arXiv subjects

Enhan Li

Publications and source records attributed to Enhan Li.

10 recordsLinked to original sources

arXiv2026

Skein and cluster algebras of punctured surfaces

We prove the full Fock--Goncharov conjecture for the $\mathcal{A}_{SL_2,Σ_{g,p}}$-cluster variety associated with the moduli space of decorated twisted $SL_2$-local systems on triangulable surfaces $Σ_{g,p}$ with at least two punctures. Equivalently, we show that the tagged skein algebra $Sk^{ta}(Σ)$, identified with the middle cluster algebra $\mathrm{mid}(\mathcal{A})$, coincides with the upper cluster algebra $U(Σ)$. Inspired by the work of Shen--Sun--Weng, we introduce a localized cluster variety $\mathring{\mathcal{A}}$ whose positive real locus is the decorated Teichmüller space $\mathcal{T}^d(Σ)$. For $p\geq2$, its ring of global sections is the normalization of the classical Roger--Yang skein algebra $Sk^{RY}_{q\to1}(Σ)$ and equals that algebra except for the four-punctured sphere. In the equality cases, the quantum Roger--Yang skein algebra $Sk^{RY}_q(Σ)$ provides a quantization of this global-section ring. We prove normality of $Sk^{ta}(Σ)$ for $p\geq2$, complementing its known Gorenstein property, and normality of $Sk^{RY}_{q\to1}(Σ)$ for every triangulable $Σ_{g,p}$ other than $Σ_{0,4}$. We also prove finite generation of $U(Σ_{g,p})$ for every triangulable $Σ_{g,p}$, including the once-punctured case.

math.AC↗

arXiv2026

Hodge--Riemann relations for $m$-positive and generalized $m$-positive forms

We study Hodge--Riemann relations for ordinary, sequential, and weak $m$-positive real $(1,1)$-forms in complex dimension $d$. For ordinary $m$-positive forms, we prove the fully mixed relations in every permitted bidegree without assuming semipositivity, generalizing results by Xiao. As a generalization of ordinary $m$-positivity, sequential $m$-positivity is defined by the hyperbolicity cones of successive directional derivatives of the determinant. We formulate a generalized mixed Hodge--Riemann conjecture for this condition and prove several cases beyond the scalar inequalities supplied by hyperbolicity. We also consider weak $m$-positivity which corresponds to the pointwise subsolution condition for the complex $m$-Hessian equation. In this setting, we prove the Hodge--Riemann relations for $p\neq q$ and in several diagonal cases, and show that the associated power map induces a pointwise diffeomorphism onto the cone of positive $(d-1,d-1)$-forms. Using Dinh and Nguyên's $L^2$ globalization method, we pass from the pointwise relations to cohomology classes on compact Kähler manifolds. Finally, we propose conjectures on a numerical criterion for sequential positivity and on solvability of the generalized $m$-Hessian equation.

math.AG↗

arXiv2026

Hodge--Riemann relations for nef bundles

We introduce the $(m,p,q)$-Lefschetz property for $(1,1)$-type endomorphisms of Hodge--Lefschetz modules, providing a framework for studying nef $(1,1)$-classes and characteristic classes of nef vector bundles on compact Kähler manifolds. Under a Hall--Rado type condition on nef twisted vector bundles, we prove Hodge--Riemann relations for products of top Chern classes and, in suitable bidegrees, for products of derived Schur classes. For products of nef $(1,1)$-classes, we show furthermore that the Hall--Rado type condition is equivalent to simultaneous Hodge--Riemann relations. Our proofs build on the purity theorem and descent lemma of Cattani, Kaplan, and Schmid. We extend the descent lemma to Schur classes of nef vector bundles. We also establish formal analogs for projective bundle modules over Hodge--Lefschetz modules, with applications to tautological classes and descent on matroid Chow rings.

