arXiv subjects

Yuqi Zhao

Publications and source records attributed to Yuqi Zhao.

At least 19 recordsLinked to original sources

arXiv2026

Tensor Amplification and Spectral Transfer for Sidorenko-Type Inequalities

We develop a tensor-amplification framework for Sidorenko-type inequalities in graphon classes. The framework applies to any admissible class, meaning a class closed under tensor powers and normalized principal restrictions. These two closure properties isolate the structural input needed for the amplification arguments, while preserving natural positivity constraints such as the doubly nonnegative constraint. For every admissible class $\mathcal{C}$, we prove two transfer principles. First, equality cases regularize optimally: if a non-matching graph $H$ is $\mathcal{C}$-Sidorenko, then every equality case $t(H,W)=p(W)^{e(H)}$ with $W\in\mathcal{C}$ is regular. Consequently, relative forcing is equivalent to relative regular-forcing for every non-matching $\mathcal{C}$-Sidorenko graph. Second, in the range $v(H)\le e(H)$, ordinary $\mathcal{C}$-Sidorenko is equivalent, as a universal property over $\mathcal{C}$, to the spectral inequality $t(H,W)\ge \rho(W)^{2e(H)-v(H)}p(W)^{v(H)-e(H)}$ for every non-zero $W\in\mathcal{C}$. The spectral transfer is obtained from a Perron-biased tensor regularization theorem detecting the Perron spectral radius on the exponential scale. We also prove quantitative near-equality variants and apply the framework to doubly nonnegative graphons and bounded doubly nonnegative kernels. This yields spectral equivalences for Sidorenko-good graphs in the range $v(F)\le e(F)$, and identifies Sidorenko-good forcing with regular-KNRS forcing for non-matching Sidorenko-good graphs.

math.CO↗

arXiv2026

$L^p$-form of the KNRS conjecture

The Kohayakawa--Nagle--R\"odl--Schacht conjecture predicts that locally dense graphs contain, asymptotically, at least as many homomorphic copies of any fixed graph as the random graph of the same edge density. We prove that every graph with at least one edge satisfies a natural $L^p$ relaxation of this conjecture in the graphon setting. More precisely, let $F$ be a graph with $m>0$ edges, and let $n$ be the number of non-isolated vertices of $F$. If $$ p\ge \binom {n}{2}/m, $$ then for every $\rho$-locally dense graphon $W$, $$ t(F,W^{\circ p})\ge \rho^{pm}. $$ Equivalently, if $$ W_F(\mathbf x)=\prod_{ij\in E(F)}W(x_i,x_j), $$ then $$ \|W_F\|_{L^p}\ge \rho^{e(F)}. $$ The proof is based on a H\"older uniformization over vertex relabellings, in the spirit of Conlon--Lee. We also prove a more general comparison principle with edge-transitive KNRS supergraphs, yielding sharper exponents whenever $F$ embeds into an edge-transitive KNRS graph. Finally, positive-semidefinite methods give theta-subdivision results: Sidorenko-good graphs are closed under arbitrary uniform theta-subdivisions; the non-uniform theta theorem of Im--Li--Liu admits a Sidorenko-good lift, under the same divisibility assumptions, after removing the parity restriction; and uniform theta-subdivisions of KNRS graphs are regular-KNRS.

math.CO↗

arXiv2026

Sidorenko Inequalities for Two-Sided Group Correlation Kernels

Sidorenko's conjecture asserts that every bipartite graph has at least the expected homomorphism density in every graph of a given edge density. Motivated by Cayley-type formulations of Sidorenko-type inequalities, we study a two-sided correlation construction on finite groups. Let $\Gamma$ be a finite group and let $f:\Gamma\to\mathbb{R}$ be a real-valued function. We define a directed kernel on $\Gamma$ by $$\mathcal C_f(x,y)=|\Gamma|^{-1}\sum_{a_1,a_2\in\Gamma:\, xa_1=a_2y} f(a_1)f(a_2)=\mathbb{E}_{z\in\Gamma} f(x^{-1}z)f(zy^{-1}).$$ When $f=\mathbf{1}_A$, this is the normalized size of the intersection $xA\cap Ay$. We prove that, for every finite directed graph $F$, $$t(F,\mathcal C_f)\geq t(\overrightarrow{K_2},\mathcal C_f)^{e(F)}=(\mathbb{E}_{g\in\Gamma}f(g))^{2e(F)}.$$ Equivalently, if $W_f^\times(x,y)=f(xy)$ is the directed product Cayley kernel on $\Gamma$, then the directed $1$-subdivision of every finite directed graph satisfies the same homomorphism-density lower bound in $W_f^\times$.

