arXiv subjects

Tian Wang

Publications and source records attributed to Tian Wang.

At least 19 recordsLinked to original sources

arXiv2026

Average twin prime conjecture for elliptic curves in arithmetic progressions

In 1988, Koblitz conjectured an asymptotic formula for the number of primes $p \le x$ for which the reduction of an elliptic curve over $\mathbb{Q}$ has prime order. Building on the work of Balog, Cojocaru, and David, who proved this conjecture on average in 2011, we extend the result to primes $p$ lying in arithmetic progressions. Our asymptotic formula holds uniformly for moduli up to a fixed power of $\log x$. We also show that the resulting average constant matches the theoretical constant predicted by Lee, Mayle, and Wang in 2025 using Galois representations.

math.NT↗

arXiv2026

Evaluating and Explaining Prompt Sensitivity of LLMs Using Interactions

The remarkable capabilities of large language models (LLMs) are often undermined by their instability. Even subtle and semantically irrelevant changes in prompts can cause dramatic fluctuations in performance, a phenomenon known as prompt sensitivity. Previous studies typically evaluate prompt sensitivity by comparing the LLM's final outputs when prompts change. However, such coarse-grained metrics fail to explain the internal reasons for prompt sensitivity. In this paper, we introduce interactions as a fine-grained tool to analyze prompt sensitivity of LLMs. Specifically, we decompose the output score of the LLM into a set of interactions. Each interaction represents a nonlinear relationship involving a set of input variables. We discover that subtle changes to prompts can trigger severe instability in interactions, even when the outputs of the LLM remain the same. To this end, we propose an Interaction-based Prompt Sensitivity (IPS) metric by quantifying changes in interactions when we introduce subtle changes to prompts. We apply the IPS metric to 50 open-source LLMs and uncover four factors that reduce the prompt sensitivity of LLMs, including supervised fine-tuning, increased model scales, dense architectures, and few-shot learning. More crucially, we discover a common mechanism by which these four factors reduce prompt sensitivity: all four factors tend to reduce the prompt sensitivity of low-order interactions (i.e., interactions involving few input variables).

cs.LG↗

arXiv2026

Infinitely many primes with a fixed Frobenius field for an elliptic curve over $\mathbb{Q}$

In 1987, Elkies proved the striking result that every elliptic curve over $\mathbb{Q}$ has infinitely many supersingular primes. Motivated by this theorem and its connection with the Lang-Trotter conjecture, we study the analogous problem for Frobenius fields of elliptic curves. For certain families of non-CM elliptic curves $E/\mathbb{Q}$ and imaginary quadratic fields $K$, we prove that there exist infinitely many primes $p$ for which the Frobenius field of $E$ at $p$ equals $K$. More precisely, letting $\pi_E(x,K)$ denote the number of such primes with $p\leq x$, we establish the unconditional bound $\pi_E(x, K)\gg_{E, K, \epsilon} (\log\log x)^{1-\epsilon}$ for every $\epsilon>0$. We also prove unconditional power-saving upper bounds for a restricted counting function associated with $\pi_E(x,K)$. The approach combines Deuring's theory of complex multiplication, properties of singular moduli, and arithmetic intersection theory on modular curves.

math.NT↗

arXiv2026

SCALE: State-Calibrated Latent Embeddings for JEPA Planning in the Right Geometry

Joint-embedding predictive world models plan by scoring predicted terminal embeddings against a goal embedding using a cost defined on the representation itself. Two prominent strategies for obtaining non-collapsed representations are to inherit a pretrained feature space, as in DINO-WM, and to learn an embedding end to end with anti-collapse regularization, as in LeWorldModel (LeWM) with SIGReg. These strategies show complementary strengths across tasks. Although task-relevant state is decodable from the full embeddings of both models, DINO-WM's leading principal components usually retain substantially more state information than LeWM's. Because Euclidean planning costs are dominated by high-variance directions, this difference affects how strongly state can influence candidate selection. We propose SCALE (State-CAlibrated Latent Embeddings) to give the end-to-end LeWM representation the favorable geometric property observed in DINO-WM. SCALE induces this property by correlating sampled pairwise latent distances with distances in a standardized task-relevant state space, without replacing LeWM's learned encoder. Across five tasks, three planning solvers, and five compute budgets, SCALE improves every task--solver average over LeWM. A latent-to-state regression control matches or exceeds SCALE's full-embedding decodability yet leaves latent--state distance alignment essentially unchanged and yields less consistent planning gains. SCALE adds a single lightweight training-time regularizer and no planning-time overhead. These results show that planning depends not only on whether task-relevant information is present, but also on whether it shapes the geometry consumed by the planner.

