arXiv subjects

Xu Zhang

Publications and source records attributed to Xu Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Positive solutions to the nonlinear Choquard equation: symmetry, uniqueness, and nondegeneracy

We study the symmetry, uniqueness, and nondegeneracy of positive solutions to the Choquard equation $-Δu+u=(I_α*u^p)u^{p-1}$ in $\mathbb{R}^N$, which have long remained open problems. For $N\geq3$, $α\in(0,N)$, and $\frac{N+α}{N}<p<\frac{N+α}{N-2}$,we prove that every positive $H^1$-solution is radially symmetric and strictly decreasing in the radial variable. The symmetry proof relies on the moving-plane method, where the sublinear singularity is controlled by analyzing the far-field behavior of the nonlocal term. Uniqueness and nondegeneracy are established through a functional framework hinging on a nonnegative joint form and a Schur complement argument.Radial nondegeneracy and Morse index one are obtained by ruling out the spectral interval $(0,p-1]$ via a strict cumulative Riesz identity, which leads to uniqueness through a Nehari two-well argument. Nondegeneracy in the full space $H^1(\mathbb{R}^N)$ follows from the spherical-harmonic decomposition of the linearized form. These results hold for the full range of $p$ when $α=2$, and for $p\geq2$ when $α\in(2,N)$. The cases $α\in(0,2)$ and $α\in(2,N)$ with $p<2$ remain open.

math.AP↗

arXiv2026

Infinitely Many Binomial Coefficients of Deficiency One

A binomial coefficient $\binom{n}{k}$ is good if all its prime divisors exceed $k$, and its deficiency is the number of $k$-smooth integers in $(n-k,n]$. A short constructive proof of the existence of infinitely many good binomial coefficients with deficiency exactly one is given, which provides an answer to a problem of Erdős, Lacampagne, and Selfridge.

math.NT↗

arXiv2026

ATrust: Adaptive Trust Boundary Expansion for Securing LLM Agents

As large language model (LLM) agents take on more complex tasks with greater autonomy, security has become a major obstacle to their broader deployment. Unlike in attacks that require complex exploitation of operating system vulnerabilities, attackers can easily hijack agents through indirect prompt injection (IPI), leading to privacy leakage, financial loss, and destructive operations. However, existing defenses often make security decisions based on limited static trusted evidence or assess observations in isolation. Such rigid trust assumptions can cause task-essential information to be unnecessarily discarded, resulting in over-defense and degraded agent functionality. To address this problem, we propose ATrust, a defense mechanism that adaptively expands the trust boundary during agent runtime. Starting from the user query as the root trust anchor, ATrust evaluates external observations against the current trust boundary and execution state, progressively admitting task-essential information as new trust anchors. This preserves necessary environmental feedback while excluding irrelevant content, whether benign or malicious, from subsequent decision-making, thereby limiting unnecessary exposure to external environment. We evaluate ATrust on AgentDojo and AgentDyn, where it achieves the strongest overall security--utility trade-off among existing defenses. With GPT-4o as the engine model, ATrust reduces the attack success rate on AgentDyn from 37.80% to 4.37% while enhancing utility by 10.00%, outperforming AuthGraph, the state-of-the-art defense, by 12.33%. These results demonstrate the effectiveness and practicality of ATrust.

cs.CR↗

arXiv2026

Generating Forbidden Words and Measures of Maximal Entropy for Subshifts

We prove that if the entropy of generating forbidden words of a subshift over a finite alphabet is strictly smaller than its topological entropy, then the subshift has only finitely many ergodic measures of maximal entropy, each of which is Bernoulli up to a finite period, and admits a characteristic measure of maximal entropy. In particular, these conclusions hold when the entropy of minimal forbidden words is strictly smaller than the topological entropy, giving a negative answer to a question of Buzzi.

math.DS↗

arXiv2026

A Comprehensive Review of Multimodal Large Language Models: Performance and Challenges Across Different Tasks

