arXiv subjects

Li Zhu

Publications and source records attributed to Li Zhu.

At least 19 recordsLinked to original sources

arXiv2026

The Optimal Coefficients-Based Criterion for Primitive Quadratic Polynomials over Finite Fields

Let $\mathbb F_q$ be a finite field and consider quadratic polynomials $f(X)=X^2+bX+c\in\mathbb F_q[X]$ with primitive constant term $c$. We construct an optimal coefficients-based determining polynomial for primitive quadratic polynomials over every finite field. More precisely, for every primitive $c\in\mathbb F_q$, its specialization is the unique monic square-free polynomial whose roots are exactly the coefficients $b$ for which $X^2+bX+c$ is primitive. The construction is based on Lucas polynomials and Lucas atoms over finite fields. In odd characteristic, the optimal determining polynomial is the $(q+1)$-st Lucas atom. In characteristic $2$, this Lucas atom has multiplicity $2$ in the variable $B$, and the optimal polynomial is obtained by removing this multiplicity through the inverse Frobenius over $A=\mathbb F_q[C]/(\Phi_{q-1}(C))$. We prove that the determining polynomial is unique for each fixed primitive constant term and, globally, unique as an element of $A[B]$. We also give equivalent criteria involving only recursively computable Lucas polynomials and, as an application, a first-zero coefficient description of the binomial order and order of an irreducible quadratic polynomial.

math.NT↗

arXiv2026

Vibrational spectroscopy identifies the bond asymmetry of hexagonal diamond

Bulk hexagonal diamond has been synthesized by independent routes, but its structure remains contested: the two recent refinements disagree even on the sign of the difference between its two inequivalent bond lengths, 238~m\AA{} apart, and both depart from an earlier 2003 refinement. Here we test the competing structures with first-principles lattice dynamics. Relaxed hexagonal diamond has an interlayer bond \emph{longer} than the intralayer bonds by 24~m\AA{} in both functionals, an effect of its eclipsed conformation that scales with polytype hexagonality. The bright zone-center $A_{1g}$ mode gauges the interlayer bond at $\approx\!-2{,}100$~\icm~\AA$^{-1}$, and neither refined coordinate reproduces the full pattern of measured modes. The only structure matching the twinned sample's three bands requires tens-of-gigapascals confining stress and lattice constants excluded by its own diffraction. Raman spectroscopy and diffraction jointly select a small positive bond asymmetry: inverting the spectrum of the phase-pure sample gives $\OB-\OA=24\pm3$~m\AA{} (95\% interval), and two determinations on separate samples give $+33\pm8$ and $+60\pm45$~m\AA. The 1{,}529~\icm{} feature cannot be assigned to homogeneous ideal 2H diamond, and the local HRTEM observation remains an open puzzle.

cond-mat.mtrl-sci↗

arXiv2026

Before Thinking, Learn to Decide: Proactive Routing for Efficient Visual Reasoning

Large multimodal models have achieved strong reasoning on complex visual tasks, but their inference efficiency is often restricted by long chains of thought. A promising solution is to pair a small draft model with a large target model, enabling cooperative inference employing a routing signal that adaptively routes queries to either the draft or target model based on their difficulties for optimal efficiency and accuracy. Yet, the remaining bottleneck is to establish a reliable query difficulty signal under multimodal settings. Existing approaches designed for language models either rely on post-hoc token probabilities, which fall short in multimodal scenarios, or depend on supervised fine-tuning, which is a data-sensitive strategy. Both paradigms perform routing only after a complete output, and ignore whether the target model can actually solve the routed instances. To address this, we propose PRP, a Proactive Routing Paradigm that enables early decision-making by jointly evaluating the competence of both the draft and target models. Our Draft Rating Learning (DRL) equips the draft model with an internal confidence estimator, while Joint Rating Learning (JRL) predicts how well the target model can handle a given query, thereby prioritizing the allocation of samples it excels at rather than the hardest ones. These ratings enable fine-grained, instance-level \textbf{Proactive Routing} and substantially accelerate inference without compromising overall performance. Extensive experiments across multiple multimodal reasoning benchmarks validate our effectiveness and efficiency.