cs.LG↗

arXiv2026

From Cheap Fakes to Pure Synthesis: Addressing the New Era of T2V Fake News Videos

Recent text-to-video (T2V) generation models enable fake news videos to be synthesized from scratch, shifting the threat beyond cheap fakes assembled from existing footage. Such news videos can closely match fabricated narratives, creating a modality alignment trap for existing detectors. Existing datasets lack pure synthesis fake news videos. Although directly prompting T2V models with descriptions of fake news videos can yield perfectly aligned samples, it reduces the fake news video detection (FNVD) to unimodal shortcuts and causes semantic-visual degeneration. To counter this, we formulate T2V-FNVD as a novel ternary classification task with three labels (real, cheap fake, and pure synthesis fake) and construct the first pure synthesis fake news video dataset (PS-FNVD). PS-FNVD includes fabricated events with aligned deception (Type 1) and true events with false visual provenance (Type 2), preventing models from exploiting unimodal shortcuts. Furthermore, we propose the Reasoning-guided T2V-FNVD (R-T2V) framework. Trained through conditioned rationale generation and supervised fine-tuning, R-T2V integrates high-level semantic logic with low-level physical generative traces to predict the ternary veracity label. Extensive experiments across 10 prevailing baselines show that R-T2V achieves the state-of-the-art performance, outperforming the second-best baseline by 12.20 percentage points in accuracy and 8.46 percentage points in macro $F_1$.

cs.AI↗

arXiv2026

InfraNet: Quality-Aware RGB Guidance for Efficient Infrared Object Detection

Robust object detection under adverse visual conditions remains a long-standing challenge for multi-modal perception systems. Existing fusion-based methods typically require both RGB and infrared (IR) inputs, and treat them equally during both training and inference, which compromises their robustness when the RGB modality becomes unreliable or unavailable. In this case, we propose \textbf{InfraNet}, an IR-centric quality-aware framework that regulates RGB guidance during training and supports flexible RGB--IR or IR-only deployment. InfraNet employs an asymmetric architecture where the primary IR pathway extracts multi-scale infrared features for predictions, while the auxiliary RGB pathway provides reliability-controlled supervisory signals. The core of InfraNet is \textbf{QualGate}, a quality-aware fusion module that learns a task-oriented control signal to suppress unreliable RGB guidance and compensate IR features during cross-modal training. Built upon InfraNet, we design two architectural variants: a lightweight IR-only architecture InfraNet-IR and an RGB--IR architecture InfraNet-RGB-IR. Our method is evaluated through extensive experiments on four benchmark datasets (LLVIP, FLIR-Aligned, M$^3$FD, and DroneVehicle), showing strong or competitive accuracy in challenging low-light and adverse weather conditions. Notably, InfraNet maintains high efficiency in IR-only inference, making it both accurate and computationally efficient.