In an era defined by the explosive growth of data and rapid technological advancements, Multimodal Large Language Models (MLLMs) stand at the forefront of artificial intelligence (AI) systems. Designed to seamlessly integrate diverse data types-including text, images, videos, audio, and physiological sequences-MLLMs address the complexities of real-world applications far beyond the capabilities of single-modality systems. In this paper, we systematically sort out the applications of MLLM in multimodal tasks such as natural language, vision, and audio. We also provide a comparative analysis of the focus of different MLLMs in the tasks, and provide insights into the shortcomings of current MLLMs, and suggest potential directions for future research. Through these discussions, this paper hopes to provide valuable insights for the further development and application of MLLM.

cs.AI↗

arXiv2026

CCD: Context-Calibrated Open-Entity Out-of-Distribution Detection in In-Context Tabular Foundation Models

In-context tabular foundation models (TFMs), such as TabPFN, predict from a labelled context without updating their parameters and are increasingly used for out-of-distribution (OOD) detection in Web applications, whose test rows come from entities absent from that context. Such applications need open-entity OOD detection: a new entity must not be mistaken for an unknown class, and an unknown class must still be caught. Existing detectors fail in this setting, and an entity-split gap hides the failure: random splits also place the test entities in the context. The failure arises because every TFM score reflects how unfamiliar a row is to the context. This produces an entity-over-class bias: known-class rows of new entities look more OOD than familiar ones, sometimes more than unknown classes. Specifically, the two OOD scores most widely used with in-context TFMs face an entity-class trade-off: the TFM's predictive confidence misses unknown classes, whereas the distance of a test row to the context flags new entities. To address this problem, we hold a group of entities out of the context and score them with the remaining context, which turns them into new entities of known classes and tells us how such rows should score. To measure detection on new entities, we build NEO-Tab (New-Entity OOD detection on Tables), 14 grouped and temporal tables on which all test rows come from new entities. We then propose Context-Calibrated Detection (CCD), which uses these group-out swaps on in-distribution data to calibrate three distances and the confidence against new-entity references. CCD weights them by their sensitivity and sharpness, keeps the model frozen and uses no OOD data. On NEO-Tab, CCD outperforms 16 existing detectors on every metric we report, and its lead holds on three TFM backbones.

cs.IR↗

arXiv2026

From Association to Causation: Improving Retrieval Precision of Retrieval-Augmented Generation via Causal Relations and an Attention Mechanism

Retrieval-Augmented Generation (RAG) grounds LLM generation on retrieved documents, but the standard terminal retrieval stage--dense-vector similarity, optionally followed by reranking--often returns documents that share keywords with the query without containing the needed information, a failure mode that grows with the knowledge base. We trace it to a conceptual gap: similarity captures only associational relations, whereas the documents that matter are linked to the query causally. We model the terminal retrieval stage with a causal graph grounded in Reichenbach's common cause principle: the keywords shared by the query and a retrieved document form a latent common cause A, and the document's residual keywords form a latent set B linking the document to the ideal output. Since a retrieved document is a collider (A -> d <- B), retrieval itself opens an associational path between the query and B, which licenses a training-free, attention-style re-scoring rule: the cosine similarity between the query embedding and the weighted centroid embedding of B. Unlike causality-enhanced RAG variants that model causal relations inside the knowledge content, our graph models the causal structure of the retrieval process itself. On a real 471-document enterprise knowledge base, the method promotes a relevant guideline from rank 6 to the top 3; on a controlled diagnostic corpus reproducing the keyword-stuffing regime, it improves the mean target rank from 2.88 to 1.25, while a trained cross-encoder reranker barely helps (2.63). Conversely, on three BEIR benchmarks the score underperforms the similarity baseline, delineating the applicability boundary: the method guards the keyword-stuffing regime of growing proprietary knowledge bases and complements neural rerankers; a corpus-level calibration gate selects the correct regime with >= 95% reliability. A fully local testbed demonstrates deployability.

