arXiv subjects
Publications and source records attributed to Jiaji Liu.
We prove a multivariate Lam--Postnikov--Pylyavskyy type inequality for hybrid Grothendieck polynomials, unifying and refining results for stable and dual stable Grothendieck polynomials established by Chan--Chen--Pak--Soskin. We also conjecture extensions of the Lam--Postnikov--Pylyavskyy inequality and a conjecture by Thomas--Yong to the (equivariant) Schubert and Grothendieck polynomial setting.
Motivated by Stanley's ``Schubert shenanigans'' paper, commendable attempts have been made to understand the principal specializations of Schubert or Grothendieck polynomials. In this paper, we prove that when a permutation $w$ does not contain the $1423$ pattern, the principal specialization of the corresponding $\beta$-Grothendieck polynomial can be expressed nonnegatively in terms of the occurrences of patterns in $w$. Using an inverse conservation principle, we further obtain the nonnegativity expansion for permutations avoiding the $1342$ pattern. Our results partially resolve conjectures raised respectively by Gao (independently observed by Gaetz), Me\'sz\'aros--Tanjaya, and Dennin. The proofs are achieved based upon a reduction algorithm performing on the classic pipe dream model of $\beta$-Grothendieck polynomials.
Developing non-collaborative dialogue agents traditionally requires the manual, unscalable codification of expert strategies. We propose \ours, a method that leverages large language models to autonomously induce both strategy actions and planning logic directly from raw transcripts. METRO formalizes expert knowledge into a Strategy Forest, a hierarchical structure that captures both short-term responses (nodes) and long-term strategic foresight (branches). Experimental results across two benchmarks show that METRO demonstrates promising performance, outperforming existing methods by an average of 9%-10%. Our further analysis not only reveals the success behind METRO (strategic behavioral diversity and foresight), but also demonstrates its robust cross-task transferability. This offers new insights into building non-collaborative agents in a cost-effective and scalable way. Our code is available at https://github.com/Humphrey-0125/METRO.
Citations provide the basis for trusting scientific claims; when they are invalid or fabricated, this trust collapses. With the advent of Large Language Models (LLMs), this risk has intensified: LLMs are increasingly used for academic writing, but their tendency to fabricate citations (``ghost citations'') poses a systemic threat to citation validity. To quantify this threat, we develop \citeb, an open-source framework for large-scale citation verification, and conduct a comprehensive study of citation validity in the LLM era through three complementary experiments. First, we benchmark 13 LLMs on citation generation task in various research domains, finding that all models hallucinate citations at rate from 14.23\% to 94.93\%. Second, we analyze 2.2 million citations from 56,381 papers at AI/ML and Security venues (2020--2025), finding that 1.07\% of papers contain invalid citations, with an 80.9\% increase in 2025. Third, we survey 97 researchers, finding that 87.2\% use AI-powered tools in their workflows, 76.7\% of reviewers do not thoroughly check references, and 74.5\% view peer review as ineffective at catching citation errors. Based on these findings, we argue that ghost citations represent a systemic threat to academic integrity, and call for coordinated efforts from community to address this challenge.
For a skew shape $\lambda/\mu$, we define the hybrid Grothendieck polynomial $${G}_{\lambda/\mu}(\textbf{x};\textbf{t};\textbf{w}) =\sum_{T\in \mathrm{SVRPP}(\lambda/\mu)} \textbf{x}^{\mathrm{ircont}(T)}\textbf{t}^{\mathrm{ceq} (T)}\textbf{w}^{\mathrm{ex}(T)}$$ as a weight generating function over set-valued reverse plane partitions of shape $\lambda/\mu$. It specializes to \begin{itemize} \item[(1)] the refined stable Grothendieck polynomial introduced by Chan--Pflueger by setting all $t_i=0$; \item[(2)] the refined dual stable Grothendieck polynomial introduced by Galashin--Grinberg--Liu by setting all $w_i=0$. \end{itemize} We show that ${G}_{\lambda/\mu}(\textbf{x};\textbf{t};\textbf{w})$ is symmetric in the $\textbf{x}$ variables. By building a crystal structure on set-valued reverse plane partitions, we obtain the expansion of ${G}_{\lambda/\mu}(\textbf{x};\textbf{t};\textbf{w})$ in the basis of Schur functions, extending previous work by Monical--Pechenik--Scrimshaw and Galashin. Based on the Schur expansion, we deduce that hybrid Grothendieck polynomials of straight shapes have saturated Newton polytopes. Finally, using Fomin--Greene's theory on noncommutative Schur functions, we give a combinatorial formula for the image of ${G}_{\lambda/\mu}(\textbf{x};\textbf{t};\textbf{w})$ (in the case $t_i=\alpha$ and $w_i=\beta$) under the omega involution on symmetric functions. The formula unifies the structures of weak set-valued tableaux and valued-set tableaux introduced by Lam--Pylyavskyy. Several problems and conjectures are motivated and discussed.
The emergence of groundbreaking large language models capable of performing complex reasoning tasks holds significant promise for addressing various scientific challenges, including those arising in complex clinical scenarios. To enable their safe and effective deployment in real-world healthcare settings, it is urgently necessary to benchmark the diagnostic capabilities of current models systematically. Given the limitations of existing medical benchmarks in evaluating advanced diagnostic reasoning, we present DiagnosisArena, a comprehensive and challenging benchmark designed to rigorously assess professional-level diagnostic competence. DiagnosisArena consists of 1,113 pairs of segmented patient cases and corresponding diagnoses, spanning 28 medical specialties, deriving from clinical case reports published in 10 top-tier medical journals. The benchmark is developed through a meticulous construction pipeline, involving multiple rounds of screening and review by both AI systems and human experts, with thorough checks conducted to prevent data leakage. Our study reveals that even the most advanced reasoning models, o3, o1, and DeepSeek-R1, achieve only 51.12%, 31.09%, and 17.79% accuracy, respectively. This finding highlights a significant generalization bottleneck in current large language models when faced with clinical diagnostic reasoning challenges. Through DiagnosisArena, we aim to drive further advancements in AI's diagnostic reasoning capabilities, enabling more effective solutions for real-world clinical diagnostic challenges. We provide the benchmark and evaluation tools for further research and development https://github.com/SPIRAL-MED/DiagnosisArena.