math.AG↗

arXiv2026

CROP: Task Relevance via Counterfactuals for Selective On-Policy Distillation

On-policy distillation (OPD) supervises a student language model on trajectories sampled from its current policy, but assigns equal credit to response tokens with unequal supervision value. Selective OPD addresses this limitation by allocating supervision non-uniformly across response tokens according to their estimated training value. Most existing criteria, however, focus primarily on optimization need, such as uncertainty or teacher-student disagreement, while task relevance, namely whether the supervision is tied to the semantic content of the current input, remains less directly characterized as a complementary dimension. To address this gap, we introduce Counterfactual Relevance for On-Policy Distillation (CROP), which operationalizes task relevance through a paraphrase-calibrated counterfactual sensitivity margin. For each source prompt, CROP constructs a validated original-paraphrase-counterfactual triplet, holds the student rollout fixed, and measures each response position by its sensitivity to a task-relevant condition change calibrated by its sensitivity to a meaning-preserving rewrite. Matched selection controls show that CROP identifies more useful supervision positions than random or lowest-relevance selection, while component comparisons confirm the value of both counterfactual sensitivity and paraphrase calibration. Across two teacher-student settings, CROP improves aggregate performance by 1.92 and 2.96 points over the strongest non-CROP selector. These results support task relevance as a complementary criterion for selective OPD and establish CROP as a model-internal, contrast-specific method for allocating token-level supervision.

cs.CL↗

arXiv2026

HACO: Hedged Agent Computing for Reliable LLM Systems

As large language model (LLM) agents move from isolated prompting to longhorizon workflows, failures increasingly arise at the role-to-instance binding boundary, where task-specific role requests must be assigned to concrete agent instances under current service, network, and query conditions. Existing agent system research has improved role specialization, workflow topology, memory, and tool use, but often assumes a fixed stable execution environment. This assumption limits deployed reliability, because the same role request can exhibit different latency, failure probability, and output quality across agent instances operating under different service regions and network conditions. We propose Hedged Agent Computing (HACO), a runtime control scheme that treats each role request as a reliability-constrained selection problem over candidate agent instances, each coupling a role type, an LLM, and a concrete execution environment. Different from routing, HACO adaptively selects a hedge set of candidates for each invocation. Its allocation rule combines optimistic ranking, which prioritizes candidates with high estimated quality, reliability, and informative uncertainty, with conservative reliability accumulation, which stops selection only after the hedge set reaches a target success probability. Through experience harvesting, HACO updates candidate and link profiles from all executed candidate traces, including quality, success, latency, and network statistics. Experiments on various benchmarks, together with runtime degradation studies, show that HACO improves robustness and output quality under changing deployment conditions, while using lower token and latency cost than exhaustive parallel execution.

cs.NI↗

arXiv2025

JAUNT: Joint Alignment of User Intent and Network State for QoE-centric LLM Tool Routing

Large Language Models (LLMs) increasingly rely on emerging protocols such as the Model Context Protocol (MCP) to invoke external tools and services. However, current tool routing mechanisms remain fragile because they only consider functional matching between users' queries and tools. In practice, user intent expressed through queries can be vague or underspecified, and the actual Quality of Experience (QoE) also depends on external factors such as link latency and server availability that are not captured by semantics alone. To address this challenge, we propose JAUNT, a framework for Joint Alignment of User intent and Network state in QoE-centric Tool routing. JAUNT introduces a dual-view alignment strategy that interprets user intent while employing LLM agents to construct network profiles, mapping numerical performance indicators into the semantic space to guide routing. We further design a benchmark that integrates diverse user request patterns with heterogeneous network states, enabling systematic evaluation of QoE outcomes. Experimental results show that JAUNT significantly improves QoE compared with several baselines, demonstrating the importance of aligning both intent and network state for scalable LLM service orchestration.

cs.NI↗

arXiv2025

NetMCP: Network-Aware Model Context Protocol Platform for LLM Capability Extension

