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Tian Wang

Publications and source records attributed to Tian Wang.

At least 37 records · Page 2Linked to original sources
arXiv2026

Circuit-Inspired High-Order Neural Networks with Unified Neural Dynamics Modeling for PDE Solving and Visual Perception

Deep networks often rely on architectural heuristics to shape representation evolution, limiting their ability to model data governed by intrinsic dynamics. We present the Circuit-inspired High-Order Neural Network (CHONN), a modular framework that treats representation evolution as a latent potential process and increases its effective order through Kirchhoff-inspired cascade composition. A single Kirchhoff Neural Cell implements a stable first-order update, while serially composed cells form higher-order dynamical operators within one block. This construction is interpretable, numerically stable and compatible with common neural backbones. Theoretical analysis shows that cascaded cells induce end-to-end high-order operators, and controlled experiments demonstrate that intra-block high-order construction differs from generic depth stacking, especially on derivative-sensitive measures. Across steady-state operator learning, long-horizon physical forecasting and ImageNet-1K recognition, CHONN improves structural fidelity, rollout stability and visual representation learning. These results identify high-order circuit composition as a general principle for neural dynamics modeling.

cs.LG↗
arXiv2026

OPeRA: A Dataset of Observation, Persona, Rationale, and Action for Evaluating LLMs on Human Online Shopping Behavior Simulation

Can large language models (LLMs) accurately simulate the next web action of a specific user? While LLMs have shown promising capabilities in generating ``believable'' human behaviors, evaluating their ability to mimic real user behaviors remains an open challenge, largely due to the lack of high-quality, publicly available datasets that capture both the observable actions and the internal reasoning of an actual human user. To address this gap, we introduce OPERA, a novel dataset of Observation, Persona, Rationale, and Action collected from real human participants during online shopping sessions. OPERA is the first public dataset that comprehensively captures: user personas, browser observations, fine-grained web actions, and self-reported just-in-time rationales. We developed both an online questionnaire and a custom browser plugin to gather this dataset with high fidelity. Using OPERA, we establish the first benchmark to evaluate how well current LLMs can predict a specific user's next action and rationale with a given persona and history. This dataset lays the groundwork for future research into LLM agents that aim to act as personalized digital twins for human.

cs.CL↗
arXiv2026

3D Primitives are a Spatial Language for VLMs

Vision-language models (VLMs) exhibit a striking paradox: they can generate executable code that reconstructs a 3D scene from geometric primitives with correct object counts, classes, and approximate positions, yet the same models fail at simpler spatial questions on the same image. We show that 3D geometric primitives (cubes, spheres, cylinders, expressed in executable code) serve as a powerful intermediate representation for spatial understanding, and exploit this through three contributions. First, we introduce \textbf{\textsc{SpatialBabel}}, a benchmark evaluating fourteen VLMs on primitive-based 3D scene reconstruction across six \emph{scene-code languages} (programming languages and declarative formats for 3D primitive scenes), revealing that a single model's object-detection F1 can vary by up to $5.7\times$ across languages. Second, we propose \textbf{Code-CoT} (Code Chain-of-Thought), a training-free inference strategy that routes spatial reasoning through primitive-based code generation. Code-CoT lifts the SpatialBabel-QA-Score by up to $+6.4$\% on primitive scenes and real-photo CV-Bench-3D accuracy by $+5.0$\% for VLMs with strong coding capabilities. Third, we propose \textbf{S$^{3}$-FT} (Self-Supervised Spatial Fine-Tuning), which self-supervisedly distills primitive spatial knowledge into general visual reasoning by parsing the model's own Three.js primitive-reconstructions into structured annotations and fine-tuning on the result, with \emph{no human labels and no teacher model}. Training on primitive images alone, S$^3$-FT improves Qwen3-VL-8B by $+4.6$ to $+8.6$\% on SpatialBabel-Primitive-QA, $+9.7$\% on CV-Bench-2D, and $+17$\% on HallusionBench; the recipe transfers across model families. These results establish geometric primitives in code as both a diagnostic and a transferable spatial vocabulary for VLMs. We will release all artifacts upon publication.

cs.CV↗
arXiv2026

On the Density of Coprime Reductions of Elliptic Curves

Given non-CM elliptic curves $E_1$ and $E_2$ over $\mathbb{Q}$, we study the natural density of primes $p$ of good reduction for which the orders of the groups $E_1(\mathbb{F}_p)$ and $E_2(\mathbb{F}_p)$ are coprime. This problem may be viewed as an elliptic curve analogue of the classical question concerning the density of coprime integer pairs. Motivated by Zywina's refinement of the Koblitz conjecture, we formulate a conjecture for the density of such primes. We prove that the series defining this constant converges and admits an almost Euler product expansion. In the case of Serre pairs, we give a closed formula for the constant and use it to prove a moments result describing the distribution of these constants as $(E_1, E_2)$ varies.

