arXiv subjects

Tao Zhang

Publications and source records attributed to Tao Zhang.

At least 91 records · Page 5Linked to original sources

arXiv2026

Incidence theorems for multivariate polynomials over finite fields

We study incidence problems for multivariate polynomials over a finite field $\mathbb{F}_q$. Given two families of $m$-variate polynomials, we count the number of triples $(f,g,x)$ such that $f$ belongs to the first family, $g$ belongs to the second family, $x\in\mathbb{F}_q^m$, and $f(x)=g(x)$. We show that for any subsets $\mathcal{L},\mathcal{L}'\subseteq V_{m,r}$, where $V_{m,r}$ denotes the vector space of all $m$-variate polynomials over $\mathbb{F}_q$ of degree at most $r$, the number of such triples is at most $$q^{m-1}|\mathcal{L}||\mathcal{L}'|+O\big(q^{\dim V_{m,r}-1}\sqrt{|\mathcal{L}||\mathcal{L}'|}\big).$$ We further show that if $\mathcal{L}$ and $\mathcal{L}'$ are contained in a subspace $V\subseteq V_{m,r}$ satisfying a suitable separating condition, then the same estimate holds with $\dim V_{m,r}$ replaced by $\dim V$. Our upper bound is essentially sharp when $q^{m-1}|\mathcal{L}||\mathcal{L}'|$ dominates the summation. As applications, we derive incidence bounds for points and multivariate polynomials. These results recover and strengthen several previously known bounds for point-line incidences and point-univariate-polynomial incidences. Our proof is spectral, relying on an expander mixing lemma for general abelian Cayley color graphs together with Fourier analysis over finite fields.

math.CO↗

arXiv2026

Linear-Quadratic Mean Field Games with Hybrid Local-Global Interactions on Manifolds

This paper studies linear-quadratic mean field games on compact Riemannian manifolds with a hybrid interaction topology. The network structure is a superposition of a deterministic graph for local geometric connectivity and a stochastic directed graph for non-local interactions. The global graph is constructed via random sampling based on a continuous kernel $K$. The out-degree of each node scales as $Θ(\log N)$ or as $Θ(N)$ to represent a sparse or dense network, respectively. In the infinite-population limit, the continuum system is governed by a coupled system of forward-backward partial differential equations, where the dynamics of the expected state incorporate the integral operator corresponding to the non-local sampling. The existence of a Nash equilibrium is established for this limit system. Furthermore, the approximation error is analyzed using operator concentration inequalities and analytic semigroup theory. Non-asymptotic high-probability error bounds between the finite-population empirical state and the continuum limit are derived. The convergence rates differ depending on the two topological regimes. Under the dense regime, the tracking error exhibits a polynomial decay rate dependent on the manifold dimension and Sobolev regularity, while under the sparse regime, the error decays at a rate of $\mathcal{O}((\log N)^{-1/2})$.

math.OC↗

arXiv2026

HRIBench: Benchmarking Interaction-Centric Human-Robot Collaboration

Current vision-language-action (VLA) benchmarks primarily evaluate isolated manipulation skills while leaving human-robot interaction structure largely unmodeled. However, real-world collaboration fundamentally requires coordination under shared agency, including intent understanding, temporal synchronization, protocol adherence, and safe interaction in dynamic environments. To address this gap, we introduce HRIBench, a diagnostic benchmark for intent-aware human-robot collaboration based on executable interaction scenarios. HRIBench represents collaborative tasks as structured scenario scripts that explicitly model agent roles, temporal dependencies, coordination constraints, and human behavior distributions. Building on this abstraction, HRIBench defines three representative interaction roles: Instructor, Collaborator, and Intruder, covering intent communication, joint coordination, and robustness under human intervention. The benchmark contains 13 role-conditioned tasks with over 650 evaluation episodes generated from diverse interaction trajectories and scene variations. Beyond binary task success, HRIBench introduces interpretable interaction-centric metrics spanning synchronization, responsiveness, protocol compliance, and safety. We evaluate adapted policies based on GR00T, pi0.5, and ACT under a unified protocol. Results show that current foundation robot policies struggle substantially in collaborative settings despite strong manipulation ability, revealing major limitations in temporal coordination and intent-aware behavior. Fine-tuning on HRIBench consistently improves collaborative performance. In a real-world adaptation study, simulation data generated by HRIBench improves GR00T N1.5's physical-task success rate from 0.10 to 0.43, demonstrating the benchmark's value for advancing interaction-centric robot learning.