Large Language Models (LLMs) remain static in functionality after training, and extending their capabilities requires integration with external data, computation, and services. The Model Context Protocol (MCP) has emerged as a standard interface for such extensions, but current implementations rely solely on semantic matching between users' requests and server function descriptions, which makes current deployments and simulation testbeds fragile under latency fluctuations or server failures. We address this gap by enhancing MCP tool routing algorithms with real-time awareness of network and server status. To provide a controlled test environment for development and evaluation, we construct a heterogeneous experimental platform, namely Network-aware MCP (NetMCP), which offers five representative network states and build a benchmark for latency sequence generation and MCP server datasets. On top of NetMCP platform, we analyze latency sequences and propose a Semantic-Oriented and Network-Aware Routing (SONAR) algorithm, which jointly optimizes semantic similarity and network Quality of Service (QoS) metrics for adaptive tool routing. Results show that SONAR consistently improves task success rate and reduces completion time and failure number compared with semantic-only, LLM-based baselines, demonstrating the value of network-aware design for production-scale LLM systems. The code for NetMCP is available at https://github.com/NICE-HKU/NetMCP.

cs.NI↗

arXiv2024

End-To-End Underwater Video Enhancement: Dataset and Model

Underwater video enhancement (UVE) aims to improve the visibility and frame quality of underwater videos, which has significant implications for marine research and exploration. However, existing methods primarily focus on developing image enhancement algorithms to enhance each frame independently. There is a lack of supervised datasets and models specifically tailored for UVE tasks. To fill this gap, we construct the Synthetic Underwater Video Enhancement (SUVE) dataset, comprising 840 diverse underwater-style videos paired with ground-truth reference videos. Based on this dataset, we train a novel underwater video enhancement model, UVENet, which utilizes inter-frame relationships to achieve better enhancement performance. Through extensive experiments on both synthetic and real underwater videos, we demonstrate the effectiveness of our approach. This study represents the first comprehensive exploration of UVE to our knowledge. The code is available at https://anonymous.4open.science/r/UVENet.

cs.CV↗

arXiv2023

UIEDP:Underwater Image Enhancement with Diffusion Prior

Underwater image enhancement (UIE) aims to generate clear images from low-quality underwater images. Due to the unavailability of clear reference images, researchers often synthesize them to construct paired datasets for training deep models. However, these synthesized images may sometimes lack quality, adversely affecting training outcomes. To address this issue, we propose UIE with Diffusion Prior (UIEDP), a novel framework treating UIE as a posterior distribution sampling process of clear images conditioned on degraded underwater inputs. Specifically, UIEDP combines a pre-trained diffusion model capturing natural image priors with any existing UIE algorithm, leveraging the latter to guide conditional generation. The diffusion prior mitigates the drawbacks of inferior synthetic images, resulting in higher-quality image generation. Extensive experiments have demonstrated that our UIEDP yields significant improvements across various metrics, especially no-reference image quality assessment. And the generated enhanced images also exhibit a more natural appearance.

cs.CV↗

arXiv2023

Timestamp-Supervised Action Segmentation from the Perspective of Clustering

Video action segmentation under timestamp supervision has recently received much attention due to lower annotation costs. Most existing methods generate pseudo-labels for all frames in each video to train the segmentation model. However, these methods suffer from incorrect pseudo-labels, especially for the semantically unclear frames in the transition region between two consecutive actions, which we call ambiguous intervals. To address this issue, we propose a novel framework from the perspective of clustering, which includes the following two parts. First, pseudo-label ensembling generates incomplete but high-quality pseudo-label sequences, where the frames in ambiguous intervals have no pseudo-labels. Second, iterative clustering iteratively propagates the pseudo-labels to the ambiguous intervals by clustering, and thus updates the pseudo-label sequences to train the model. We further introduce a clustering loss, which encourages the features of frames within the same action segment more compact. Extensive experiments show the effectiveness of our method.

cs.CV↗