arXiv subjects

Ruiyi Yang

Publications and source records attributed to Ruiyi Yang.

At least 19 recordsLinked to original sources

arXiv2026

The exponent of harmonic LCM avoidance

Fix $k\ge 3$, and let $f_k(N)$ be the largest harmonic sum of a subset of $[N]$ containing no $k$ distinct integers with a common pairwise least common multiple. We prove that $f_k(N)=(\log N)^{\gamma_k+o(1)}$ for a well-defined exponent $\gamma_k\in(0,1]$. Following the weighted-pressure idea of Chojecki, we give a self-contained proof of variational formulas for $\gamma_k$ in terms of weighted sunflower-free families. We then eliminate the continuous weight: if $M_k(n,r)$ is the largest size of an $r$-uniform $k$-cosunflower-free family on $[n]$, then \[ \gamma_k=\sup_{n\ge1,\ 1\le r\le n}\frac{r}{en}M_k(n,r)^{1/r}. \] This finite-block formula yields a direct transfer principle from uniform set-system constructions, recovers the Tang--Zhang bounds, and gives $0.438899\ldots<\gamma_3\le0.889881\ldots$.

math.CO↗

arXiv2026

GuardianAgent: Policy-Conditioned Risk-Adaptive Anonymization with Verified Adversarial Escalation

Privacy protection for live web traffic requires more than detecting private spans. Agent-based privacy protection systems must determine whether an outgoing action complies with the destination site's privacy policy, then apply only the level of rewriting or sanitisation justified by the residual disclosure risk. We present GuardianAgent, a policy-conditioned anonymization framework that couples structured risk assessment with verified adaptive rewriting. GuardianAgent computes risk through AMRSF (Adaptive Multi-factor Risk Scoring Formula), an explicit controller that combines policy-violation likelihood with data sensitivity, recipient transmission, purpose legitimacy, contextual basis, and policy transparency, rather than relying on an LLM to assign risk directly. This risk score determines both the allow/transform/deny decision and the initial anonymization level. For efficiency, GuardianAgent uses an evidential fast path for low-uncertainty policy matches and invokes an LLM slow path only for uncertain cases. For rewriting, it applies a five-level hierarchy driven by a verified adversarial guesser: guesses trigger escalation only when supported by the original text, preventing hallucinated attacker confidence from causing unnecessary over-anonymization. Experiments across three benchmarks spanning legal text (TAB), Reddit posts (SynthPAI), and multi-format synthetic PII records (PII-Masking-300k) show that GuardianAgent achieves the strongest privacy-utility trade-off among published baselines and is the only method to reach more than 0.90 privacy in all three domains, remaining robust under a backbone switch. Action-context stress tests further show that the same outgoing text receives different decisions and anonymization strengths under different recipients, purposes, action bases, and policy-transparency conditions.

cs.AI↗

arXiv2026

Exterior power sums

We prove that for every fixed $\lambda>0$ and all sufficiently large $n$, any $z_1,\dots,z_n\in\C$ with $|z_j|\geq1$ satisfy $\max_{2\leq k\leq n+1}|\sum_j z_j^k|>e^{-\lambda n}$. Consequently, the $n$th root of the optimal maximum tends to $1$, so no constant $C>1$ in Erd\H{o}s 973 can exist. The proof combines a truncated exponential factorization with overconvergence on an open set outside the unit disk and a normal-family obstruction for Cauchy transforms.

math.CO↗

arXiv2026

Functional Multi-Target Detection via Bispectrum Inversion

This paper develops a functional theory for multi-target detection, where a compactly supported signal is recovered from a single noisy observation containing many unknown translations of the signal. Our formulation allows continuous, off-grid translations and correlated stationary Gaussian process noise, extending beyond the discrete, grid-aligned, white-noise models common in prior work. We analyze two uninitialized recovery algorithms based on autocorrelation analysis; in particular, both algorithms first estimate the signal's bispectrum via a debiased third-order empirical autocorrelation. The signal is then recovered from the estimated bispectrum using either a functional frequency marching scheme or a Kotlarski-type deconvolution formula. For both algorithms, we prove non-asymptotic recovery guarantees for compactly supported signals without bandlimiting assumptions. The resulting error bounds depend on the smoothness of the signal and the accuracy of bispectrum estimation, with the latter governed by the noise characteristics and the number of signal occurrences. Numerical experiments validate our theory and demonstrate accurate recovery in low-SNR regimes.