math.NT↗
arXiv2026

LLM Agents Enable User-Governed Personalization Beyond Platform Boundaries

Personalization today is fundamentally platform-centric: services build user representations from the behavioral fragments they observe. Yet no platform can construct a complete picture of the user, as competitive incentives, legal constraints, user privacy concerns, and epistemic limits create persistent data barriers. This paper argues for a shift from platform-centric personalization to user-governed personalization, where only the user can integrate fragmented contexts across platforms and the offline world. The key asymmetry lies in data access: only users can aggregate their own cross-platform and offline information. Large language model (LLM) agents make such integration practically feasible for the first time by enabling reasoning over heterogeneous personal data and transforming users' cross-context information into actionable personalization capabilities. We provide proof-of-concept evidence that users equipped with cross-platform data exports and an off-the-shelf LLM agent can outperform single-platform personalization baselines. We conclude by outlining a research agenda for building scalable user-governed personalization systems.

cs.IR↗
arXiv2026

CodeRL+: Improving Code Generation via Reinforcement with Execution Semantics Alignment

While Large Language Models (LLMs) excel at code generation by learning from vast code corpora, a fundamental semantic gap remains between their training on textual patterns and the goal of functional correctness, which is governed by formal execution semantics. Reinforcement Learning with Verifiable Rewards (RLVR) approaches attempt to bridge this gap using outcome rewards from executing test cases. However, solely relying on binary pass/fail signals is inefficient for establishing a well-aligned connection between the textual representation of code and its execution semantics, especially for subtle logical errors within the code. In this paper, we propose CodeRL+, a novel approach that integrates execution semantics alignment into the RLVR training pipeline for code generation. CodeRL+ enables the model to infer variable-level execution trajectory, providing a direct learning signal of execution semantics. CodeRL+ can construct execution semantics alignment directly using existing on-policy rollouts and integrates seamlessly with various RL algorithms. Extensive experiments demonstrate that CodeRL+ outperforms post-training baselines (including RLVR and Distillation), achieving a 4.6% average relative improvement in pass@1. CodeRL+ generalizes effectively to other coding tasks, yielding 15.5% and 4.4% higher accuracy on code-reasoning and test-output-generation benchmarks, respectively. CodeRL+ shows strong applicability across diverse RL algorithms and LLMs. Furthermore, probe analyses provide compelling evidence that CodeRL+ strengthens the alignment between code's textual representations and its underlying execution semantics.

cs.SE↗
arXiv2026

Bounds for the distribution of the Frobenius traces associated to a generic abelian variety

Let $A$ be an abelian variety defined over $\mathbb{Q}$ and of dimension $g$. Assume that, for each sufficiently large prime $\ell$, $A$ has a surjective residual modulo $\ell$ Galois representation. For $t\in \mathbb{Z}$ and $x>0$, denote by $π_A(x, t)$ the number of primes $p \leq x$ for which the Frobenius trace $a_{1, p}(A)$ associated to $A \pmod p$ equals $t$. Assuming the Generalized Riemann Hypothesis for Dedekind zeta functions (GRH), we obtain that $π_A(x, 0) \ll_A x^{1 - \frac{1}{2g^2+g+1}}/(\log x)^{1 - \frac{2}{2g^2+g+1}}$ and $π_A(x, t) \ll_A x^{1 - \frac{1}{2g^2+g+2}}/(\log x)^{1 - \frac{2}{2g^2+g+2}}$ if $t \neq 0$, and deduce that almost all primes $p$ satisfy $|a_{1, p}(A)| > p^{\frac{1}{2 g^2 + g + 1}}/ (\log p)^{\frac{2}{2g^2+g+1}+\varepsilon}$ for any $\varepsilon>0$. Assuming, in addition to GRH, Artin's Holomorphy Conjecture and a Pair Correlation Conjecture for Artin L-functions, we obtain that $π_A(x, 0) \ll_A x^{1 - \frac{1}{g+1}}/(\log x)^{1 - \frac{4}{g+1}}$ and $π_A(x, t) \ll_A x^{1 - \frac{1}{g+2}}/(\log x)^{1 - \frac{4}{g+2}}$ if $t \neq 0$, and deduce that almost all primes $p$ satisfy $|a_{1, p}(A)|> p^{\frac{1}{g + 2} - \varepsilon }$ for any $\varepsilon>0$.

