arXiv subjects

Yuyao Yang

Publications and source records attributed to Yuyao Yang.

7 recordsLinked to original sources

arXiv2026

Asymptotic Uniformity of Permanents of Random Matrices over Finite Fields of Odd Characteristic

Let $q$ be an odd prime power, and let $A_n=(a_{ij})\in\mathbb F_q^{n\times n}$ be a random matrix whose entries are independent and uniformly distributed on $\mathbb F_q$. The permanent of $A_n$ is defined by $\operatorname{per}(A_n)=\sum_{\sigma\in S_n}\prod_{i=1}^n a_{i,\sigma(i)}$, where $S_n$ denotes the symmetric group on $[n]$. Ghasemi, Gross, and Kopparty conjectured the zero-mass asymptotic $\Pr[\operatorname{per}(A_n)=0]=1/q+o(1)$ for every fixed odd prime power $q$, and Hunter, Kwan, and Sauermann subsequently stated its equivalent full-distribution formulation: for every fixed $q$ and every $x\in\mathbb F_q$, \[ \lim_{n\to\infty}\Pr[\operatorname{per}(A_n)=x]=\frac1q. \] In this paper, we prove this conjecture. More precisely, we prove that there is an absolute constant $C>0$ such that \[\frac12\sum_{x\in\mathbb F_q}\left|\Pr[\operatorname{per}(A_n)=x]-\frac1q\right|\le C\frac{\log n}{n}\] for every odd prime power $q$ and every $n\ge 7$. The estimate is uniform in $q$, so the conclusion remains valid for every sequence $q=q(n)$ of odd prime powers.

math.CO↗

arXiv2026

Compactness of abundance in asymmetric hypergraph removal lemmas

Fix an integer $r\ge 2$ and a finite simple $r$-uniform hypergraph $F$ with at least one edge and no isolated vertices. An $n$-vertex $r$-graph is $\epsilon$-far from being $F$-free if at least $\epsilon n^r$ edges must be deleted to destroy every copy of $F$. A finite $r$-graph $H$ is $F$-abundant if there are constants $c,C>0$ such that every sufficiently large $\epsilon$-far host contains at least $c\epsilon^C n^{v(H)}$ labelled copies of $H$. A family is $F$-abundant when one member has this lower bound in each host, although the member may depend on the host and on $\epsilon$, while $c$ and $C$ are common to the family. We prove that every abundant family contains an abundant member. We prove the analogous coloured theorem for $F$-partite hosts containing edge-disjoint part-respecting copies of $F$ such that every vertex lies in at least $\epsilon n^{r-1}$ of them. The case $r=2$ yields the coloured and uncoloured graph compactness theorems, answers Question 5.2 of Gir\~ao, Hurley, Illingworth and Michel, and proves their Conjecture 5.1 [J. Lond. Math. Soc., 2024]. We also obtain an explicit bound $\lfloor 2r(C+1)\rfloor$ for the order of the non-isolated core of a selected witness. Moreover, we give several applications. For example, we construct translation-invariant linear systems from abundant coloured hypergraphs, obtain a square-root bound for an equation associated with a cycle of bounded length, give a one-sided tester based on one fixed graph when distance from the property gives a polynomial lower bound on distance from being $F$-free, and prove that no algorithm decides whether a family of finite simple graphs enumerated by a Turing machine is $K_3$-abundant.

math.CO↗

arXiv2026

Paths of Odd Order in Graphs with Given Edge Density

We determine the asymptotic maximum number of unlabelled copies of $P_{2r+1}$ in graphs with prescribed edge density, where $r\ge1$ is fixed and $P_{2r+1}$ denotes the path on $2r+1$ vertices. If an $n$ vertex graph $G$ has edge density $c=2e(G)/n^2$, then the maximum is $\frac12S_r(c)n^{2r+1}+O(n^{2r})$ for $0<c\le c_r$, and $\frac12c^{r+1/2}n^{2r+1}+O(n^{2r})$ for $c_r\le c<1$, where $S_r(c)$ is the value given by the quasi-star construction and $c_r\in(0,1)$ is an explicit algebraic transition point. Thus the quasi-star construction is asymptotically extremal below the transition, while the quasi-clique construction is asymptotically extremal above the transition. This extends the quasi-star versus quasi-clique theorem of Ahlswede and Katona for $P_3$ and the theorem of Nagy for $P_5$ to all paths with an odd number of vertices. The proof reduces the problem to threshold graphons and then to two endpoint families. The three-step endpoint is handled by reducing the required inequality to coefficient nonnegativity in a Bernstein expansion, which is proved by a direct combinatorial argument.