cs.RO↗

arXiv2026

MetaTune: Adjoint-based Meta-tuning via Robotic Differentiable Dynamics

Disturbance observer-based control has shown promise in robustifying robotic systems against uncertainties. However, tuning such systems remains challenging due to the strong coupling between controller gains and observer parameters. In this work, we propose MetaTune, a unified framework for joint auto-tuning of feedback controllers and disturbance observers through differentiable closed-loop meta-learning. MetaTune integrates a portable neural policy with physics-informed gradients derived from differentiable system dynamics, enabling adaptive gains across tasks and operating conditions. We develop an adjoint method that efficiently computes the meta-gradients with respect to adaptive gains backward in time to directly minimize the cost-to-go. Compared to existing forward methods, our approach reduces the computational complexity to be linear in the data horizon. On quadrotor control tasks, MetaTune achieves competitive or improved tracking performance while reducing gradient computation time by more than 50\%. In PX4-Gazebo hardware-in-the-loop simulation, the learned policy transfers zero-shot and reduces tracking RMSE by about 15--20\% in aggressive flight and up to 40\% under strong disturbances.

cs.RO↗

arXiv2026

Measurement of solar $pp$ neutrino flux with the new PandaX-4T data

We report a new measurement of the solar proton--proton ($pp$) neutrino flux via neutrino--electron elastic scattering using the PandaX-4T Run 2 data set collected between 2024 and 2026, corresponding to an exposure of 1.9 tonne$\cdot$yr. Before Run 2 data taking, the detector underwent a series of upgrades to improve its response and background conditions. Time variations of radioactive noble-gas impurities are constrained using the physics data themselves, complemented by measurements from the gas-assay system. The analysis introduced improvements in the data processing chain, detector response characterization, and background models. A blind spectral analysis was then performed on the electronic-recoil data across a wide energy range from 20 to 1000 keV. In combination with the Run 0 data published earlier, the fitted $pp$ flux is $(8.5 \pm 3.5)\times 10^{10}$ $\mathrm{cm^{-2}s^{-1}}$, consistent with the prediction of the Standard Solar Model. With a statistical significance of $2.2σ$ above background, this marks the first positive indication of solar $pp$ neutrino--electron scattering below an electronic-recoil energy of 165 keV.

hep-ex↗

arXiv2026

PixelEyes: Decoupling Perception and Reasoning for Pinpoint Visual Evidence Seeking

This paper explores multi-turn visual reasoning and observes that MLLMs repeatedly fail to localize the target, leading to long, redundant trajectories. We attribute this failure to the entanglement of reasoning and perception within a single model, the MLLM reasons and localizes simultaneously, and inaccurate localization triggers additional reasoning turns that bloat the trajectory. To solve this problem, we propose PixelEyes, a multi-turn visual reasoning agent that explicitly decouples reasoning from perception, i.e., the reasoner decides what to look for, while a specialized perception tool answers where it is. Specifically, PixelEyes introduces 1) Mask-guided Visual Search. A referring segmentation model is invoked to provide mask-precise localization, freeing the reasoner from the need to compensate for imprecise grounding. 2) Semantic-region Breadth-first Search (BFS). To eliminate redundant loops caused by repeatedly cropping incorrect sub-regions, we organize exploration as a breadth-first search over semantic regions. To internalize these capabilities, we construct the PixelEyes-6K dataset by resynthesizing expert trajectories from existing data. This explicitly embeds our mask-guided search and BFS logic into the model. We further introduce Pinpoint-Bench, a zero-hint visual search benchmark, i.e., no location cues are provided in the question, with instance-level masks and bounding boxes that separate localization failures from reasoning failures, enabling fine-grained analysis of failure modes such as inattentional blindness. Recent state-of-the-art MLLMs and visual reasoning agents leave large headroom on Pinpoint-Bench, demonstrating its quality and difficulty. Code and models are open-sourced.

cs.CV↗

arXiv2026

Differentiable Physics-Informed Adaptive Koopman Control for Stable Flight under Unknown Disturbances