math.NT↗
arXiv2026

Detecting Data Contamination from Reinforcement Learning Post-training for Large Language Models

Data contamination poses a significant threat to the reliable evaluation of Large Language Models (LLMs). This issue arises when benchmark samples may inadvertently appear in training sets, compromising the validity of reported performance. While detection methods have been developed for the pre-training and Supervised Fine-Tuning stages, a critical research gap exists for the increasingly significant phase of Reinforcement Learning (RL) post-training. As RL post-training becomes pivotal for advancing LLM reasoning, the absence of specialized contamination detection methods in this paradigm presents a critical vulnerability. To address this, we conduct the first systematic study of data detection within RL post-training scenario and propose Self-Critique. Our method is motivated by a key observation: after RL phase, the output entropy distribution of LLMs tends to collapse into highly specific and sparse modes. Self-Critique probes for the underlying policy collapse, i.e., the model's convergence to a narrow reasoning path, which causes this entropy reduction. To facilitate this research, we also introduce RL-MIA, a benchmark constructed to simulate this specific contamination scenario. Extensive experiments show that Self-Critique significantly outperforms baseline methods across multiple models and contamination tasks, achieving an AUC improvement of up to 30%. Whereas existing methods are close to a random guess for RL-phase contamination, our method makes detection possible.

cs.CL↗
arXiv2026

Adaptation of Agentic AI: A Survey of Post-Training, Memory, and Skills

Large language model (LLM) agents are moving beyond prompting alone. ChatGPT marked the rise of general-purpose LLM assistants, DeepSeek showed that on-policy reinforcement learning with verifiable rewards can improve reasoning and tool use, and OpenClaw highlights a newer direction in which agents accumulate persistent memory and reusable skills. Yet the research landscape remains fragmented across post-training, retrieval, memory, and skill systems. This survey studies these developments under a single notion of \emph{adaptation}: improving an agent, its tools, or their interaction after pretraining. We organize the field with a four-paradigm framework spanning agent adaptation and tool adaptation. On the agent side, A1 (tool-execution-signaled) and A2 (agent-output-signaled) improve the agent itself through supervised fine-tuning, preference optimization, and reinforcement learning with verifiable rewards. On the tool side, T1 (agent-agnostic) provides reusable pre-trained modules any agent can call, while T2 (agent-supervised) uses the agent's outputs to train memory systems, skill libraries, or lightweight subagents. Using this framework, we review post-training methods, adaptive memory architectures, and agent skills; compare their trade-offs in cost, flexibility, and generalization; and summarize evaluation practices across deep research, software development, computer use, and drug discovery. We conclude by outlining open problems in agent-tool co-adaptation, continual learning, safety, and efficient deployment.

cs.AI↗
arXiv2026

LISTA-Transformer Model Based on Sparse Coding and Attention Mechanism and Its Application in Fault Diagnosis

Driven by the continuous development of models such as Multi-Layer Perceptron, Convolutional Neural Network (CNN), and Transformer, deep learning has made breakthrough progress in fields such as computer vision and natural language processing, and has been successfully applied in practical scenarios such as image classification and industrial fault diagnosis. However, existing models still have certain limitations in local feature modeling and global dependency capture. Specifically, CNN is limited by local receptive fields, while Transformer has shortcomings in effectively modeling local structures, and both face challenges of high model complexity and insufficient interpretability. In response to the above issues, we proposes the following innovative work: A sparse Transformer based on Learnable Iterative Shrinkage Threshold Algorithm (LISTA-Transformer) was designed, which deeply integrates LISTA sparse encoding with visual Transformer to construct a model architecture with adaptive local and global feature collaboration mechanism. This method utilizes continuous wavelet transform to convert vibration signals into time-frequency maps and inputs them into LISTA-Transformer for more effective feature extraction. On the CWRU dataset, the fault recognition rate of our method reached 98.5%, which is 3.3% higher than traditional methods and exhibits certain superiority over existing Transformer-based approaches.

cs.CV↗
arXiv2026

HiLoRA: Hierarchical Low-Rank Adaptation for Personalized Federated Learning

Vision Transformers (ViTs) have been widely adopted in vision tasks due to their strong transferability. In Federated Learning (FL), where full fine-tuning is communication heavy, Low-Rank Adaptation (LoRA) provides an efficient and communication-friendly way to adapt ViTs. However, existing LoRA-based federated tuning methods overlook latent client structures in real-world settings, limiting shared representation learning and hindering effective adaptation to unseen clients. To address this, we propose HiLoRA, a hierarchical LoRA framework that places adapters at three levels: root, cluster, and leaf, each designed to capture global, subgroup, and client-specific knowledge, respectively. Through cross-tier orthogonality and cascaded optimization, HiLoRA separates update subspaces and aligns each tier with its residual personalized objective. In particular, we develop a LoRA-Subspace Adaptive Clustering mechanism that infers latent client groups via subspace similarity analysis, thereby facilitating knowledge sharing across structurally aligned clients. Theoretically, we establish a tier-wise generalization analysis that supports HiLoRA's design. Experiments on ViT backbones with CIFAR-100 and DomainNet demonstrate consistent improvements in both personalization and generalization.

