{[q]}$ where $I$ is an $m$ -primary ideal of $R$. In the graded case, we define the notion of diagonal $F$-threshold of $R$ as the limit of the top socle degree of $R/m^{[q]}$ over $q$ when $q \to \infty$. Diagonal $F$-threshold exists as a positive number (rational number in the latter case) when: (1) $R$ is either a complete intersection or $R$ is $F$-pure on the punctured spectrum; (2) $R$ is a two dimensional normal domain. In the latter case, we also discuss its geometric interpretation and apply it to determine the strong semistability of the syzygy bundle of $(x^d, y^d,z^d)$ over the smooth projective curve in $\mathbb P^2$ defined by $x^n+y^n+z^n=0$. The rest of this paper concerns a different question about how the length of the socle of $R/I^{[q]}$ vary as $q$ varies. We give explicit calculations of the length of the socle of $R/m^{[q]}$ for a class of hypersurface rings which attain the minimal Hilbert-Kunz function. We finally show, under mild conditions, the growth of such length function and the growth of the second Betti numbers of $R/m^{[q]}$ differ by at most a constant, as $q \to \infty$.

math.AC↗
arXiv2012

Frobenius criteria of freeness and Gorensteinness

Let $F^n(-)$ be the Frobenius functor of Peskine and Szpiro. In this note, we show that the maximal Cohen-Macaulayness of $F^n(M)$ forces $M$ to be free, provided $M$ has a rank. We apply this result to obtain several Frobenius related criteria for the Gorensteinness of a local ring $R$, one of which improves a previous characterization due to Hanes and Huneke. We also establish a special class of finite length modules over Cohen-Macaulay rings, which are rigid against Frobenius.

math.AC↗
arXiv2007

Characterizations of Regular Local Rings in Positive Characteristics

In this note, we provide several characterizations of regular local rings in positive characteristics, in terms of the Hilbert-Kunz multiplicity and its higher $\tor$ counterparts $ıt_i=\underset{n \to \infty}{\lim} ł(\tor_i(k,{}^{f^n} R))/p^{nd}$. We also apply the characterizations to improve a recent result by Bridgeland and Iyengar in the characteristic $p$ case. Our proof avoids using the existence of big Cohen-Macaulay modules, which is the major tool in the proof of Bridgeland and Iyengar.

math.AC↗
arXiv2007

Asymptotic vanishing conditions which force regularity in local rings of prime characteristic

Let $(R,\m,k)$ be a local (Noetherian) ring of positive prime characteristic $p$ and dimension $d$. Let $G_\dt$ be a minimal resolution of the residue field $k$, and for each $i\ge 0$, let $\gothic t_i(R) = \lim_{e\to \8} {\length(H_i(F^e(G_\dt)))}/{p^{ed}}$. We show that if $\gothic t_i(R) = 0$ for some $i>0$, then $R$ is a regular local ring. Using the same method, we are also able to show that if $R$ is an excellent local domain and $\Tor_i^R(k,R^+) = 0$ for some $i>0$, then $R$ is regular (where $R^+$ is the absolute integral closure of $R$). Both of the two results were previously known only for $i = 1$ or 2 via completely different methods.

math.AC↗
arXiv2005

The Upper Bound of Frobenius Related Length Functions

In this paper, we study the asymptotic behavior of lengths of $\tor$ modules of homologies of complexes under the iterations of the Frobenius functor in positive characteristic. We first give upper bounds to this type of length functions in lower dimensional cases and then construct a counterexample to the general situation. The motivation of studying such length functions arose initially from an asymptotic length criterion given in [D4] which is a sufficient condition to a special case of nonnegativity of $χ_\infty$. We also provide an example to show that this sufficient condition does not hold in general.

math.AC↗