cs.CL↗

arXiv2026

Benchmarking Multi-Modal Graph-based Social Media Popularity Prediction

Social media popularity prediction aims to forecast the future reach or influence of online content from early-stage observations. Accurate prediction enables key downstream applications, such as advertising optimization and strategic content planning by users, creators, and platforms. Despite substantial progress, existing popularity prediction works often fail to jointly consider multimodal content and temporal social interaction signals. Moreover, the literature remains highly fragmented across datasets, modalities, observation windows, prediction targets, and evaluation protocols. This fragmentation prevents fair comparison and obscures a systematic understanding of how textual, visual, temporal, and interaction-based signals jointly shape popularity dynamics. To address these challenges, we introduce MMG-Pop, a Multi-modal Graph-based Popularity Prediction benchmark, which unifies datasets, modalities, temporal interaction signals, and representative baselines under a standardized evaluation protocol. Furthermore, we propose MMG-PopNet, a unified multi-modal graph-based network that jointly models the aforementioned multi-modal signals and graph-structured social interactions. Extensive experiments on MMG-Pop, comprising four datasets across Bluesky and Reddit platforms, demonstrate the superior performance of MMG-PopNet and yield new insights into cross-platform training generalization, multi-task prediction benefits, multi-modality contributions, and LLM prediction limitation. These findings establish a unified foundation for future research on social dynamics modeling and intervention under heterogeneous modalities and socially-aware agentic ecosystem paradigms.

cs.SI↗

arXiv2026

StepGuard: Guarding Web Navigation via Single-Step Calibration

Web navigation requires agents to follow natural language goals, interact with web pages, and produce accurate answers. While recent advances leverage vision-language models and reinforcement learning, existing methods still suffer from single-step fragility due to reward misalignment and error propagation. To tackle the reward entanglement, we design Dynamic Dual-Policy Optimization (DDPO), which dynamically switches between a navigation-first mode for exploration and an answer-first mode for question-answering to mitigate reward conflict. To calibrate the single-step error, we propose Confidence-Guided Adaptive Navigation Reflection (CANR), a mechanism that estimates per-step confidence, triggers reflection only when necessary, and uses contrastive rewards to encourage self-correction to calibrate the single-step inaccuracy. With the above as the main components, we finally develop our StepGuard, a new framework of Guarding Web Navigation via Single-Step Calibration. Experiments demonstrate that our approach significantly improves navigation and answer accuracy, setting new state-of-the-art performance on standard web navigation benchmarks.

cs.AI↗

arXiv2026

A Voxel-Based Quantum Computing Method (VBQC) for Solid Mechanics Problem

Quantum computing presents a promising method to overcome the efficiency and memory constraints in large-scale mechanical problems, with numerous successful applications demonstrated in fluid mechanics. However, solid mechanics problems usually require irregular grids for spatial discretization, due to the Lagrange formulations and complex boundaries, which makes the quantum simulation of the system matrix, e.g., the mass or stiffness matrix which is often referred to as the Hamiltonian in quantum computing, difficult to be effectively conducted. This study proposes a voxel-based quantum computing method (VBQC) for the quantum simulation of Hamiltonians in solid mechanics. VBQC applies voxel grids to discretize the spatial domain, thereby enabling the system matrix to exhibit the tridiagonal fractal property. Based on this property, the system matrix can be decomposed into three groups of fundamental matrices, $\mathbf{k}_{n}$, $\mathbf{c}_{n}$, and $\mathbf{q}_{n}$. This decomposition process is referred to as the KCQ decomposition. By integrating the KCQ decomposition with the quantum Fourier transform and the quantum multiplexer, VBQC enables efficient quantum simulation of Hamiltonians in solid mechanics. Three specific solid problems with different dimensions and numbers of variables are applied to preliminarily verify the correctness of the proposed VBQC for solid mechanics problems.

