arXiv subjects

Chengsong You

Publications and source records attributed to Chengsong You.

8 recordsLinked to original sources

arXiv2026

Mockenhaupt's Three-Term Hardy-Littlewood Majorant Conjecture

For an integer $k \ge 0$, let $f_k(x) = 1 + e(x) + e((k+2)x)$ and $g_k(x) = 1 + e(x) - e((k+2)x)$ on $\mathbb{T} = \mathbb{R}/\mathbb{Z}$, where $e(x) = e^{2\pi i x}$. Mockenhaupt conjectured that $\|g_k\|_{L^p(\mathbb{T})} > \|f_k\|_{L^p(\mathbb{T})}$ whenever $2k < p < 2k+2$. The conjecture was previously known for $k \le 5$. We give a single analytic proof valid for every $k \ge 4$; in particular, this settles all previously open cases $k \ge 6$ and establishes the conjecture for every $k \ge 0$. The proof reduces the norm comparison to resonant Fourier coefficients on the two-torus and represents these coefficients, after analytic continuation, by triple-Bessel integrals. Neumann's product formula and the Weber-Schafheitlin formula yield a quantitative positive lower bound for the leading mode, while the remaining odd modes are controlled by a uniform tail estimate. The leading mode is then shown to dominate the tail for every $k \ge 4$. AI Usage. The mathematical argument of this paper was produced by the auto-research system Apex Math, an AI system built by Apex Intelligence. See Appendix A for the complete AI usage statement.

math.CA↗

arXiv2026

Contractibility of the complex of incompressible Seifert surfaces: the knot case of Kakimizu's problem

Let $K \subset S^3$ be a non-trivial knot and let $IS(K)$ be the simplicial complex whose vertices are the ambient isotopy classes of incompressible Seifert surfaces in the exterior $E(K)$, a finite set of distinct vertices spanning a simplex exactly when its classes admit simultaneously pairwise disjoint representatives. Kakimizu proved that $IS(K)$ is connected; whether it is contractible was asked by Przytycki and Schultens, who also identified the obstruction, namely that the projection used in the connectedness proof is not known to be well defined on isotopy classes. We prove that $IS(K)$ is contractible, and likewise every truncation $IS_\ell(K)$ on the vertices of genus at most $\ell$. The argument factors through a purely combinatorial theorem: every non-empty connected flag exchange complex is contractible, where an exchange complex carries a complexity function subject to two axioms which require only that an exchanging vertex exist, never that one be selected. That is what circumvents the obstruction. We locate the combinatorial theorem precisely against the existing literature -- it is not implied by dismantlability, and, when all descending links are finite, it follows from Zaremsky's descending-link criterion by a reindexing (Section 7.4) -- and we record what remains genuinely open. Two extensions are proved: the truncations above, and the case of links satisfying a linking condition that forces every spanning surface to be connected.

math.GT↗

arXiv2026

KnowFeat: Knowledge-Guided Feature Engineering via LLM Agents

Automated feature engineering with large language models (LLMs) can produce semantically meaningful features for tabular data, yet existing methods lack structured domain knowledge, rigorous verification, and explainable provenance. We propose KnowFeat, a knowledge-guided feature engineering framework that organizes domain knowledge into five types -- schema metadata, regulatory indicators, detection rules, expert opinions, and court document evidence -- and injects them as structured context into an LLM agent. A three-stage verification pipeline filters candidates through code execution, statistical quality checks, and model effectiveness evaluation. Every accepted feature carries a provenance record tracing its design to specific knowledge assets. Under a strict held-out protocol that eliminates feature-selection leakage, KnowFeat ranks first (avg. rank 2.3) across twelve public benchmarks among seven methods (one-sided Wilcoxon p=0.017), with a peak gain of +11.6 pp AUC on a telecom churn dataset. On a real-world Bitcoin anti-money laundering (AML) dataset (Elliptic) and a synthetic digital currency AML benchmark (SimECNY), KnowFeat maintains competitive detection performance with full provenance traceability.

cs.DB↗

arXiv2026

R$^2$A: Learning Persona Policies Through Persona Representation Learning and Runtime Alignment

The same Persona behavior can be beneficial in one context but harmful in another, causing static Persona elicitation to perform inconsistently across tasks. We introduce the Persona Selection--Realization Framework, which models behavior generation through a latent Persona state and decomposes it into Persona Selection and Persona Realization. The discrepancies between static Persona elicitation and an ideal Persona policy in these two components define the Selection Gap and Realization Gap, respectively. Building on this framework, we propose R$^2$A, a two-stage approach for learning Persona policies. Persona Representation Learning uses structured Who--How--What presentations to encode the target Persona's objective, conditional behavioral principles, and trajectory-level manifestations. Persona Runtime Alignment then removes the explicit Persona specification and jointly calibrates behavior selection and trajectory realization using task feedback. Across 12 evaluation settings covering the four principles of the Accountable-Professional Persona studied in this work, R$^2$A overall outperforms both the base model and static Persona elicitation. Ablation results further show that Persona Representation Learning is critical for preventing Runtime Alignment from producing behaviorally imbalanced policies and for achieving more stable Persona policy learning.

cs.CL↗

arXiv2026

ProRetrieval: Learning to Orchestrate Hybrid Search via Executable Program Synthesis