math.CO↗

arXiv2026

Conjugacy Class Averages and Sidorenko's Conjecture

Sidorenko's conjecture asserts that for every bipartite graph $H$ and every graph $G$, \[ t(H,G)\geq t(K_2,G)^{e(H)}. \] A result of Szegedy shows that, in order to prove the conjecture, it suffices to verify the corresponding inequality on a special family of highly symmetric bipartite Cayley type hosts arising from symmetric groups. Motivated by this reduction, we study Cayley type bipartite kernels associated with functions on finite groups and their conjugacy class averages. Our first result gives a reduction through conjugacy averaging: for a fixed bipartite graph $H$, if the $H$-density of each Cayley type host is at least the $H$-density of its conjugacy class average, then $H$ is strong Sidorenko, and hence Sidorenko. Our second result proves a Sidorenko-type inequality for 1-subdivision graphs on conjugacy-averaged Cayley kernels associated with arbitrary real-valued functions on finite groups.

math.CO↗

arXiv2026

From Language to Action: Enhancing LLM Task Efficiency with Task-Aware MCP Server Recommendation

The rapid expansion of the model context protocol (MCP) ecosystem enables large language model (LLM)-based agents to access a wide range of external tools via a standardized interface. However, identifying appropriate MCP servers for a specific development task remains challenging. Existing studies primarily focus on measuring the MCP ecosystem or optimizing tool invocation mechanisms, while systematic recommendation frameworks and reproducible benchmarks for real-world development tasks remain largely unexplored. To address this limitation, we formulate task-oriented MCP server recommendation as a structured retrieval-and-ranking problem that jointly considers semantic relevance and engineering constraints. We first construct Task2MCP, a task-centered dataset that systematically associates taxonomy-grounded development tasks with curated MCP servers. This dataset provides structured supervision and a reproducible evaluation environment for research on MCP tool recommendations. Building on this dataset, we propose T2MRec, a task-to-MCP server recommendation model. It models semantic relevance and structural compatibility to construct an initial candidate set. Then it improves coverage and ranking quality through centroid-based candidate expansion and constrained LLM-based re-ranking. In addition, we design and implement an interactive MCP server recommendation agent prototype that operates in conversational environments to support dynamic decision-making. The agent assists developers in efficiently evaluating and integrating tools by providing recommended MCP servers together with usage guidelines.

cs.SE↗

arXiv2026

KGCE: Knowledge-Augmented Dual-Graph Evaluator for Cross-Platform Educational Agent Benchmarking with Multimodal Language Models

With the rapid adoption of multimodal large language models (MLMs) in autonomous agents, cross-platform task execution capabilities in educational settings have garnered significant attention. However, existing benchmark frameworks still exhibit notable deficiencies in supporting cross-platform tasks in educational contexts, especially when dealing with school-specific software (such as XiaoYa Intelligent Assistant, HuaShi XiaZi, etc.), where the efficiency of agents often significantly decreases due to a lack of understanding of the structural specifics of these private-domain software. Additionally, current evaluation methods heavily rely on coarse-grained metrics like goal orientation or trajectory matching, making it challenging to capture the detailed execution and efficiency of agents in complex tasks. To address these issues, we propose KGCE (Knowledge-Augmented Dual-Graph Evaluator for Cross-Platform Educational Agent Benchmarking with Multimodal Language Models), a novel benchmarking platform that integrates knowledge base enhancement and a dual-graph evaluation framework. We first constructed a dataset comprising 104 education-related tasks, covering Windows, Android, and cross-platform collaborative tasks. KGCE introduces a dual-graph evaluation framework that decomposes tasks into multiple sub-goals and verifies their completion status, providing fine-grained evaluation metrics. To overcome the execution bottlenecks of existing agents in private-domain tasks, we developed an enhanced agent system incorporating a knowledge base specific to school-specific software. The code can be found at https://github.com/Kinginlife/KGCE.

cs.AI↗

arXiv2025

Self-Organizing Agent Network for LLM-based Workflow Automation

Recent multi-agent frameworks built upon large language models (LLMs) have demonstrated remarkable capabilities in complex task planning. However, in real-world enterprise environments, business workflows are typically composed through modularization and reuse of numerous subprocesses, resulting in intricate workflows characterized by lengthy and deeply nested execution paths. Such complexity poses significant challenges for LLM-driven orchestration, as extended reasoning chains and state-space explosions severely impact planning effectiveness and the proper sequencing of tool invocations. Therefore, developing an orchestration method with controllable structures capable of handling multi-layer nesting becomes a critical issue. To address this, we propose a novel structure-driven orchestration framework Self-Organizing Agent Network (SOAN). SOAN incrementally builds a formalized agent network by identifying and encapsulating structural units as independent agents, enhancing modularity and clarity in orchestration. Extensive evaluations were performed using multiple benchmarks as well as a real-world enterprise workflow dataset. Experimental results demonstrate that SOAN significantly outperforms state-of-the-art methods in terms of adaptability, fault tolerance, and execution efficiency.