cs.CE↗

arXiv2026

Dataset-aware entropy-maximized active learning for machine-learned interatomic potentials

We present an active learning framework for efficiently generating training data for machine-learned interatomic potentials (MLIPs). The method combines local entropy-driven molecular dynamics with global dataset-aware filtering: a per-configuration entropy term biases MD trajectories toward structurally diverse snapshots, while a global entropy measure, the log-determinant of the fingerprint covariance matrix of the entire dataset, selects only those configurations that provide genuinely new information. We employ dual covariance modes (per-atom for disordered structures and per-config for ordered phases) to achieve broad coverage of configuration space. Combined with a pre-trained foundation model (Allegro-OAM-L) and analytical fingerprint gradients from Gaussian overlap matrix eigenvalues, the framework produces high-quality domain-specific potentials with near- or sub-meV/atom accuracy on test data drawn from the same distribution at training-set sizes of order $10^{2}$ to $10^{3}$ entropy-selected DFT-labeled structures. We demonstrate the method on three systems spanning diverse bonding types and pressure-driven phase transitions: carbon (covalent), silicon (covalent/metallic), and NaCl (ionic). In learning curve comparisons against random molecular dynamics sampling at matched training set sizes ($N = 100$ to $800$), evaluated over three independent training-set draws per condition, entropy-driven sampling achieves a factor of approximately $3$ to $10$ lower energy MAE at $N = 800$ on in-distribution holdouts across the three systems, with the magnitude of the gain depending on the bonding type and the size at which the random-MD baseline saturates.

cond-mat.mtrl-sci↗

arXiv2026

Physiology-Aware Masked Cross-Modal Reconstruction for Biosignal Representation Learning

Biosignals acquired from different locations on the body often provide temporally ordered views of the same underlying physiological process. However, most existing self supervised learning methods treat these signals as interchangeable views, overlooking the directional temporal dynamics that link them. A canonical example is the relationship between electrocardiography (ECG), which captures the electrical activation initiating each heartbeat, and photoplethysmography (PPG), which records the resulting peripheral pulse delayed by vascular dynamics. To capture this structured relationship, we introduce xMAE, a biosignal pretraining framework that leverages masked cross modal reconstruction across temporally ordered biosignals as a training time constraint to encourage physiologically meaningful timing structure in the learned representations. We show that pretraining with xMAE yields representations that outperform both unimodal and multimodal baselines on 15 of 19 downstream tasks, including cardiovascular outcome prediction, abnormal laboratory test detection, sleep staging, and demographic inference, while generalizing across devices, body locations, and acquisition settings. Further analysis suggests that the ECG PPG timing structure is reflected in the learned PPG representations. More broadly, xMAE demonstrates the effectiveness of incorporating temporal structure into multimodal pretraining when signals observe different stages of a shared underlying process. Code is available at https://github.com/hzhou3/xMAE.

cs.LG↗

arXiv2026

AdapTime: Enabling Adaptive Temporal Reasoning in Large Language Models

Large language models have demonstrated strong reasoning capabilities in general knowledge question answering. However, their ability to handle temporal information remains limited. To address this limitation, existing approaches often involve external tools or manual verification and are tailored to specific scenarios, leading to poor generalizability. Moreover, these methods apply a fixed pipeline to all questions, overlooking the fact that different types of temporal questions require distinct reasoning strategies, which leads to unnecessary processing for simple cases and inadequate reasoning for complex ones. To this end, we propose AdapTime, an adaptive temporal reasoning method that dynamically executes reasoning steps based on the input context. Specifically, it involves three temporal reasoning actions: reformulate, rewrite and review, with an LLM planner guiding the reasoning process. AdapTime integrates seamlessly with state-of-the-art LLMs and significantly enhances their temporal reasoning capabilities without relying on external support. Extensive experiments demonstrate the effectiveness of our approach.