eess.SP↗

arXiv2026

STAR: Failure-Aware Markovian Routing for Multi-Agent Spatiotemporal Reasoning

Compositional spatiotemporal reasoning often requires a system to invoke multiple heterogeneous specialists, such as geometric, temporal, topological, and trajectory agents. A central question is how such a system should route among specialists when execution does not simply succeed or fail, but fails in qualitatively different ways. Existing tool-augmented and multi-agent LLM systems typically leave this routing decision implicit in language generation, making recovery ad hoc, difficult to interpret, and hard to optimize. This paper presents STAR (Spatio-Temporal Agent Router), a failure-aware routing framework that externalizes inter-agent control as a state-conditioned transition policy over the current agent, task type, and typed execution status. At the center of STARis an agent routing matrix that combines expert-specified nominal routes with recovery transitions learned from execution traces. Because the matrix conditions on distinct failure states, the router can respond differently to malformed outputs, missing dependencies, and tool--query mismatches, rather than collapsing them into a generic retry signal. Specialists execute through a tool-grounded extract--compute--deposit protocol and write intermediate results to a shared blackboard for downstream fusion. Results prove that retaining unsuccessful traces during training enlarges the support of the routing policy on error states, enabling recovery transitions that success-only training cannot represent. Across three spatiotemporal benchmarks and eight backbone LLMs, STAR improves over multiple baselines with the clearest gains on queries whose execution deviates from the nominal routing path. Router-specific ablations and recovery analyses further show that typed failure-aware routing, rather than specialist composition alone, is a key factor for these improvements.

cs.AI↗

arXiv2026

MAGE: Multi-Agent Self-Evolution with Co-Evolutionary Knowledge Graphs

Self-evolving language-model agents must decide what to learn next and how to preserve what they have learned across iterations. Existing systems typically carry this cross-iteration knowledge as natural-language feedback, flat episodic memory, or implicit reinforcement signals, none of which cleanly supports a frozen weak backbone at inference time. This paper introduces MAGE (Multi-Agent Graph-guided Evolution), a framework that externalizes self-knowledge into a four-subgraph co-evolutionary knowledge graph. Its experience subgraph stores both teacher-written failure corrections and the learner's own past correct reasoning traces, which are retrieved as task-conditioned guidance for a frozen execution model. During evolution, the graph, a task-level search bandit, and a skill-level routing bandit are updated from the same reward stream, while the learner's backbone remains unchanged. We further provide structural analysis showing how append-only memory growth, bounded curriculum coverage, and task-filtered retrieval together support stable improvement of the retrieval substrate for frozen-learner evolution. Across nine benchmarks spanning mathematical reasoning, multi-hop and open-domain question answering, spatio-temporal analysis, financial numerical reasoning, medical multiple-choice, an open-world survival game, and web navigation, MAGE achieves strong performance against prompt-based frozen-backbone baselines. Ablations show that self-harvested success traces and teacher-written corrections are complementary, with success memories contributing most on reasoning-template-heavy tasks and corrective memories supporting harder composition and interaction settings.

cs.AI↗

arXiv2026

TrajPrism: A Multi-Task Benchmark for Language-Grounded Urban Trajectory Understanding

Urban mobility is naturally expressed both as trajectories in space and as natural-language descriptions of travel intent, constraints, and preferences. However, prior work rarely evaluates these two modalities together on the same real-world trajectories: trajectory modeling often stays geometry-centric, while language-centric mobility benchmarks frequently target route planning and tool use rather than fine-grained, verifiable alignment between text and the underlying route. We introduce TrajPrism, a multi-task benchmark for language-trajectory alignment that unifies (i) instruction-conditioned trajectory generation, (ii) language-driven semantic trajectory retrieval, and (iii) trajectory captioning, together with an evaluation protocol that measures trajectory fidelity, retrieval quality, and language groundedness. We construct TrajPrism by pairing real urban trajectories with judge-filtered language annotations generated under a four-dimensional travel-intent taxonomy. The benchmark contains 300K selected trajectories across Porto, San Francisco, and Beijing, yielding 2.1M task instances from three instruction variants, three retrieval queries, and one caption per trajectory. We further develop proof-of-concept models for each task: TrajAnchor for instruction-conditioned trajectory generation, TrajFuse for semantic trajectory retrieval, and TrajRap for trajectory captioning. These models instantiate the proposed tasks and show that geometry-only trajectory baselines leave a large gap on our protocol, especially where language is part of the input-output interface. We release TrajPrism with code and a reproducible annotation pipeline that is designed to be portable across cities, given compatible trajectory inputs and map resources.