Real-world retrieval often composes structured constraints with semantic intents over text and images through arbitrary Boolean logic. Existing hybrid pipelines such as reciprocal rank fusion or self-querying retrievers admit only a fixed form of composition, while recent reinforcement-learning retrievers train the language model as a query generator for a single backend, leaving the orchestration of heterogeneous retrieval paths outside its action space. We propose ProRetrieval, which recasts the language model as a retrieval orchestrator: given a natural-language query, it synthesizes an executable program in a hybrid DSL interleaving SQL operators over structured fields with vector-retrieval primitives over text and images, with SQL itself providing the logical algebra that fuses heterogeneous candidate sets. We train Qwen3-4B with GRPO and DAPO under a hierarchical four-term reward, and evaluate on two new benchmarks built from Amazon products and Enron email. Our 4B model surpasses GPT-5.5 (Hit@1 0.81 vs. 0.69 on e-commerce; 0.91 vs. 0.86 on email) and Claude Opus 4.7 and a comprehensive suite of retrieval, LLM-augmented, structured-query, and graph-based baselines. Code: https://anonymous.4open.science/r/ProRetrieval/; data: https://huggingface.co/datasets/anonymous-7219/ProRetrieval.

cs.IR↗

arXiv2026

DocPC: Document-Level Visual Retrieval via Representative Page Composition

Visual document retrieval has advanced by encoding page screenshots with vision-language models, bypassing OCR pipelines. However, existing methods remain page-centric, misaligned with real-world scenarios requiring complete document retrieval. A naive page-then-document aggregation suffers from linear indexing cost and degraded retrieval when relevance spans multiple pages. We propose DocPC, a document-level visual retrieval framework based on Representative Page Composition: selecting representative pages and composing them into a single grid image for document-level indexing, reducing indexed images, vectors, and storage by 10.1x and end-to-end indexing time by roughly 7.7x. To handle multi-positive supervision prevalent at the document level, we combine multi-positive contrastive learning with sparsely scheduled listwise optimization. We also introduce DocViRe, a benchmark with multi-positive relevance annotations. DocPC-ColQwen achieves NDCG@5 of 44.09 on DocViRe, outperforming the strongest page-level baseline at 38.91 while reducing storage by 10.1x. Code is available at https://anonymous.4open.science/r/DocPC-Document-Level-Visual-Retrieval-via-Representative-Page-Composition-1D52. Data is available at https://huggingface.co/datasets/anonymous-7219/docpc.

cs.IR↗

arXiv2026

ASI-Bench: At the Dawn of Artificial Superintelligence

Artificial superintelligence (ASI) requires AI to move beyond mastering existing knowledge toward exploring the unknown, creating new knowledge, and turning new ideas into verifiable results. However, the capabilities of today's AI systems are still largely built on learning, compressing, and applying existing human knowledge. Accordingly, existing benchmarks primarily test whether AI can produce correct answers based on learned knowledge, or whether it can complete tasks under extensive human guidance. We therefore introduce ASI-Bench, the first benchmark to jointly evaluate AI systems' capabilities of innovative exploration and autonomous scientific execution across general research domains, and the first to progressively withdraw human methodological guidance within the same research project to test how far AI can proceed on its own. Built by over 40 experts with the cost of 31,000+ human hours, ASI-Bench contains 60 project-level research tasks across 11 scientific domains and progressively reduces methodological guidance to test whether AI can independently select methods, conduct research, and produce verifiable results. All tasks undergo expert review, AI-assisted auditing, sandbox execution, and scorer validation. Across 18 state-of-the-art agent--model configurations, the average score drops from 50.91 with full methodological guidance to 29.10 with only the method specified and 26.62 when agents must determine the method themselves. This sharp decline shows that current systems remain heavily dependent on human guidance and are still far from autonomously conducting end-to-end, project-level scientific research. ASI-Bench is open to the world. We invite researchers and builders everywhere to contribute new tasks, challenge the limits of today's AI, and help accelerate humanity's collective path toward artificial superintelligence at https://asibench.apexin.ai/submit.

cs.AI↗

arXiv2025

UniEdit: A Unified Knowledge Editing Benchmark for Large Language Models

Model editing aims to enhance the accuracy and reliability of large language models (LLMs) by efficiently adjusting their internal parameters. Currently, most LLM editing datasets are confined to narrow knowledge domains and cover a limited range of editing evaluation. They often overlook the broad scope of editing demands and the diversity of ripple effects resulting from edits. In this context, we introduce UniEdit, a unified benchmark for LLM editing grounded in open-domain knowledge. First, we construct editing samples by selecting entities from 25 common domains across five major categories, utilizing the extensive triple knowledge available in open-domain knowledge graphs to ensure comprehensive coverage of the knowledge domains. To address the issues of generality and locality in editing, we design an Neighborhood Multi-hop Chain Sampling (NMCS) algorithm to sample subgraphs based on a given knowledge piece to entail comprehensive ripple effects to evaluate. Finally, we employ proprietary LLMs to convert the sampled knowledge subgraphs into natural language text, guaranteeing grammatical accuracy and syntactical diversity. Extensive statistical analysis confirms the scale, comprehensiveness, and diversity of our UniEdit benchmark. We conduct comprehensive experiments across multiple LLMs and editors, analyzing their performance to highlight strengths and weaknesses in editing across open knowledge domains and various evaluation criteria, thereby offering valuable insights for future research endeavors.

cs.CL↗