cs.CL↗

arXiv2026

MultiDx: A Multi-Source Knowledge Integration Framework towards Diagnostic Reasoning

Diagnostic prediction and clinical reasoning are critical tasks in healthcare applications. While Large Language Models (LLMs) have shown strong capabilities in commonsense reasoning, they still struggle with diagnostic reasoning due to limited domain knowledge. Existing approaches often rely on internal model knowledge or static knowledge bases, resulting in knowledge insufficiency and limited adaptability, which hinder their capacity to perform diagnostic reasoning. Moreover, these methods focus solely on the accuracy of final predictions, overlooking alignment with standard clinical reasoning trajectories. To this end, we propose MultiDx, a two-stage diagnostic reasoning framework that performs differential diagnosis by analyzing evidence collected from multiple knowledge sources. Specifically, it first generates suspected diagnoses and reasoning paths by leveraging knowledge from web search, SOAP-formatted case, and clinical case database. Then it integrates multi-perspective evidence through matching, voting, and differential diagnosis to generate the final prediction.~Extensive experiments on two public benchmarks demonstrate the effectiveness of our approach.

cs.CL↗

arXiv2026

SoK: Security of Autonomous LLM Agents in Agentic Commerce

Autonomous large language model (LLM) agents such as OpenClaw are pushing agentic commerce from human-supervised assistance toward machine actors that can negotiate, purchase services, manage digital assets, and execute transactions across on-chain and off-chain environments. Protocols such as the Trustless Agents standard (ERC-8004), Agent Payments Protocol (AP2), OKX Agent Payments Protocol (APP), the HTTP 402-based payment protocol (x402), Agent Commerce Protocol (ACP), the Agentic Commerce standard (ERC-8183), and Machine Payments Protocol (MPP) enable this transition, but they also create an attack surface that existing security frameworks do not capture well. This Systematization of Knowledge (SoK) develops a unified security framework for autonomous LLM agents in commerce and finance. We organize threats along five dimensions: agent integrity, transaction authorization, inter-agent trust, market manipulation, and regulatory compliance. From a systematically curated public corpus of academic papers, protocol documents, industry reports, and incident evidence, we derive 12 cross-layer attack vectors and show how failures propagate from reasoning and tooling layers into custody, settlement, market harm, and compliance exposure. We then propose a layered defense architecture addressing authorization gaps left by current agent-payment protocols. Overall, our analysis shows that securing agentic commerce is inherently a cross-layer problem that requires coordinated controls across LLM safety, protocol design, identity, market structure, and regulation. We conclude with a research roadmap and a benchmark agenda for secure autonomous commerce.

cs.CR↗

arXiv2026

Can Video Diffusion Models Predict Past Frames? Bidirectional Cycle Consistency for Reversible Interpolation

Video frame interpolation aims to synthesize realistic intermediate frames between given endpoints while adhering to specific motion semantics. While recent generative models have improved visual fidelity, they predominantly operate in a unidirectional manner, lacking mechanisms to self-verify temporal consistency. This often leads to motion drift, directional ambiguity, and boundary misalignment, especially in long-range sequences. Inspired by the principle of temporal cycle-consistency in self-supervised learning, we propose a novel bidirectional framework that enforces symmetry between forward and backward generation trajectories. Our approach introduces learnable directional tokens to explicitly condition a shared backbone on temporal orientation, enabling the model to jointly optimize forward synthesis and backward reconstruction within a single unified architecture. This cycle-consistent supervision acts as a powerful regularizer, ensuring that generated motion paths are logically reversible. Furthermore, we employ a curriculum learning strategy that progressively trains the model from short to long sequences, stabilizing dynamics across varying durations. Crucially, our cyclic constraints are applied only during training; inference requires a single forward pass, maintaining the high efficiency of the base model. Extensive experiments show that our method achieves state-of-the-art performance in imaging quality, motion smoothness, and dynamic control on both 37-frame and 73-frame tasks, outperforming strong baselines while incurring no additional computational overhead.