Uncertainties and disturbances in robotic systems, such as aerodynamic forces, are fundamentally outcomes of physical interactions with the environment, manifesting as learnable spatiotemporal sequences rather than random noise. However, achieving high-precision control for robotic systems operating in unstructured environments is often hindered by complex unmodeled dynamics and external disturbances. While learning-based methods offer powerful approximation capabilities, they typically suffer from heavy reliance on offline training and lack theoretical guarantees. Conversely, traditional robust control strategies are predominantly reactive, limited to instantaneous estimation without the foresight to anticipate future disturbance trends. To bridge this gap, this paper proposes a differentiable data-enabled Koopman control framework termed DEKC. Unlike black-box approaches, DEKC adopts a hybrid modeling strategy that retains the nominal physics model while employing a deep neural network to parameterize the lifting function of Koopman operator for unknown residual dynamics. Crucially, the framework formulates disturbances as a dynamical system, learning their temporal evolution in a global linear space. This enables the prediction of future disturbance trajectories, which are explicitly integrated into controller for preemptive compensation. Furthermore, an online backward gradient update mechanism is introduced to ensure real-time adaptation to time-varying uncertainties. Numerical simulations on a tethered space robot demonstrate the efficacy of the proposed DEKC in mitigating highly coupled uncertainties. Complementing these results, real-world experiments on a quadrotor substantiate its superiority in tracking agile trajectories under uncertainties induced by aerodynamics and suspended payload.

eess.SY↗

arXiv2026

A Delsarte Linear Programming Approach to the Erdős--Falconer Distance Problem over Finite Fields

We introduce a Delsarte linear programming approach to the finite field Erdős--Falconer distance problem. Let $q$ be an odd prime power, let $n$ be even, and let $Q$ be a non-degenerate quadratic form on $\mathbb{F}_q^n$. For $E\subset \mathbb{F}_q^n$, define \[ Δ_Q(E)=\{Q(x-y):\ x,y\in E\}. \] We prove that, for every fixed $0<α<\frac{1}{2}$, there exist constants $C_α>0$ and $q_α$ such that if $q\ge q_α$ and $|E|\ge C_αq^{\frac n2+\frac13},$ then \[ |Δ_Q(E)|>1+α(q-1). \] In particular, $Δ_Q(E)$ contains a positive proportion of the elements of $\mathbb{F}_q$, and hence $|Δ_Q(E)|\gg q$. Our result applies uniformly to all non-degenerate quadratic forms in even-dimensional finite field vector spaces. In the Euclidean case \[ Q(x)=x_1^2+\cdots+x_n^2, \] it improves, for every even $n\ge 4$ over arbitrary finite fields, the general exponent $\frac{n+1}{2}$ obtained by Iosevich and Rudnev to $\frac n2+\frac13.$ The proof is based on the association scheme arising from the level sets of $Q$. By analyzing the corresponding eigenvalues through Gauss sums and Kloosterman sums, we construct a suitable feasible solution to the Delsarte linear program. This provides a new algebraic-combinatorial method for obtaining distance set estimates over finite fields.

math.CO↗

arXiv2026

CrossWeaver: Cross-modal Weaving for Arbitrary-Modality Semantic Segmentation

Multimodal semantic segmentation has shown great potential in leveraging complementary information across diverse sensing modalities. However, existing approaches often rely on carefully designed fusion strategies that either use modality-specific adaptations or rely on loosely coupled interactions, thereby limiting flexibility and resulting in less effective cross-modal coordination. Moreover, these methods often struggle to balance efficient information exchange with preserving the unique characteristics of each modality across different modality combinations. To address these challenges, we propose CrossWeaver, a simple yet effective multimodal fusion framework for arbitrary-modality semantic segmentation. Its core is a Modality Interaction Block (MIB), which enables selective and reliability-aware cross-modal interaction within the encoder, while a lightweight Seam-Aligned Fusion (SAF) module further aggregates the enhanced features. Extensive experiments on multiple multimodal semantic segmentation benchmarks demonstrate that our framework achieves state-of-the-art performance with minimal additional parameters and strong generalization to unseen modality combinations.