cs.CV↗
arXiv2026

Shop-R1: Rewarding LLMs to Simulate Human Behavior in Online Shopping via Reinforcement Learning

Large Language Models (LLMs) have recently demonstrated strong potential in generating 'believable human-like' behavior in web environments. Prior work has explored augmenting training data with LLM-synthesized rationales and applying supervised fine-tuning (SFT) to enhance reasoning ability, which in turn can improve downstream action prediction. However, the performance of such approaches remains inherently bounded by the reasoning capabilities of the model used to generate the rationales. In this paper, we introduce Shop-R1, a novel reinforcement learning (RL) framework aimed at enhancing the reasoning ability of LLMs for simulation of real human behavior in online shopping environments. Specifically, Shop-R1 decomposes the human behavior simulation task into two stages: rationale generation and action prediction, each guided by distinct reward signals. For rationale generation, we leverage internal model signals (e.g., logit distributions) to guide the reasoning process in a self-supervised manner. For action prediction, we propose a hierarchical reward structure with difficulty-aware scaling to prevent reward hacking and enable fine-grained reward assignment. This design evaluates both high-level action types and the correctness of fine-grained sub-action details (attributes and values), rewarding outputs proportionally to their difficulty. Experimental results show that our method achieves a relative improvement of over 65% compared to the baseline. The project page is available at https://damon-demon.github.io/shop-r1.html.

cs.CL↗
arXiv2026

Ordinary primes for $\mathrm{GL}_2$-type abelian varieties and weight $2$ modular forms

Let $A$ be a $g$-dimensional abelian variety defined over a number field $F$. It is conjectured that the set of ordinary primes of $A$ over $F$ has positive density, and this is known to be true when $g=1, 2$, or for certain abelian varieties with extra endomorphisms. In this paper, we extend the family of abelian varieties whose sets of ordinary primes have positive density. Specifically, we show that if the endomorphism algebra of $A$ contains a number field $K$ of degree $g$, then under certain conditions on the fields $F$ and $K$, the set of ordinary primes of $A$ over $F$ has positive density. This includes $\mathrm{GL}_2$-type abelian varieties over $\mathbb{Q}$ (resp. quadratic number fields) of dimension $q$ or $2q$ (resp. $q$) for any rational prime $q$. The proof is carried out in the general setting of compatible systems of Galois representations, and as a consequence, it also implies a positive density result for the sets of ordinary primes of certain modular forms of weight $2$.

math.NT↗
arXiv2026

Rec-R1: Bridging Generative Large Language Models and User-Centric Recommendation Systems via Reinforcement Learning

We propose Rec-R1, a general reinforcement learning framework that bridges large language models (LLMs) with recommendation systems through closed-loop optimization. Unlike prompting and supervised fine-tuning (SFT), Rec-R1 directly optimizes LLM generation using feedback from a fixed black-box recommendation model, without relying on synthetic SFT data from proprietary models such as GPT-4o. This avoids the substantial cost and effort required for data distillation. To verify the effectiveness of Rec-R1, we evaluate it on two representative tasks: product search and sequential recommendation. Experimental results demonstrate that Rec-R1 not only consistently outperforms prompting- and SFT-based methods, but also achieves significant gains over strong discriminative baselines, even when used with simple retrievers such as BM25. Moreover, Rec-R1 preserves the general-purpose capabilities of the LLM, unlike SFT, which often impairs instruction-following and reasoning. These findings suggest Rec-R1 as a promising foundation for continual task-specific adaptation without catastrophic forgetting.

cs.IR↗
arXiv2026

SFT Doesn't Always Hurt General Capabilities: Revisiting Domain-Specific Fine-Tuning in LLMs