cs.CV↗

arXiv2026

Look, Compare and Draw: Differential Query Transformer for Automatic Oil Painting

This work introduces a new approach to automatic oil painting that emphasizes the creation of dynamic and expressive brushstrokes. A pivotal challenge lies in mitigating the duplicate and common-place strokes, which often lead to less aesthetic outcomes. Inspired by the human painting process, \ie, observing, comparing, and drawing, we incorporate differential image analysis into a neural oil painting model, allowing the model to effectively concentrate on the incremental impact of successive brushstrokes. To operationalize this concept, we propose the Differential Query Transformer (DQ-Transformer), a new architecture that leverages differentially derived image representations enriched with positional encoding to guide the stroke prediction process. This integration enables the model to maintain heightened sensitivity to local details, resulting in more refined and nuanced stroke generation. Furthermore, we incorporate adversarial training into our framework, enhancing the accuracy of stroke prediction and thereby improving the overall realism and fidelity of the synthesized paintings. Extensive qualitative evaluations, complemented by a controlled user study, validate that our DQ-Transformer surpasses existing methods in both visual realism and artistic authenticity, typically achieving these results with fewer strokes. The stroke-by-stroke painting animations are available on our project website.

cs.CV↗

arXiv2026

BCH and LCD cyclic codes of length $n=\lambda(q^m+1)$ over finite fields

BCH and LCD cyclic codes of length $n=\lambda(q^m+1)$ with $\lambda\mid q-1$ are studied. A complete characterization of $q$-cyclotomic cosets modulo $n$ is given: Theorem \ref{th4} provides a necessary and sufficient condition for any $0\le \gamma<n$ to be a coset leader, and for odd $m$, the two largest coset leaders are explicitly determined (Theorem \ref{th9} and Theorem \ref{th14}). Based on these results, the dimensions of several families of BCH codes are determined, and the lower bound on the minimal distance of $\mathcal{C}_{(q,n,2\delta+1,n-\delta+1)}$ is raised to $2(\delta+1)$ (Theorem \ref{th15}--\ref{th5}). Notably, several of these codes are optimal. When $m$ is odd, the necessary and sufficient condition for the BCH code $\mathcal{C}_{(q,n,\delta,0)}$ to be dually-BCH is proved (Theorem \ref{th11}). Finally, an exact enumeration of all LCD cyclic codes of this length is derived (Theorem \ref{th3}). All of the above results extend previous results that were limited to $\lambda=1$.

cs.IT↗

arXiv2026

Cultivating Forensic Reasoning for Generalizable Multimodal Manipulation Detection

Recent advances in generative AI have significantly enhanced the realism of multimodal media manipulation, thereby posing substantial challenges to manipulation detection. Existing manipulation detection and grounding approaches predominantly focus on manipulation type classification under result-oriented supervision, which not only lacks interpretability but also tends to overfit superficial artifacts. In this paper, we argue that generalizable detection requires incorporating explicit forensic reasoning, rather than merely classifying a limited set of manipulation types, which fails to generalize to unseen manipulation patterns. To this end, we propose REFORM, a reasoning-driven framework that shifts learning from outcome fitting to process modeling. REFORM adopts a three-stage curriculum that first induces forensic rationales, then aligns reasoning with final judgments, and finally refines logical consistency via reinforcement learning. To support this paradigm, we introduce ROM, a large-scale dataset with rich reasoning annotations. Extensive experiments show that REFORM establishes new state-of-the-art performance with superior generalization, achieving 81.52% ACC on ROM, 76.65% ACC on DGM4, and 74.9 F1 on MMFakeBench.