cs.AI↗

arXiv2026

Jailbreak Connectivity: Towards Diverse, Transferable, and Universal Multimodal Large Language Model Jailbreak

Multimodal large language models (MLLMs) are vulnerable to visual jailbreak attacks that bypass safety safeguards. Existing methods typically optimize isolated adversarial examples, limiting attack diversity, transferability, and generalization. We propose Jailbreak Connectivity (JC), a framework based on the observation that effective adversarial inputs can be connected through low-loss regions in image space. JC optimizes continuous adversarial paths: path sampling yields diverse jailbreak images, lightweight surrogate classifiers guide cross-model transfer, and a distribution-level objective enables universal attacks across harmful queries. On MM-SafetyBench, JC achieves average attack success rates of 84.01%, 85.77%, and 97.95% on Qwen3-VL-8B-Instruct, InternVL3.5-8B, and Gemma-3-12B-IT, respectively, exceeding the strongest baselines by up to 68.36 percentage points. In black-box evaluations, JC improves attack success rates over FigStep by 24.69 and 27.34 percentage points on GPT-5.6 and Gemini 3.1 Pro, respectively. These findings reveal structured vulnerabilities in MLLM safety alignment and inform more comprehensive security evaluation.

cs.LG↗

arXiv2026

Observability of wave equations with time- and space-dependent potentials: a counterexample under GCC and a positive criterion on the disk

We show that the geometric control condition (GCC) does not guarantee internal observability for a wave equation with a smooth time-dependent potential. On a bounded connected domain with analytic boundary, we construct a nonempty open observation set such that the pair satisfies GCC and the free Dirichlet wave is observable. For this same domain and observation set, we construct a smooth $2π$-periodic potential for which there exists a nonzero smooth Dirichlet wave that vanishes on the observed cylinder for all time. The wave is the unique mild solution in the space $X_Ω=L^2(Ω)\times H^{-1}(Ω)$ on every finite time interval, so no finite observation horizon yields an observability inequality for this fixed potential. The construction starts from a real-valued local counterexample to unique continuation across a noncharacteristic hyperplane. This local statement is of independent interest, since earlier constructions for the wave operator use complex-valued waves and potentials. The global counterexample is then obtained by joining flat oscillatory solutions along the edges of a polygonal observation set, repairing their sum at the vertices without changing its zero set, and using a spatial transition to a common time-independent pair near the boundary. The planar construction also yields counterexamples in every space dimension $n\ge3$. For comparison, and to identify a geometry that supplies both propagation and continuation, we show on the unit disk that an observation region containing a central disk and a neighborhood of an embedded cross-cut yields observability for every weak wave at sufficiently large observation time, with constants uniform over bounded measurable potentials. The proof uses a cut, logarithmic polar coordinates, and a Carleman weight whose favorable flux is confined to the observed artificial boundary.

math.OC↗

arXiv2026

Recall or Relearn? A Mixture of In-Context Experts for Recurring Concept Drift

Tabular foundation models (TFMs) are being applied to Web data streams such as network intrusion detection, where they adapt by updating the labelled rows of their context without retraining. When a past concept returns after leaving the context, a TFM faces a recall-or-relearn decision between restoring stored rows of the concept and relearning it from new labels. We propose MICE (Mixture of In-Context Experts), a training-free learner that cuts the stream into segments at detected changes. It merges a closed segment into a stored context when the TFM's estimated additional error on the segment is within a tolerance, under a capacity limit on stored contexts. A fast level weights the stored contexts and first-in-first-out (FIFO) windows by the log-loss of their predictions on the last labelled batch. We show that, with pure stored contexts and a margin condition, this fast level gains over relearning, in expected accuracy, the normalised positive area between the stored context's accuracy and the TFM's learning curve, up to a first-batch term. A slow level mixes the fast level's prediction with that of the FIFO window of the last labelled rows and bounds the discounted half-Brier regret of MICE against this window at every time. Learning curves measured beforehand predict the ordering of the observed recall gains. MICE outperforms reset, which empties the context at detected drifts, on grid streams with random boundary phases. Merging keeps fewer experts than pools that store every segment, and with fixed segmentation a time-matched snapshot pool matches MICE on the shifted grid. On real streams, MICE has the highest mean accuracy of all policies we compare.