math.CO↗

arXiv2025

RECODE-H: A Benchmark for Research Code Development with Interactive Human Feedback

Large language models (LLMs) show the promise in supporting scientific research implementation, yet their ability to generate correct and executable code remains limited. Existing works largely adopt one-shot settings, ignoring the iterative and feedback-driven nature of realistic workflows of scientific research development. To address this gap, we present RECODE-H, a benchmark of 102 tasks from research papers and repositories that evaluates LLM agents through multi-turn interactions with LLM-simulated human feedback. It includes structured instructions,unit tests, and a five-level feedback hierarchy to reflect realistic researcher-agent collaboration. We further present ReCodeAgent, a framework that integrates feedback into iterative code generation. Experiments with leading LLMs, including GPT-5, Claude-Sonnet-4, DeepSeek-V3.1, and Gemini 2.5, show substantial performance gains with richer feedback, while also highlighting ongoing challenges in the generation of complex research code. RECODE-H establishes a foundation for developing adaptive, feedback-driven LLM agents in scientific research implementation

cs.CL↗

arXiv2025

Towards Agentic RAG with Deep Reasoning: A Survey of RAG-Reasoning Systems in LLMs

Retrieval-Augmented Generation (RAG) lifts the factuality of Large Language Models (LLMs) by injecting external knowledge, yet it falls short on problems that demand multi-step inference; conversely, purely reasoning-oriented approaches often hallucinate or mis-ground facts. This survey synthesizes both strands under a unified reasoning-retrieval perspective. We first map how advanced reasoning optimizes each stage of RAG (Reasoning-Enhanced RAG). Then, we show how retrieved knowledge of different type supply missing premises and expand context for complex inference (RAG-Enhanced Reasoning). Finally, we spotlight emerging Synergized RAG-Reasoning frameworks, where (agentic) LLMs iteratively interleave search and reasoning to achieve state-of-the-art performance across knowledge-intensive benchmarks. We categorize methods, datasets, and open challenges, and outline research avenues toward deeper RAG-Reasoning systems that are more effective, multimodally-adaptive, trustworthy, and human-centric. The collection is available at https://github.com/DavidZWZ/Awesome-RAG-Reasoning.

cs.CL↗

arXiv2025

From Web Search towards Agentic Deep Research: Incentivizing Search with Reasoning Agents

Information retrieval is a cornerstone of modern knowledge acquisition, enabling billions of queries each day across diverse domains. However, traditional keyword-based search engines are increasingly inadequate for handling complex, multi-step information needs. Our position is that Large Language Models (LLMs), endowed with reasoning and agentic capabilities, are ushering in a new paradigm termed Agentic Deep Research. These systems transcend conventional information search techniques by tightly integrating autonomous reasoning, iterative retrieval, and information synthesis into a dynamic feedback loop. We trace the evolution from static web search to interactive, agent-based systems that plan, explore, and learn. We also introduce a test-time scaling law to formalize the impact of computational depth on reasoning and search. Supported by benchmark results and the rise of open-source implementations, we demonstrate that Agentic Deep Research not only significantly outperforms existing approaches, but is also poised to become the dominant paradigm for future information seeking. All the related resources, including industry products, research papers, benchmark datasets, and open-source implementations, are collected for the community in https://github.com/DavidZWZ/Awesome-Deep-Research.

cs.IR↗

arXiv2016

Mixing in modulated turbulence. Numerical results

Direct numerical simulations are carried out to investigate scalar mixing in an isotropic turbulent flow with a time-periodic forcing. For high amplitudes of the modulation, it is shown that the average mixing rate is negatively affected at low frequencies. In this limit the mixing time scale increases, whereas the typical velocity timescale decreases. We further determine the frequency response of scalar statistics to a periodic scalar-forcing.

physics.flu-dyn↗