Supervised Fine-Tuning (SFT) on domain-specific datasets is a common approach to adapt Large Language Models (LLMs) to specialized tasks but is often believed to degrade their general capabilities. In this work, we revisit this trade-off and present both empirical and theoretical insights. First, we show that SFT does not always hurt: using a smaller learning rate can substantially mitigate general performance degradation while preserving comparable target-domain performance. We then provide a theoretical analysis that explains these phenomena and further motivates a new method, Token-Adaptive Loss Reweighting (TALR). Building on this, and recognizing that smaller learning rates alone do not fully eliminate general-performance degradation in all cases, we evaluate a range of strategies for reducing general capability loss, including L2 regularization, LoRA, model averaging, FLOW, and our proposed TALR. Experimental results demonstrate that while no method completely eliminates the trade-off, TALR consistently outperforms these baselines in balancing domain-specific gains and general capabilities. Finally, we distill our findings into practical guidelines for adapting LLMs to new domains: (i) using a small learning rate to achieve a favorable trade-off, and (ii) when a stronger balance is further desired, adopt TALR as an effective strategy.

cs.CL↗
arXiv2026

Matrix as Plan: Structured Logical Reasoning with Feedback-Driven Replanning

As knowledge and semantics on the web grow increasingly complex, enhancing Large Language Models (LLMs)' comprehension and reasoning capabilities has become particularly important. Chain-of-Thought (CoT) prompting has been shown to enhance the reasoning capabilities of LLMs. However, it still falls short on logical reasoning tasks that rely on symbolic expressions and strict deductive rules. Neuro-symbolic methods address this gap by enforcing formal correctness through external solvers. Yet these solvers are highly format-sensitive, and small instabilities in model outputs can lead to frequent processing failures. The LLM-driven approaches avoid parsing brittleness, but they lack structured representations and process-level error-correction mechanisms. To further enhance the logical reasoning capabilities of LLMs, we propose MatrixCoT, a structured CoT framework with a matrix-based plan. Specifically, we normalize and type natural language expressions and attach explicit citation fields, and introduce a matrix-based planning method to preserve global relations among steps. The plan thus becomes a verifiable artifact and execution becomes more stable. For verification, we also add a feedback-driven replanning mechanism. Under semantic-equivalence constraints, it identifies omissions and defects, rewrites and compresses the dependency matrix, and produces a more trustworthy final answer. Experiments on five logical-reasoning benchmarks and five LLMs show that, without relying on external solvers, MatrixCoT enhances both the robustness and interpretability of LLMs when tackling complex symbolic reasoning tasks, while maintaining competitive performance.

cs.AI↗
arXiv2026

Large Language Models to Enhance Multi-task Drone Operations in Simulated Environments

Benefiting from the rapid advancements in large language models (LLMs), human-drone interaction has reached unprecedented opportunities. In this paper, we propose a method that integrates a fine-tuned CodeT5 model with the Unreal Engine-based AirSim drone simulator to efficiently execute multi-task operations using natural language commands. This approach enables users to interact with simulated drones through prompts or command descriptions, allowing them to easily access and control the drone's status, significantly lowering the operational threshold. In the AirSim simulator, we can flexibly construct visually realistic dynamic environments to simulate drone applications in complex scenarios. By combining a large dataset of (natural language, program code) command-execution pairs generated by ChatGPT with developer-written drone code as training data, we fine-tune the CodeT5 to achieve automated translation from natural language to executable code for drone tasks. Experimental results demonstrate that the proposed method exhibits superior task execution efficiency and command understanding capabilities in simulated environments. In the future, we plan to extend the model functionality in a modular manner, enhancing its adaptability to complex scenarios and driving the application of drone technologies in real-world environments.

cs.RO↗
arXiv2026

Edge-Optimized Multimodal Learning for UAV Video Understanding via BLIP-2

The demand for real-time visual understanding and interaction in complex scenarios is increasingly critical for unmanned aerial vehicles. However, a significant challenge arises from the contradiction between the high computational cost of large Vision language models and the limited computing resources available on UAV edge devices. To address this challenge, this paper proposes a lightweight multimodal task platform based on BLIP-2, integrated with YOLO-World and YOLOv8-Seg models. This integration extends the multi-task capabilities of BLIP-2 for UAV applications with minimal adaptation and without requiring task-specific fine-tuning on drone data. Firstly, the deep integration of BLIP-2 with YOLO models enables it to leverage the precise perceptual results of YOLO for fundamental tasks like object detection and instance segmentation, thereby facilitating deeper visual-attention understanding and reasoning. Secondly, a content-aware key frame sampling mechanism based on K-Means clustering is designed, which incorporates intelligent frame selection and temporal feature concatenation. This equips the lightweight BLIP-2 architecture with the capability to handle video-level interactive tasks effectively. Thirdly, a unified prompt optimization scheme for multi-task adaptation is implemented. This scheme strategically injects structured event logs from the YOLO models as contextual information into BLIP-2's input. Combined with output constraints designed to filter out technical details, this approach effectively guides the model to generate accurate and contextually relevant outputs for various tasks.

cs.CV↗