cs.LG↗

arXiv2026

Efficient Remote Sensing Image-Text Retrieval via Interaction-Free Recall and Text-Guided Reranking

Remote sensing (RS) image-text retrieval plays a critical role in understanding massive RS imagery. However, the dense multi-object distribution and complex backgrounds in RS imagery make it difficult to simultaneously achieve fine-grained cross-modal alignment and efficient retrieval. Existing methods either rely on complex cross-modal interactions that lead to low retrieval efficiency, or depend on large-scale vision-language adaptation, which requires massive data and computational resources. To address these issues, we develop a fast-then-fine (FTF) retrieval framework centered on interaction-free multi-granular recall and parameter-free text-guided cross-modal reranking with the Balanced Text-guided Interaction Block (BTIB). Specifically, interaction-free multi-granular recall pre-computes gallery embeddings and matches them with the corresponding query embedding without full-gallery token-level text-image interaction, while text-guided cross-modal reranking with BTIB refines local semantic correspondence within the top-K candidate set. Furthermore, an inter- and intra-modal loss is designed to jointly optimize cross-modal alignment across multi-granular representations. Extensive experiments on public benchmarks demonstrate that the FTF achieves competitive retrieval accuracy while significantly improving retrieval efficiency compared with existing methods.

cs.CV↗

arXiv2026

EvoRouter: Cost-Efficient Multi-Agent Routing via Insight-Guided On-Policy Distillation

Serving web queries at scale with multi-agent systems requires jointly configuring large language models, collaboration modes, agent counts, interaction rounds, and skills. However, the resulting configuration space grows combinatorially, while sparse execution rewards provide limited fine-grained supervision for interdependent planning decisions. We propose EvoRouter, a self-evolving multi-agent routing framework driven by insight-guided on-policy distillation. A dedicated expert periodically synthesizes performance-cost feedback from configuration trajectories across tasks into reusable conditional routing insights about capability requirements, returns from resource scaling, and interactions among configuration choices. A privileged teacher combines these evolving insights with current execution feedback to provide dense token-level supervision for the router's own planning trajectories through on-policy distillation. Cost-aware reinforcement learning jointly optimizes task performance and computational cost. Together, these training signals internalize execution insights into the routing policy. The updated policy generates new trajectories that support subsequent insight extraction, forming an execution-driven self-improvement loop. We evaluate EvoRouter on 19 in-domain datasets spanning five domains and two out-of-domain benchmarks. EvoRouter achieves an average in-domain accuracy of 68.69%, outperforming the strongest routing baseline by 7.23 percentage points while reducing inference compute cost by 50.95%. Our code is open-sourced at https://github.com/CenYangtze/EvoRouter.

cs.AI↗

arXiv2026

The ALMA-QUARKS survey: A Keplerian Circumbinary Disk Candidate in the High-mass Star-forming Region IRAS 08303-4303

We present the ALMA Band 6 continuum and molecular line observations of IRAS 08303-4303, a high-mass star-forming region, with an angular resolution of $\sim 0.3''$ ($\sim 700$ au at the distance of 2.35 kpc). Six dense condensations are identified in the 1.3 mm continuum, and at least four of them are associated with molecular outflows. The estimated outflow parameters, particularly mass outflow rates $\geq 10^{-4}$ $M_{\odot}$ yr$^{-1}$, suggest that the driving sources are high-mass young stellar objects. Two of the condensations are forming a wide protobinary system with a separation of $\sim 900$ au. They reside within a single rotating structure, identified as a circumbinary disk which has a mass of about 2 $M_{\odot}$. This structure is traced by multiple molecular lines and exhibits a Keplerian rotation pattern. Based on the Keplerian rotation assumption, the enclosed mass is derived to be between 32 and 61 $M_{\odot}$: 22-43 $M_{\odot}$ for the primary and 10-18 $M_{\odot}$ for the secondary. The circumbinary disk is on the whole gravitationally stable, yet some parts with Toomre $Q < 2$ indicate potential fragmentation. Various molecular lines reveal a streamer-like structure connecting to the circumbinary disk, suggesting transfer of material from the envelope to the protobinary system through it. Despite the observational rarity of such circumbinary disks around high-mass YSOs, the high binary fraction among massive stars underscores their significance. This source, therefore, serves as a key laboratory for understanding the formation of high-mass binary systems.

