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Haoran Luo

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Artificial Intelligence math.CO math.PR

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preprint2026arXiv

Cumulative Path-Level Semantic Reasoning for Inductive Knowledge Graph Completion

Conventional Knowledge Graph Completion (KGC) methods aim to infer missing information in incomplete Knowledge Graphs (KGs) by leveraging existing information, which struggle to perform effectively in scenarios involving emerging entities. Inductive KGC methods can handle the emerging entities and relations in KGs, offering greater dynamic adaptability. While existing inductive KGC methods have achieved some success, they also face challenges, such as susceptibility to noisy structural information during reasoning and difficulty in capturing long-range dependencies in reasoning paths. To address these challenges, this paper proposes the Cumulative Path-Level Semantic Reasoning for inductive knowledge graph completion (CPSR) framework, which simultaneously captures both the structural and semantic information of KGs to enhance the inductive KGC task. Specifically, the proposed CPSR employs a query-dependent masking module to adaptively mask noisy structural information while retaining important information closely related to the targets. Additionally, CPSR introduces a global semantic scoring module that evaluates both the individual contributions and the collective impact of nodes along the reasoning path within KGs. The experimental results demonstrate that CPSR achieves state-of-the-art performance.

preprint2026arXiv

HEDP: A Hybrid Energy-Distance Prompt-based Framework for Domain Incremental Learning

Domain Incremental Learning is a critical scenario that requires models to continuously adapt to new data domains without retraining. However, domain shifts often cause severe performance degradation. To address this, we propose Hybrid Energy-Distance Prompt, a domain-incremental framework inspired by Helmholtz free energy. HEDP introduces an energy regularization loss to enhance the separability of domain representations and a hybrid energy-distance weighted mechanism that fuses energy-based and distance-based cues to improve domain selection and generalization. Experiments on multiple benchmarks, including CORe50, show that HEDP achieves superior performance on unseen domains with a 2.57\% accuracy gain, effectively mitigating catastrophic forgetting and enhancing open-world adaptability. Our code is \href{https://github.com/dannis97500/HEDP/}{available here}.

preprint2026arXiv

Maximum number of points in general position in a random subset of finite $3$ -dimensional spaces

Let $α(\mathbb{F}_q^{d},p)$ be the maximum possible size of a point set in general position in the $p$ -random subset of $\mathbb{F}_q^d$ . In this note, we determine the order of magnitude of $α(\mathbb{F}_q^{3},p)$ up to a polylogarithmic factor by proving a balanced supersaturation result for the sets of $4$ points in the same plane.

preprint2026arXiv

MAXS: Meta-Adaptive Exploration with LLM Agents

Large Language Model (LLM) Agents exhibit inherent reasoning abilities through the collaboration of multiple tools. However, during agent inference, existing methods often suffer from (i) locally myopic generation, due to the absence of lookahead, and (ii) trajectory instability, where minor early errors can escalate into divergent reasoning paths. These issues make it difficult to balance global effectiveness and computational efficiency. To address these two issues, we propose meta-adaptive exploration with LLM agents https://github.com/exoskeletonzj/MAXS, a meta-adaptive reasoning framework based on LLM Agents that flexibly integrates tool execution and reasoning planning. MAXS employs a lookahead strategy to extend reasoning paths a few steps ahead, estimating the advantage value of tool usage, and combines step consistency variance and inter-step trend slopes to jointly select stable, consistent, and high-value reasoning steps. Additionally, we introduce a trajectory convergence mechanism that controls computational cost by halting further rollouts once path consistency is achieved, enabling a balance between resource efficiency and global effectiveness in multi-tool reasoning. We conduct extensive empirical studies across three base models (MiMo-VL-7B, Qwen2.5-VL-7B, Qwen2.5-VL-32B) and five datasets, demonstrating that MAXS consistently outperforms existing methods in both performance and inference efficiency. Further analysis confirms the effectiveness of our lookahead strategy and tool usage.

preprint2026arXiv

SkillFlow: Flow-Driven Recursive Skill Evolution for Agentic Orchestration

In recent years, a variety of powerful LLM-based agentic systems have been applied to automate complex tasks through task orchestration. However, existing orchestration methods still face key challenges, including strategy collapse under reward maximization, high gradient variance with opaque credit assignment, and unguided skill evolution whose decisions are typically made by directly prompting an LLM to judge rather than derived from principled training signals. To address these challenges, we propose SkillFlow, a flow-based framework that takes a trainable Supervisor as the agent and a structured environment with dynamic skill library and frozen executor, automating task orchestration through multi-turn interaction. SkillFlow employs Tempered Trajectory Balance (TTB), a regression-based flow-matching loss that samples trajectories proportional to reward, preserving diverse orchestration strategies rather than collapsing to a single mode. The same flow objective yields a jointly learned backward policy that provides transparent per-step credit assignment at zero additional inference cost. Building on these flow diagnostics, a recursive skill evolution mechanism determines when to evolve, what skills to create or prune, and where decision gaps lie -- closing the loop from training signal to autonomous capability growth. Experimental results on 14 datasets show that SkillFlow significantly outperforms baselines across question answering, mathematical reasoning, code generation, and real-world interactive decision making tasks. Our code is available at https://anonymous.4open.science/r/SkillFlow-E850.

