arXiv subjects

Weiqi Jiang

Publications and source records attributed to Weiqi Jiang.

6 recordsLinked to original sources

arXiv2026

Real stability of layer-refined antichain polynomials for three-chain products with a two-element factor

For all positive integers $n,k$, we prove that the layer-refined antichain polynomial of the product poset $[2]\times[n]\times[k]$ is real stable. Jacobi-polynomial interlacing further shows that its diagonal specialization, the ordinary antichain polynomial of the same poset, has only simple, strictly negative zeros. For the special family $[2]\times[m]\times[m+1]$, explicit reciprocal identities give palindromicity; reciprocal pairing of the simple negative zeros then shows that every coefficient in the gamma expansion is strictly positive. Thus we prove Conjecture 4.3 of Ding and Dong and resolve all parts of their Conjecture 4.5, while strengthening its stated gamma-positivity consequence. The enumerative input is an explicit first-crossing reflection for two lattice paths, specialized from work of Krattenthaler and Sulanke.

math.CO↗

arXiv2026

Type-Voltage Covers and Finite Locally Kneser Graphs

For every $d\geq3$ we construct a connected graph of order $2\binom{3d+1}{d}$ that is locally $K(2d+1,d)$. Fix a block $A$ and put $a'=\min(|A|,3d+1-|A|)$. Among the loopless binary voltages on the fixed labeled base $K(3d+1,d)$ that depend only on the intersection types with $A$, the local-neighborhood-preserving assignments form, modulo gauge, an $\mathbb F_2$-space of dimension $[q^{a'-5}]\binom{d}{3}_q$, with explicit canonical coordinates. Adjacent-line rigidity holds on $2d+2\leq n\leq3d$: every loopless fixed-block type-invariant local-neighborhood-preserving binary voltage is gauge trivial. Dropping type invariance over the fixed labeled $K(10,3)$, we classify all local-neighborhood-preserving binary voltage assignments and find that $H^1(M_3(10);\mathbb F_2)$ has dimension 42. Under base relabeling by $S_{10}$ these classes form 1,245,395 orbits, of which 1,245,394 consist of connected covers; an explicit class has orbit size 126 and stabilizer $S_5\wr C_2$. The proofs combine a triangle-voltage criterion and cohomology with a simplicial collapse and Burnside enumeration.

math.CO↗

arXiv2026

Bezoutian Decoupling for Conformal Yang--Mills Multiplets in $(A)dS$

Metsaev exhibited generic and decoupled formulations of conformal Yang--Mills theory in $(A)dS_6$, $(A)dS_8$, and $(A)dS_{10}$, and conjectured the corresponding relations in higher even dimensions. Motivated by the low-dimensional matrices in Appendix C, we identify and diagonalize a natural all-$N$ Bezoutian continuation of the three generic Gram forms. The monic Hankel cutoff, the evaluation pattern in Appendix C, and the conjectured mass nodes determine this continuation uniquely. Its vector and radical Gram-form diagonalization identities hold for every $D=d+1=2N+4$, $N\geq1$. The continuation is the Bezout matrix of $z\prod_{i=1}^N(z-ρi(2N+1-i))$ and $1$; evaluation at its simple roots produces the Vandermonde congruence appearing in the field redefinition. The same calculation gives closed formulas for the inverse, determinant, and inertia, and identifies the normalization weights with Johnson-graph multiplicities. Any nonlinear coefficient algebra already specified in the generic formulation is transported by this change of basis. The result does not construct such an algebra in arbitrary dimension. At $N=4$, we impose associativity, Frobenius invariance, and a fixed flat specialization; these algebraic constraints still admit a one-parameter family of pairwise distinct products in a fixed generic basis.

hep-th↗

arXiv2026

Image Feature Fusion-based Federated Client Unlearning (FCU)

Major data protection regulations all mention the "right to be forgotten," and that's what pushed federated unlearning (FU) techniques forward. But one stubborn issue remains: catastrophic forgetting--you erase the target knowledge, yet somehow you also end up throwing out essential retained knowledge, which then hurts the model's global generalization. To get a better balance between unlearning effectiveness and generalization ability, we propose something called Image Feature Fusion-based Federated Client Unlearning (IFF-FCU). The idea is to bring in a linear Image Feature Fusion mechanism (Mixup) that dynamically creates mixed samples, bridging the gap between forget-distribution and retain-distribution. What this strategy does isn't just deleting a few discrete data points--it theoretically widens and regularizes the forgetting boundary. We ran extensive experiments on medical imaging benchmarks (RSNA-ICH and ISIC2018), and the results show that our approach achieves reasonably good unlearning. For instance, on the ICH dataset, IFF-FCU achieves a highly competitive Error deviation from the retrained gold standard, demonstrating robust improvements over existing baselines.

cs.LG↗

arXiv2026

PRL-Bench: A Comprehensive Benchmark Evaluating LLMs' Capabilities in Frontier Physics Research

The paradigm of agentic science requires AI systems to conduct robust reasoning and engage in long-horizon, autonomous exploration. However, current scientific benchmarks remain confined to domain knowledge comprehension and complex reasoning, failing to evaluate the exploratory nature and procedural complexity of real-world research. In this work, we present research-oriented evaluations in theoretical and computational physics, a natural testbed with comprehensive domain knowledge, complex reasoning, and verifiable end-to-end workflows without reliance on experiments. Here we introduce PRL-Bench (Physics Research by LLMs), a benchmark designed to systematically map the capability boundaries of LLMs in executing end-to-end physics research. Constructed from 100 curated papers from the latest issues of Physical Review Letters since August 2025 and validated by domain experts, PRL-Bench covers five major theory- and computation-intensive subfields of modern physics: astrophysics, condensed matter physics, high-energy physics, quantum information, and statistical physics. Each task in the benchmark is designed to replicate the core properties of authentic scientific research, including exploration-oriented formulation, long-horizon workflows, and objective verifiability, thereby reconstructing the essential reasoning processes and research workflows of real physics research. Evaluation across frontier models shows that performance remains limited, with the best overall score below 50, revealing a pronounced gap between current LLM capabilities and the demands of real scientific research. PRL-Bench serves a reliable testbed for accessing next generation AI scientists advancing AI systems toward autonomous scientific discovery.

cs.LG↗

arXiv2026

GraphScout: Empowering Large Language Models with Intrinsic Exploration Ability for Agentic Graph Reasoning

Knowledge graphs provide structured and reliable information for many real-world applications, motivating increasing interest in combining large language models (LLMs) with graph-based retrieval to improve factual grounding. Recent Graph-based Retrieval-Augmented Generation (GraphRAG) methods therefore introduce iterative interaction between LLMs and knowledge graphs to enhance reasoning capability. However, existing approaches typically depend on manually designed guidance and interact with knowledge graphs through a limited set of predefined tools, which substantially constrains graph exploration. To address these limitations, we propose GraphScout, a training-centric agentic graph reasoning framework equipped with more flexible graph exploration tools. GraphScout enables models to autonomously interact with knowledge graphs to synthesize structured training data which are then used to post-train LLMs, thereby internalizing agentic graph reasoning ability without laborious manual annotation or task curation. Extensive experiments across five knowledge-graph domains show that a small model (e.g., Qwen3-4B) augmented with GraphScout outperforms baseline methods built on leading LLMs (e.g., Qwen-Max) by an average of 16.7\% while requiring significantly fewer inference tokens. Moreover, GraphScout exhibits robust cross-domain transfer performance. Our code will be made publicly available~\footnote{https://github.com/Ying-Yuchen/_GraphScout_}.

cs.AI↗