astro-ph.SR↗

arXiv2026

On the sum of least prime factors in short intervals

Let $p(n)$ denote the least prime factor of $n$ and $L_C(x)=Cx^{1/2}(\log x)^2$ with $C>0$. The sum of $p(n)/n$ over composite $n$ lying in the short interval $[x,\,x+L_C(x)]$, a question raised by Erdős and Graham, is studied. (i) The constant $c=8$ in the mean asymptotic is estimated \[ S(x)=\sum_{n 0$, the window sums $μ_C(x):=\sum_{x\le n\le x+L_C(x)}p(n)/n$ over composites have mean $4C$: $\frac1X\sum_{x\le X}μ_C(x)=4C+O_C(1/\log X)$, and second moment $\frac1X\sum_{x\le X}(μ_C(x)-4C)^2=O_C(1)$. (iii)Under the Maier-consistent bounded-fluctuation hypothesis, $μ_C(x)=4C+O_C(1)$ holds uniformly in $x$, and the Erdős--Graham question has an affirmative answer. Unconditionally, the uniform statement remains open; proving it would require resolving short-interval prime estimates at scale $(\log y)^2$.

math.NT↗

arXiv2026

REATS: LLM Reasoning-based Ensemble Learning for Adaptive Time Series Forecasting

Due to the diversity of real-world time series, no single forecasting model consistently dominates across all samples. Ensemble learning addresses this by combining complementary model strengths, yet existing methods rely on fixed rules or black-box models based solely on numerical inputs, failing to leverage LLM reasoning for interpretable weighting decisions. We propose REATS, which leverages LLM reasoning capabilities as an intelligent ensemble router that jointly processes textual temporal pattern descriptions and numerical features to produce interpretable, sample-adaptive ensemble weights through chain-of-thought reasoning. To enable effective LLM-based ensembling, we study its key design choices and propose: (i) a structured input pipeline that transforms raw time series into hybrid textual--numerical representations with fixed token cost, enabling rule-based chain-of-thought construction without API dependency, augmented with retrieved similar-sample priors; (ii) a diverse multi-row weight supervision scheme coupled with a token-efficient percentage-table format that reduces numerical complexity and mitigates LLM hallucinations; and (iii) a two-stage fine-tuning framework combining SFT with GRPO, where a reciprocal reward mapping transforms the continuous unbounded MSE gap into bounded signals with amplified near-oracle sensitivity, addressing the uniform sensitivity and outlier-dominated advantage compression inherent in naive reward designs for regression-based GRPO. Experiments on eight benchmarks demonstrate that REATS outperforms competitive ensemble baselines while providing natural language explanations and demonstrating strong transfer learning and out-of-domain generalization to unseen candidate models.

cs.LG↗

arXiv2026

A Unified Interface Neural Network for Elliptic Interface Problems

We develop a Unified Interface Neural Network (UINN) framework for elliptic interface problems with discontinuous coefficients. A single shared network provides a unified representation of the solution in both subdomains, while a projection--correction construction embeds the solution and flux jump conditions directly into the neural trial space. This design aligns with the classical numerical principle of incorporating interfacial physics into the approximation basis to construct interface-unfitted numerical methods. The jump conditions are therefore satisfied exactly for any network parameters. Compared with methods based on separate phase networks and numerical formulations with interface penalty terms, UINN provides a unified representation with exact enforcement of interfacial jump conditions and interface-penalty-free optimization. Those features streamline the numerical formulations and can enhance training robustness. Numerical experiments on smooth interfaces at modestly large and high coefficient contrasts demonstrate UINN's solution accuracy, near-machine-precision satisfaction of the interface jump conditions, and enhanced robustness.