cs.MA↗

arXiv2025

The Sweet Danger of Sugar: Debunking Representation Learning for Encrypted Traffic Classification

Recently we have witnessed the explosion of proposals that, inspired by Language Models like BERT, exploit Representation Learning models to create traffic representations. All of them promise astonishing performance in encrypted traffic classification (up to 98% accuracy). In this paper, with a networking expert mindset, we critically reassess their performance. Through extensive analysis, we demonstrate that the reported successes are heavily influenced by data preparation problems, which allow these models to find easy shortcuts - spurious correlation between features and labels - during fine-tuning that unrealistically boost their performance. When such shortcuts are not present - as in real scenarios - these models perform poorly. We also introduce Pcap-Encoder, an LM-based representation learning model that we specifically design to extract features from protocol headers. Pcap-Encoder appears to be the only model that provides an instrumental representation for traffic classification. Yet, its complexity questions its applicability in practical settings. Our findings reveal flaws in dataset preparation and model training, calling for a better and more conscious test design. We propose a correct evaluation methodology and stress the need for rigorous benchmarking.

cs.NI↗

arXiv2025

Sidorenko-Type Inequalities for Even Subdivisions over Finite Abelian Groups

Sidorenko's conjecture asserts that every bipartite graph $H$ has the property that, for any host graph $G$, the homomorphism density from $H$ to $G$ is asymptotically at least as large as in a quasirandom graph with the same edge density as $G$. While the conjecture remains still very open, Szegedy showed that it suffices to verify the inequality when the host graph is a Cayley graph over a finite group. In this paper, we prove that Sidorenko's conjecture holds for all even subdivisions of arbitrary graphs when the host graph is a Cayley graph over an abelian group. That is, if each edge of a graph is replaced by a path of even length (allowing different lengths for different edges), then the resulting graph satisfies the Sidorenko's inequality in any abelian Cayley host graph. Our approach reduces the homomorphism count to the evaluation of certain averages over solution sets of linear systems over finite abelian groups, and proceeds using Fourier-analytic techniques.

math.CO↗

arXiv2024

An El-Zahar Type Theorem in $3$-graphs under Codegree Condition

A $3$-uniform loose cycle, denoted by $C_t$, is a $3$-graph on $t$ vertices whose vertices can be arranged cyclically so that each hyperedge consists of three consecutive vertices, and any two consecutive hyperedges share exactly one vertex. The length of $C_t$ is the number of its hyperedges. We prove that for any $\eta>0$, there exists an $n_0=n_0(\eta)$ such that for any $n\geq n_0$ the following holds. Let $\mathcal{C}$ be a $3$-graph consisting of vertex-disjoint loose cycles $C_{n_1}, C_{n_2}, \ldots, C_{n_r}$ such that $\sum_{i=1}^{r}n_i=n$. Let $k$ be the number of loose cycles with odd lengths in $\mathcal{C}$. If $\mathcal{H}$ is a $3$-graph on $n$ vertices with minimum codegree at least $(n+2k)/4+\eta n$, then $\mathcal{H}$ contains $\mathcal{C}$ as a spanning subhypergraph. The degree condition is approximately tight. This generalizes the result of K\"{u}hn and Osthus for loose Hamilton cycle and the result of Mycroft for loose cycle factors in $3$-graphs. Our proof relies on the regularity lemma and a transversal blow-up lemma recently developed by the first author and Staden.

math.CO↗

arXiv2024

TVDiag: A Task-oriented and View-invariant Failure Diagnosis Framework with Multimodal Data