cs.CV↗

arXiv2026

The Arithmetic Singleton Bound on the Hamming Distances of Simple-rooted Constacyclic Codes over Finite Fields

In this work, We introduce a new upper bound on the Hamming distance of simple-root constacyclic codes over finite fields, which we call the arithmetic Singleton bound. The main technical tool is the notion of a multiple equal-difference (MED) representation. Via the MED representations of the defining set of the generator polynomial of a simple-root constacyclic code, we obtain a family of upper bounds on its Hamming distance, among which the weakest one coincides with the Singleton bound, while the strongest one is defined to be the arithmetic Singleton bound for this code. Consequently, the arithmetic Singleton bound is always at least as strong as the classical Singleton bound, and is in fact strictly stronger in numerous nontrivial cases. The arithmetic Singleton bound partially measures the restriction on the Hamming distance of a simple-root constacyclic code imposed by its arithmetic structure. In particular, for an irreducible constacyclic code, the MED representations of the defining set of its generator polynomial are completely determined, via which the arithmetic Singleton bound is computed concretely. Finally for any simple-root cyclic code the arithmetic Singleton bound and the BCH bound are compared.

cs.IT↗

arXiv2026

Semantic-Deviation-Anchored Multi-Branch Fusion for Unsupervised Anomaly Detection and Localization in Unstructured Conveyor-Belt Coal Scenes

Reliable foreign-object anomaly detection and pixel-level localization in conveyor-belt coal scenes are essential for safe and intelligent mining operations. This task is particularly challenging due to the highly unstructured environment: coal and gangue are randomly piled, backgrounds are complex and variable, and foreign objects often exhibit low contrast, deformation, occlusion, resulting in coupling with their surroundings. These characteristics weaken the stability and regularity assumptions that many anomaly detection methods rely on in structured industrial settings, leading to notable performance degradation. To support evaluation and comparison in this setting, we construct \textbf{CoalAD}, a benchmark for unsupervised foreign-object anomaly detection with pixel-level localization in coal-stream scenes. We further propose a complementary-cue collaborative perception framework that extracts and fuses complementary anomaly evidence from three perspectives: object-level semantic composition modeling, semantic-attribution-based global deviation analysis, and fine-grained texture matching. The fused outputs provide robust image-level anomaly scoring and accurate pixel-level localization. Experiments on CoalAD demonstrate that our method outperforms widely used baselines across the evaluated image-level and pixel-level metrics, and ablation studies validate the contribution of each component. The code is available at https://github.com/xjpp2016/USAD.

cs.CV↗

arXiv2026

Enhancing Conversational Agents via Task-Oriented Adversarial Memory Adaptation

Conversational agents struggle to handle long conversations due to context window limitations. Therefore, memory systems are developed to leverage essential historical information. Existing memory systems typically follow a pipeline of offline memory construction and update, and online retrieval. Despite the flexible online phase, the offline phase remains fixed and task-independent. In this phase, memory construction operates under a predefined workflow and fails to emphasize task relevant information. Meanwhile, memory updates are guided by generic metrics rather than task specific supervision. This leads to a misalignment between offline memory preparation and task requirements, which undermines downstream task performance. To this end, we propose an Adversarial Memory Adaptation mechanism (AMA) that aligns memory construction and update with task objectives by simulating task execution. Specifically, first, a challenger agent generates question answer pairs based on the original dialogues. The constructed memory is then used to answer these questions, simulating downstream inference. Subsequently, an evaluator agent assesses the responses and performs error analysis. Finally, an adapter agent analyzes the error cases and performs dual level updates on both the construction strategy and the content. Through this process, the memory system receives task aware supervision signals in advance during the offline phase, enhancing its adaptability to downstream tasks. AMA can be integrated into various existing memory systems, and extensive experiments on long dialogue benchmark LoCoMo demonstrate its effectiveness.

cs.CL↗