physics.comp-ph↗

arXiv2026

ANCHOR: Audio-Visually Grounded Chain-of-Thought Reasoning Benchmark

Multimodal large language models (MLLMs) perform well on audio-visual question answering, but correct answers do not necessarily imply that their stated reasoning is grounded in relevant perceptual evidence. Existing benchmarks mainly evaluate final-answer accuracy, offering limited insight into whether model-generated rationales correctly identify visual regions, temporal intervals, and audio events supporting predictions. We introduce ANCHOR, a benchmark and evaluation framework for measuring grounded-rationale alignment in multimodal reasoning, comprising 2,319 videos and 8,272 question-answer pairs with structured reasoning traces, temporal evidence, spatial bounding boxes, and salient audio cues, including a human-refined test set of 224 videos and 975 question-answer pairs. We separately measure answer correctness, hallucination, logical divergence, and conciseness, with direct spatial and temporal grounding measurements on a focused subset. Across the full benchmark, twelve contemporary MLLMs show a substantial alignment gap: models with comparable answer performance can differ markedly in whether their explanations are supported by annotated evidence. On a matched subset of 100 videos and 446 question-answer pairs, rankings remain highly stable across human-refined, Gemini-generated, and GPT-generated references (mean Pearson r=0.99), providing evidence against model-reference circularity within this subset. Grounding-cue ablations of three MLLMs on the full human-refined test set reveal a consistent modality hierarchy: removing video reduces accuracy by 38.4-41.8 points, while removing bounding boxes (3.2-7.7 points) and audio (4.2-5.6 points) causes smaller, complementary, model-dependent drops. These findings show answer-only evaluation obscures important grounding failures and position ANCHOR as a testbed for evaluating accurate and evidence-aligned audio-visual reasoning.

cs.CV↗

arXiv2026

Long-horizon Forecasting of Sodium-ion Battery Charge-profile Evolution and Degradation using Autoregressive Deep Sequence Models

Accurate long-horizon battery ageing prediction remains challenging because degradation alters not only scalar health indicators but also the shape and duration of electrochemical cycling profiles. Here, we introduce an autoregressive deep sequence-learning framework to forecast voltage-current profiles and state-of-health (SOH) evolution in NVPF/hard-carbon sodium-ion batteries. Stacked LSTM (Batt-LSTM) and hybrid CNN-LSTM (Batt-LSTM-C) models learn from voltage, current, and cycle-index sequences to generate future cycling profiles iteratively from measured data. Scheduled sampling mitigates the training-inference mismatch during autoregressive rollout, extending stable forecasting horizons from a few tens of cycles to as many as 600 cycles while preserving local waveform fidelity. Horizon-dependent benchmarking against classical machine-learning models evaluates voltage mean absolute error (MAE), global and local dynamic time warping (DTW), and SOH MAE across five forecasting horizons. Batt-LSTM with scheduled sampling achieves the lowest voltage MAE at horizons from 5,000 to 20,000 time steps. The predicted profiles also enable extraction of capacity-, resistance-, and energy-based SOH indicators, together with internal-resistance evolution. Monte Carlo dropout and deep ensembles estimate predictive spread at local profile and global degradation-trajectory scales. Fine-tuning on an independent ageing dataset improves cross-cell adaptation, with rolling-horizon updates reducing SOH prediction error to 3.844 percentage points for a 200-cycle horizon. These results show that curve-level forecasting retains diagnostically relevant electrochemical information beyond scalar SOH regression and offers a route toward uncertainty-aware, adaptive battery-health monitoring.

physics.chem-ph↗