Microservice-based systems often suffer from reliability issues due to their intricate interactions and expanding scale. With the rapid growth of observability techniques, various methods have been proposed to achieve failure diagnosis, including root cause localization and failure type identification, by leveraging diverse monitoring data such as logs, metrics, or traces. However, traditional failure diagnosis methods that use single-modal data can hardly cover all failure scenarios due to the restricted information. Several failure diagnosis methods have been recently proposed to integrate multimodal data based on deep learning. These methods, however, tend to combine modalities indiscriminately and treat them equally in failure diagnosis, ignoring the relationship between specific modalities and different diagnostic tasks. This oversight hinders the effective utilization of the unique advantages offered by each modality. To address the limitation, we propose \textit{TVDiag}, a multimodal failure diagnosis framework for locating culprit microservice instances and identifying their failure types (e.g., Net-packets Corruption) in microservice-based systems. \textit{TVDiag} employs task-oriented learning to enhance the potential advantages of each modality and establishes cross-modal associations based on contrastive learning to extract view-invariant failure information. Furthermore, we develop a graph-level data augmentation strategy that randomly inactivates the observability of some normal microservice instances during training to mitigate the shortage of training data. Experimental results show that \textit{TVDiag} outperforms state-of-the-art methods in multimodal failure diagnosis, achieving at least a 55.94\% higher $HR@1$ accuracy and over a 4.08\% increase in F1-score across two datasets.

cs.SE↗

arXiv2024

Root Cause Localization for Microservice Systems in Cloud-edge Collaborative Environments

With the development of cloud-native technologies, microservice-based software systems face challenges in accurately localizing root causes when failures occur. Additionally, the cloud-edge collaborative environment introduces more difficulties, such as unstable networks and high latency across network segments. Accurately identifying the root cause of microservices in a cloud-edge collaborative environment has thus become an urgent problem. In this paper, we propose MicroCERCL, a novel approach that pinpoints root causes at the kernel and application level in the cloud-edge collaborative environment. Our key insight is that failures propagate through direct invocations and indirect resource-competition dependencies in a cloud-edge collaborative environment characterized by instability and high latency. This will become more complex in the hybrid deployment that simultaneously involves multiple microservice systems. Leveraging this insight, we extract valid contents from kernel-level logs to prioritize localizing the kernel-level root cause. Moreover, we construct a heterogeneous dynamic topology stack and train a graph neural network model to accurately localize the application-level root cause without relying on historical data. Notably, we released the first benchmark hybrid deployment microservice system in a cloud-edge collaborative environment (the largest and most complex within our knowledge). Experiments conducted on the dataset collected from the benchmark show that MicroCERCL can accurately localize the root cause of microservice systems in such environments, significantly outperforming state-of-the-art approaches with an increase of at least 24.1% in top-1 accuracy.

cs.SE↗

arXiv2024

Code Reviewer Recommendation Based on a Hypergraph with Multiplex Relationships

Code review is an essential component of software development, playing a vital role in ensuring a comprehensive check of code changes. However, the continuous influx of pull requests and the limited pool of available reviewer candidates pose a significant challenge to the review process, making the task of assigning suitable reviewers to each review request increasingly difficult. To tackle this issue, we present MIRRec, a novel code reviewer recommendation method that leverages a hypergraph with multiplex relationships. MIRRec encodes high-order correlations that go beyond traditional pairwise connections using degree-free hyperedges among pull requests and developers. This way, it can capture high-order implicit connectivity and identify potential reviewers. To validate the effectiveness of MIRRec, we conducted experiments using a dataset comprising 48,374 pull requests from ten popular open-source software projects hosted on GitHub. The experiment results demonstrate that MIRRec, especially without PR-Review Commenters relationship, outperforms existing stateof-the-art code reviewer recommendation methods in terms of ACC and MRR, highlighting its significance in improving the code review process.

cs.SE↗

arXiv2024

Cavity-enhanced narrowband spectral filters using rare-earth ions doped in thin-film lithium niobate

On-chip optical filters are fundamental components in optical signal processing. While rare-earth ion-doped crystals offer ultra-narrow optical filtering via spectral hole burning, their applications have primarily been limited to those using bulk crystals, restricting their utility. In this work, we demonstrate cavity-enhanced spectral filtering based on rare-earth ions in an integrated nonlinear optical platform. We incorporate rare-earth ions into high quality-factor ring resonators patterned in thin-film lithium niobate. By spectral hole burning at 4K in a critically coupled resonance mode, we achieve bandpass filters ranging from 7 MHz linewidth, with 13.0 dB of extinction, to 24 MHz linewidth, with 20.4 dB of extinction. By reducing the temperature to 100 mK to eliminate phonon broadening, we achieve an even narrower linewidth of 681 kHz, which is comparable to the narrowest filter linewidth demonstrated in an integrated photonic device, while only requiring a small device footprint. Moreover, the cavity enables reconfigurable filtering by varying the cavity coupling rate. For instance, as opposed to the bandpass filter, we demonstrate a bandstop filter utilizing an under-coupled ring resonator. Such versatile integrated spectral filters with high extinction ratio and narrow linewidth could serve as fundamental components for optical signal processing and optical memories on-a-chip.