cs.CV↗

arXiv2026

LASER: Load-Aware Serving with Early-Exit for Reasoning LLMs at the Edge

Large reasoning models (LRMs) such as DeepSeek-R1 have achieved strong performance through extended chain-of-thought (CoT) generation. However, deploying them on edge devices raises a conflict between long CoT sequences and constrained resources. Recent confidence-based early exit methods reduce CoT length for individual requests, yet they apply fixed thresholds from a single-request perspective, ignoring multi-request concurrency and load fluctuation in edge serving. To bridge this gap, we propose \underline{L}oad-\underline{A}ware \underline{S}erving with \underline{E}arly-exit for \underline{R}easoning (LASER). LASER couples two complementary designs: (1) a load-aware adaptive exit threshold that adjusts the confidence bar based on real-time system load within an empirically validated robust range, and (2) a difficulty- and load-aware reasoning budget pre-allocation that assigns compute resources by request difficulty and system capacity. We formulate the problem as a joint optimization of reasoning quality and service latency. Experiments on two reasoning models, four benchmarks, and diverse load conditions show that LASER reduces average latency by 17--38\% and improves service-level objective (SLO) satisfaction by 3--6\% over fixed-threshold baselines, at an average accuracy cost of only 1\%.

cs.DC↗

arXiv2026

RISE: Relay Inference and Online Scheduling for Efficient Edge-Device Collaborative Diffusion Model Services

Text-to-image diffusion models are increasingly deployed at the network edge to serve heterogeneous workloads with diverse quality and latency requirements. However, existing deployment strategies choose either large edge-side models with high fidelity but high latency or lightweight device-side models that offer speed at the cost of semantic coherence. Moreover, these approaches rarely split the denoising workload between models of different sizes across edge servers and user devices. To bridge this gap, we propose RISE, a method for edge-device diffusion model services that combines relay inference with online scheduling. Driven by the finding that the latent intensity exhibits minimal deviation after a model handoff, RISE uses a training-free relay mechanism that exploits the shared latent space within a model family: the large model on the edge handles the early denoising steps that shape semantic structure, then passes the intermediate latent to a small device-side model for detail refinement. To deploy this mechanism as a practical service, a contextual bandit scheduler selects the best relay configuration based on prompt complexity, user preferences, network quality and real-time node loads. Experiments on two benchmarks show that RISE's relay mechanism achieves up to 2.1$\times$ speedup while preserving full-model quality, and its context-aware scheduler effectively balances quality and latency under mixed workloads.

cs.DC↗

arXiv2026

CONCORD: Asynchronous Sparse Aggregation for Device-Cloud RAG under Document Isolation

Retrieval-augmented generation (RAG) has emerged as a pivotal technique for improving language models by incorporating external knowledge at inference time. As device-cloud collaborative inference makes it feasible to deploy small language models on edge devices, a new setting arises in which private documents remain on the device and public knowledge resides in the cloud. Privacy and policy constraints often forbid raw document exchange, creating a document-isolated dual-end RAG setting. However, existing methods rely on frequent remote synchronization and dense evidence transfer, limiting throughput under realistic latency and bandwidth conditions. To address this issue, we propose CONCORD, an asynchronous sparse aggregation framework for dual-end RAG under document isolation. CONCORD treats the cloud as an asynchronously arriving evidence source rather than a continuously synchronized co-generator. Specifically, we introduce waiting debt control to decide whether each decoding step should continue waiting for remote participation based on the observed return of waiting. We also design a certificate-guided minimal supplementation mechanism that requests only the remote evidence needed to determine the current greedy decision. Steps that consult the cloud preserve the same greedy token as dense dual-end aggregation, while the remaining steps commit locally without remote evidence. Experiments on Natural Questions and WikiText-2 show that CONCORD improves end-to-end throughput over baselines by $1.66\times$ and $2.15\times$, respectively, while reducing per-token communication by over two orders of magnitude and maintaining comparable answer quality and perplexity.

cs.AI↗

arXiv2026

ConCise: Training-Free Conclusion-Chain State Compression for Cost-Efficient Multi-Step RAG Services