preprint2022arXiv

Maximal 3-wise Intersecting Families with Minimum Size: the Odd Case

A family $\mathcal{F}$ on ground set $\{1,2,\ldots, n\}$ is maximal $k$ -wise intersecting if every collection of $k$ sets in $\mathcal{F}$ has non-empty intersection, and no other set can be added to $\mathcal{F}$ while maintaining this property. Erdős and Kleitman asked for the minimum size of a maximal $k$ -wise intersecting family. Complementing earlier work of Hendrey, Lund, Tompkins and Tran, who answered this question for $k=3$ and large even $n$ , we answer it for $k=3$ and large odd $n$ . We show that the unique minimum family is obtained by partitioning the ground set into two sets $A$ and $B$ with almost equal sizes and taking the family consisting of all the proper supersets of $A$ and of $B$ . A key ingredient of our proof is the stability result by Ellis and Sudakov about the so-called $2$ -generator set systems.

preprint2022arXiv

Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions

For every integer $t \ge 0$ , denote by $F_5^t$ the hypergraph on vertex set $\{1,2,\ldots, 5+t\}$ with hyperedges $\{123,124\} \cup \{34k : 5 \le k \le 5+t\}$ . We determine $\mathrm{ex}(n,F_5^t)$ for every $t\ge 0$ and sufficiently large $n$ and characterize the extremal $F_5^t$ -free hypergraphs. In particular, if $n$ satisfies certain divisibility conditions, then the extremal $F_5^t$ -free hypergraphs are exactly the balanced complete tripartite hypergraphs with additional hyperedges inside each of the three parts $(V_1,V_2,V_3)$ in the partition; each part $V_i$ spans a $(|V_i|,3,2,t)$ -design. This generalizes earlier work of Frankl and Füredi on the Turán number of $F_5:=F_5^0$ . Our results extend a theory of Erdős and Simonovits about the extremal constructions for certain fixed graphs. In particular, the hypergraphs $F_5^{6t}$ , for $t\geq 1$ , are the first examples of hypergraphs with exponentially many extremal constructions and positive Turán density.

preprint2022arXiv

Sharp threshold for the Erdős-Ko-Rado theorem

For positive integers $n$ and $k$ with $n\geq 2k+1$ , the Kneser graph $K(n,k)$ is the graph with vertex set consisting of all $k$ -sets of $\{1,\dots,n\}$ , where two $k$ -sets are adjacent exactly when they are disjoint. The independent sets of $K(n,k)$ are $k$ -uniform intersecting families, and hence the maximum size independent sets are given by the Erdős-Ko-Rado Theorem. Let $K_p(n,k)$ be a random spanning subgraph of $K(n,k)$ where each edge is included independently with probability $p$ . Bollobás, Narayanan, and Raigorodskii asked for what $p$ does $K_p(n,k)$ have the same independence number as $K(n,k)$ with high probability. For $n=2k+1$ , we prove a hitting time result, which gives a sharp threshold for this problem at $p=3/4$ . Additionally, completing work of Das and Tran and work of Devlin and Kahn, we determine a sharp threshold function for all $n>2k+1$ .

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Haoran Luo

Research overview

Is this your work?

8 publications

Cumulative Path-Level Semantic Reasoning for Inductive Knowledge Graph Completion

HEDP: A Hybrid Energy-Distance Prompt-based Framework for Domain Incremental Learning

Maximum number of points in general position in a random subset of finite $3$ -dimensional spaces

MAXS: Meta-Adaptive Exploration with LLM Agents

SkillFlow: Flow-Driven Recursive Skill Evolution for Agentic Orchestration

Maximal 3-wise Intersecting Families with Minimum Size: the Odd Case

Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions

Sharp threshold for the Erdős-Ko-Rado theorem

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Building this map preview

Haoran Luo

Research overview

Is this your work?

8 publications

Cumulative Path-Level Semantic Reasoning for Inductive Knowledge Graph Completion

HEDP: A Hybrid Energy-Distance Prompt-based Framework for Domain Incremental Learning

Maximum number of points in general position in a random subset of finite 333-dimensional spaces

MAXS: Meta-Adaptive Exploration with LLM Agents

SkillFlow: Flow-Driven Recursive Skill Evolution for Agentic Orchestration

Maximal 3-wise Intersecting Families with Minimum Size: the Odd Case

Non-degenerate Hypergraphs with Exponentially Many Extremal Constructions

Sharp threshold for the Erdős-Ko-Rado theorem

See the researcher in context

Building this map preview

Maximum number of points in general position in a random subset of finite $3$ -dimensional spaces