physics.optics↗

arXiv2023

Cavity enhanced emission from a silicon T center

Silicon T centers present the promising possibility to generate optically active spin qubits in an all-silicon device. However, these color centers exhibit long excited state lifetimes and a low Debye-Waller factor, making them dim emitters with low efficiency into the zero-phonon line. Nanophotonic cavities can solve this problem by enhancing radiative emission into the zero-phonon line through the Purcell effect. In this work we demonstrate cavity-enhanced emission from a single T center in a nanophotonic cavity. We achieve a two-orders of magnitude increase in brightness of the zero-phonon line relative to waveguide-coupled emitters, a 23% collection efficiency from emitter to fiber, and an overall emission efficiency into the zero-phonon line of 63.4%. We also observe a lifetime enhancement of 5, corresponding to a Purcell factor exceeding 18 when correcting for the emission to the phonon sideband. These results pave the way towards efficient spin-photon interfaces in silicon photonics.

physics.optics↗

arXiv2023

Hybrid Si-GaAs photonic crystal cavity for lasing and bistability

The heterogeneous integration of silicon with III-V materials provides a way to overcome silicon's limited optical properties toward a broad range of photonic applications. Hybrid modes are a promising way to make heterogeneous Si/III-V devices, but it is still unclear how to engineer these modes to make photonic crystal cavities. Herein, using 3D finite-difference time-domain simulation, a hybrid Si-GaAs photonic crystal cavity design enables cavity mode confinement in GaAs without directly patterning that operates at telecom wavelengths. The hybrid cavity consists of a patterned silicon waveguide nanobeam that is evanescently coupled to a GaAs slab with quantum dots. We show that by engineering the hybrid modes, we can control the degree of coupling to the active material, which leads to a tradeoff between cavity quality factor and optical gain and nonlinearity. With this design, we demonstrate a cavity mode in the Si-GaAs heterogeneous region, which enables strong interaction with the quantum dots in the GaAs slab for applications such as low-power-threshold lasing and optical bistability (156 nW and 18.1 ${\mu}$W, respectively). This heterogeneous integration of an active III-V material with silicon via a hybrid cavity design suggests a promising approach for achieving on-chip light generation and low-power nonlinear platforms.

physics.optics↗

arXiv2022

Realization of advanced passive silicon photonic devices with subwavelength-grating structures developed by efficient inverse design

The realization of ultra-compact passive silicon photonic devices is becoming more and more important for the future large-scale photonic integration as desired for many systems. Although some compact silicon photonic devices have been demonstrated by using inverse design, the device performance is still insufficient for real applications. Here, we propose and realize several representative ultra-compact advanced passive silicon photonic devices with decent performances by introducing subwavelength-grating (SWG) structures developed by our high-efficiency inverse design method. These devices are designed by optimally manipulating the multimode excitation and the multimode interference in a region defined with SWG structures. These SWG structures with excellent feature-size uniformity are more fabrication-friendly than those random nano-structures used in previous inverse-designed photonic devices. The high-efficiency of our inverse design method is attributed to a novel search-space-dimension control strategy and the efficient problem-oriented electromagnetic-field solvers available for SWG structures. Specifically, we present the realization of a 6-channel mode (de)multiplexer, a broadband 90°-hybrid, and a two-channel flat-top wavelength demultiplexer as some examples, which can hardly be realized by previously reported inverse design approaches. These devices exhibit ultra-compact footprints as well as decent performances when compared to the counterparts developed by the classical theory.

physics.optics↗

arXiv2021

An atomic frequency comb memory in rare-earth doped thin-film lithium niobate

Atomic frequency combs memories that coherently store optical signals are a key building block for optical quantum computers and quantum networks. Integrating such memories into compact and chip-scale devices is essential for scalable quantum technology, but to date most demonstrations have been in bulk materials or waveguides with large cross-sections, or using fabrication techniques not easily adaptable to wafer scale processing. We demonstrate compact chip-integrated atomic frequency comb storage in rare earth doped thin-film lithium niobate. Our optical memory exhibits a broad storage bandwidth exceeding 100 MHz, and optical storage time of over 250 ns. The enhanced optical confinement in this device structure enables three orders of magnitude reduction in optical power as compared to large ion-diffused waveguides for the same Rabi frequency. These compact atomic frequency comb memories pave the way towards scalable, highly efficient, electro-optically tunable quantum photonic systems that can store and manipulate light on a compact chip.

quant-ph↗