cs.AI↗

arXiv2025

DAComp: Benchmarking Data Agents across the Full Data Intelligence Lifecycle

Real-world enterprise data intelligence workflows encompass data engineering that turns raw sources into analytical-ready tables and data analysis that convert those tables into decision-oriented insights. We introduce DAComp, a benchmark of 210 tasks that mirrors these complex workflows. Data engineering (DE) tasks require repository-level engineering on industrial schemas, including designing and building multi-stage SQL pipelines from scratch and evolving existing systems under evolving requirements. Data analysis (DA) tasks pose open-ended business problems that demand strategic planning, exploratory analysis through iterative coding, interpretation of intermediate results, and the synthesis of actionable recommendations. Engineering tasks are scored through execution-based, multi-metric evaluation. Open-ended tasks are assessed by a reliable, experimentally validated LLM-judge, which is guided by hierarchical, meticulously crafted rubrics. Our experiments reveal that even state-of-the-art agents falter on DAComp. Performance on DE tasks is particularly low, with success rates under 20%, exposing a critical bottleneck in holistic pipeline orchestration, not merely code generation. Scores on DA tasks also average below 40%, highlighting profound deficiencies in open-ended reasoning and demonstrating that engineering and analysis are distinct capabilities. By clearly diagnosing these limitations, DAComp provides a rigorous and realistic testbed to drive the development of truly capable autonomous data agents for enterprise settings. Our data and code are available at https://da-comp.github.io

cs.CL↗

arXiv2025

Bayesian Optimization on Networks

This paper studies optimization on networks modeled as metric graphs. Motivated by applications where the objective function is expensive to evaluate or only available as a black box, we develop Bayesian optimization algorithms that sequentially update a Gaussian process surrogate model of the objective to guide the acquisition of query points. To ensure that the surrogates are tailored to the network's geometry, we adopt Whittle-Mat\'ern Gaussian process prior models defined via stochastic partial differential equations on metric graphs. In addition to establishing regret bounds for optimizing sufficiently smooth objective functions, we analyze the practical case in which the smoothness of the objective is unknown and the Whittle-Mat\'ern prior is represented using finite elements. Numerical results demonstrate the effectiveness of our algorithms for optimizing benchmark objective functions on a synthetic metric graph and for Bayesian inversion via maximum a posteriori estimation on a telecommunication network.

stat.ML↗

arXiv2025

RELOOP: Recursive Retrieval with Multi-Hop Reasoner and Planners for Heterogeneous QA

Retrieval-augmented generation (RAG) remains brittle on multi-step questions and heterogeneous evidence sources, trading accuracy against latency and token/tool budgets. This paper introduces RELOOP, a structure aware framework using Hierarchical Sequence (HSEQ) that (i) linearize documents, tables, and knowledge graphs into a reversible hierarchical sequence with lightweight structural tags, and (ii) perform structure-aware iteration to collect just-enough evidence before answer synthesis. A Head Agent provides guidance that leads retrieval, while an Iteration Agent selects and expands HSeq via structure-respecting actions (e.g., parent/child hops, table row/column neighbors, KG relations); Finally the head agent composes canonicalized evidence to genearte the final answer, with an optional refinement loop to resolve detected contradictions. Experiments on HotpotQA (text), HybridQA/TAT-QA (table+text), and MetaQA (KG) show consistent EM/F1 gains over strong single-pass, multi-hop, and agentic RAG baselines with high efficiency. Besides, RELOOP exhibits three key advantages: (1) a format-agnostic unification that enables a single policy to operate across text, tables, and KGs without per-dataset specialization; (2) \textbf{guided, budget-aware iteration} that reduces unnecessary hops, tool calls, and tokens while preserving accuracy; and (3) evidence canonicalization for reliable QA, improving answers consistency and auditability.

cs.CL↗

arXiv2025

Divide by Question, Conquer by Agent: SPLIT-RAG with Question-Driven Graph Partitioning

Retrieval-Augmented Generation (RAG) systems empower large language models (LLMs) with external knowledge, yet struggle with efficiency-accuracy trade-offs when scaling to large knowledge graphs. Existing approaches often rely on monolithic graph retrieval, incurring unnecessary latency for simple queries and fragmented reasoning for complex multi-hop questions. To address these challenges, this paper propose SPLIT-RAG, a multi-agent RAG framework that addresses these limitations with question-driven semantic graph partitioning and collaborative subgraph retrieval. The innovative framework first create Semantic Partitioning of Linked Information, then use the Type-Specialized knowledge base to achieve Multi-Agent RAG. The attribute-aware graph segmentation manages to divide knowledge graphs into semantically coherent subgraphs, ensuring subgraphs align with different query types, while lightweight LLM agents are assigned to partitioned subgraphs, and only relevant partitions are activated during retrieval, thus reduce search space while enhancing efficiency. Finally, a hierarchical merging module resolves inconsistencies across subgraph-derived answers through logical verifications. Extensive experimental validation demonstrates considerable improvements compared to existing approaches.

cs.AI↗

arXiv2025

Beyond Single Pass, Looping Through Time: KG-IRAG with Iterative Knowledge Retrieval