Multi-step retrieval-augmented generation (RAG) has been widely deployed as LLM-powered web services for complex question answering, where iterative retrieval-reasoning rounds deliver strong multi-hop accuracy. However, this paradigm causes historical documents and reasoning traces to accumulate across rounds, inflating cumulative input tokens approximately as $O(N^2)$ with progressively increasing noise density. In API-based service architectures, such growth directly amplifies per-request billing cost, network payload, and response latency. Existing compression approaches rely on pretrained modules or GPU-level KV cache access, introducing model hosting overhead incompatible with API-native, Serverless, and edge-side deployments. To address this issue, this paper proposes ConCise, a training-free state-layer protocol that restructures cross-round context transmission for multi-step RAG services. Specifically, ConCise replaces raw-text accumulation with an append-only chain of structured conclusions, compressing cumulative context growth from $O(N^2)$ to approximately $O(N)$. Furthermore, a fused generation mechanism is introduced to jointly emit reasoning and conclusions in a single API call, eliminating repeated input billing from serial dual-invocation overhead. Extensive experiments across twelve paired configurations spanning three models, two datasets, and two representative frameworks demonstrate that ConCise achieves 64.63\% average token savings while maintaining acceptable accuracy, providing a plug-and-play, deployment-friendly solution for cost-efficient multi-step RAG service optimization.

cs.IR↗

arXiv2026

HeraSys: Collaborative Serving of Multiple LLM Workflows via Fine-Grained End-to-End Optimization

The proliferation of Large Language Models (LLMs) has shifted serving systems from processing isolated requests to orchestrating high-concurrency, multi-tenant agentic workflows. However, existing solutions typically prioritize intra-workflow optimization, largely neglecting the significant potential for inter-workflow optimization. In this paper, we propose HeraSys, an LLM serving system designed to optimize the end-to-end performance of concurrent workflows. Through fine-grained orchestration, HeraSys eliminates cross-workflow computational redundancy via structural node merging and reuse. Furthermore, HeraSys introduces a load-aware joint scheduling policy that dynamically manages execution order by evaluating both inter- and intra-query priorities. By integrating a resource skewing mechanism with adaptive batching and pipeline decomposition, HeraSys effectively mitigates tail latency while maintaining low average latency, thereby substantially improving system throughput. Extensive experiments demonstrate that HeraSys reduces P99 latency by up to 2.17$\times$ and increases serving throughput by up to 1.85$\times$ under strict latency guarantees.

cs.AI↗

arXiv2026

MemoVAD: Resource-Efficient Video Anomaly Detection via Dynamic Semantic Memory in Edge Computing Scenarios

Deploying Video Anomaly Detection (VAD) in real-world surveillance faces a fundamental tension between the demand for high-level semantics to ensure effectiveness and the limited computational resources of edge devices. Vision-Language Models (VLMs) provide rich open-vocabulary semantics, but their latency and computational cost preclude on-device deployment. To address the challenge, we propose MemoVAD, an edge-cloud collaborative framework that selectively incorporates VLM semantics into streaming VAD. MemoVAD runs most inference on the edge with a lightweight detector and a causal Temporal Context Encoder (TCE) to model temporal dependencies. Specifically, we introduce an Uncertainty-Aware Gating (UAG) policy grounded in Subjective Logic to model perceived uncertainty and query the cloud-based VLM only for high-uncertainty and semantically novel clips. Besides, a Dynamic Semantic Memory (DSM) is designed to cache VLM-verified prototypes for efficient retrieval, enabling the edge model to progressively incorporate VLM-level semantics via a semantic adapter. Experiments on UCF-Crime and XD-Violence datasets via a real edge device show that MemoVAD substantially reduces communication overhead while surpassing state-of-the-art performance.

cs.CV↗

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

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

Joint Sato-Tate Laws for Transformations of Hecke Eigenvalues: The Vertical Case

We introduce a framework within which a large class of joint equidistribution problems can be studied and resolved with effective error terms. This involves proving a higher dimensional and $\mu$-analogue of the Erd\"{o}s-Tur\'{a}n inequality, and utilizing the theory of the Hardy-Krause (H-K) variation from analysis, where, in particular, we formulate a technique to approximate a broad class of relevant functions by functions of bounded H-K variation. Our main focus will be on the vertical Sato-Tate problem for spaces of cusp forms and for families of elliptic curves over finite fields. In particular, we obtain novel results concerning the distribution of arithmetic relations, and, more generally, multi-dimensional functions of Fourier coefficients and Frobenius traces.

math.NT↗

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

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

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↗