Graph Retrieval-Augmented Generation (GraphRAG) has proven highly effective in enhancing the performance of Large Language Models (LLMs) on tasks that require external knowledge. By leveraging Knowledge Graphs (KGs), GraphRAG improves information retrieval for complex reasoning tasks, providing more precise and comprehensive retrieval and generating more accurate responses to QAs. However, most RAG methods fall short in addressing multi-step reasoning, particularly when both information extraction and inference are necessary. To address this limitation, this paper presents Knowledge Graph-Based Iterative Retrieval-Augmented Generation (KG-IRAG), a novel framework that integrates KGs with iterative reasoning to improve LLMs' ability to handle queries involving temporal and logical dependencies. Through iterative retrieval steps, KG-IRAG incrementally gathers relevant data from external KGs, enabling step-by-step reasoning. The proposed approach is particularly suited for scenarios where reasoning is required alongside dynamic temporal data extraction, such as determining optimal travel times based on weather conditions or traffic patterns. Experimental results show that KG-IRAG improves accuracy in complex reasoning tasks by effectively integrating external knowledge with iterative, logic-based retrieval. Additionally, three new datasets: weatherQA-Irish, weatherQA-Sydney, and trafficQA-TFNSW, are formed to evaluate KG-IRAG's performance, demonstrating its potential beyond traditional RAG applications.

cs.AI↗

arXiv2024

Model-free Estimation of Latent Structure via Multiscale Nonparametric Maximum Likelihood

Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this paper, we propose a model-free approach for estimating such latent structures whenever they are present, without assuming they exist a priori. Given an arbitrary density $p_0$, we construct a multiscale representation of the density and propose data-driven methods for selecting representative models that capture meaningful discrete structure. Our approach uses a nonparametric maximum likelihood estimator to estimate the latent structure at different scales and we further characterize their asymptotic limits. By carrying out such a multiscale analysis, we obtain coarseto-fine structures inherent in the original distribution, which are integrated via a model selection procedure to yield an interpretable discrete representation of it. As an application, we design a clustering algorithm based on the proposed procedure and demonstrate its effectiveness in capturing a wide range of latent structures.

stat.ME↗

arXiv2024

SSTKG: Simple Spatio-Temporal Knowledge Graph for Intepretable and Versatile Dynamic Information Embedding

Knowledge graphs (KGs) have been increasingly employed for link prediction and recommendation using real-world datasets. However, the majority of current methods rely on static data, neglecting the dynamic nature and the hidden spatio-temporal attributes of real-world scenarios. This often results in suboptimal predictions and recommendations. Although there are effective spatio-temporal inference methods, they face challenges such as scalability with large datasets and inadequate semantic understanding, which impede their performance. To address these limitations, this paper introduces a novel framework - Simple Spatio-Temporal Knowledge Graph (SSTKG), for constructing and exploring spatio-temporal KGs. To integrate spatial and temporal data into KGs, our framework exploited through a new 3-step embedding method. Output embeddings can be used for future temporal sequence prediction and spatial information recommendation, providing valuable insights for various applications such as retail sales forecasting and traffic volume prediction. Our framework offers a simple but comprehensive way to understand the underlying patterns and trends in dynamic KG, thereby enhancing the accuracy of predictions and the relevance of recommendations. This work paves the way for more effective utilization of spatio-temporal data in KGs, with potential impacts across a wide range of sectors.

cs.AI↗

arXiv2023

Gaussian Process Regression under Computational and Epistemic Misspecification

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Lo\`eve expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Our theory also accounts for epistemic misspecification in the choice of kernel parameters.

math.NA↗

arXiv2023

Optimization on Manifolds via Graph Gaussian Processes

This paper integrates manifold learning techniques within a \emph{Gaussian process upper confidence bound} algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

stat.ML↗

arXiv2023

Alignment of Density Maps in Wasserstein Distance

In this paper we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance between the density maps after a rigid transformation. The induced loss function enjoys a more benign landscape than its Euclidean counterpart and Bayesian optimization is employed for computation. Numerical experiments show improved accuracy and efficiency over existing algorithms on the alignment of real protein molecules. In the context of aligning heterogeneous pairs, we illustrate a potential need for new distance functions.

eess.IV↗

arXiv2022

Uniform Consistency in Nonparametric Mixture Models

We study uniform consistency in nonparametric mixture models as well as closely related mixture of regression (also known as mixed regression) models, where the regression functions are allowed to be nonparametric and the error distributions are assumed to be convolutions of a Gaussian density. We construct uniformly consistent estimators under general conditions while simultaneously highlighting several pain points in extending existing pointwise consistency results to uniform results. The resulting analysis turns out to be nontrivial, and several novel technical tools are developed along the way. In the case of mixed regression, we prove $L^1$ convergence of the regression functions while allowing for the component regression functions to intersect arbitrarily often, which presents additional technical challenges. We also consider generalizations to general (i.e. non-convolutional) nonparametric mixtures.

math.ST↗