cs.CV↗

arXiv2026

AgentX: Towards Agent-Driven Self-Iteration of Industrial Recommender Systems

Recommendation algorithm iteration is moving from an artisanal, engineer-bound process toward an industrialized research loop, but this transition remains blocked by a structural execution bottleneck: the idea-to-launch cycle still depends on human engineers to generate hypotheses, modify production code, launch A/B experiments, and attribute online results. Innovation therefore scales linearly with headcount rather than compounding with evidence, compute, and accumulated experimental knowledge. We present AgentX, a production-deployed multi-agent system that fundamentally restructures this production function. AgentX operates as a self-evolving development engine: it autonomously generates, implements, evaluates, and learns from recommendation experiments at a scale and pace that no manual workflow can sustain. The system orchestrates four tightly coupled stages in a closed loop. A Brainstorm Agent synthesizes evidence from historical experiments, system architecture, data analysis, and external research into ranked, executable proposals. A Developing Agent translates each proposal into production-ready code through repository-grounded generation and multi-dimensional reliability verification. An Evaluation Agent conducts safe online rollout with guardrail-vetoed A/B judgment, converting both successes and failures into structured knowledge assets. A Harness Evolution layer (SGPO) then distills execution trajectories into semantic-gradient updates that continuously sharpen the agents themselves -- making the system not merely automated, but self-improving.

cs.AI↗

arXiv2026

Zero-shot Tweet-Level Stance Detection Enhanced by External Knowledge and Reflective Chain-of-Thought Reasoning

Zero-shot tweet-level stance detection confronts two primary challenges: (1) mitigating the context sparsity inherent in short texts, and (2) establishing the relevance between implicit targets and textual content. While existing methods primarily focus on incorporating external knowledge, they neglect the intrinsic semantic cues embedded within key intra-textual entities. Furthermore, current models exhibit limited capability in determining the relevance of unseen targets to the given text, thereby struggling to differentiate between "neutral" and "irrelevant" stance labels. To address these issues, we first construct a four-class, multi-topic Japanese tweet dataset. To our knowledge, this is the first Japanese tweet-level dataset for stance detection. We then propose KIRP, a zero-shot stance detection framework. It integrates external knowledge with entity reorganization for data augmentation and employs prompt chaining for reasoning. Specifically, the framework incorporates knowledge graphs to supplement and reorganize key textual entities, while reflective Chain-of-Thought (CoT) reasoning extracts and validates implicit targets. To better distinguish "neutral" from "irrelevant" labels, we adopt stance-aware contrastive learning to capture discriminative features and design a three-layer iterative prototype network for fine-grained classification. Experimental results on SemEval-2016, WT-WT, and KIRP-D show that KIRP achieves state-of-the-art performance. KIRP obtains F1 scores of 84.05% (three-class) on SemEval-2016, and 84.99% and 79.18% (four-class) on WT-WT and KIRP-D, respectively.

cs.CL↗

arXiv2026

From Uncertain to Safe: Conformal Adaptation of Diffusion Models for Safe PDE Control

The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requirements crucial in real-world applications. To address this limitation, we propose Safe Diffusion Models for PDE Control (SafeDiffCon), which introduce the uncertainty quantile as model uncertainty quantification to achieve optimal control under safety constraints through both post-training and inference phases. Firstly, our approach post-trains a pre-trained diffusion model to generate control sequences that better satisfy safety constraints while achieving improved control objectives via a reweighted diffusion loss, which incorporates the uncertainty quantile estimated using conformal prediction. Secondly, during inference, the diffusion model dynamically adjusts both its generation process and parameters through iterative guidance and fine-tuning, conditioned on control targets while simultaneously integrating the estimated uncertainty quantile. We evaluate SafeDiffCon on three control tasks: 1D Burgers' equation, 2D incompressible fluid, and controlled nuclear fusion problem. Results demonstrate that SafeDiffCon is the only method that satisfies all safety constraints, whereas other classical and deep learning baselines fail. Furthermore, while adhering to safety constraints, SafeDiffCon achieves the best control performance. The code can be found at https://github.com/AI4Science-WestlakeU/safediffcon.

cs.LG↗

arXiv2026

Solving Inverse Problems of Chaotic Systems with Bidirectional Conditional Flow Matching

Modeling chaotic systems is crucial yet challenging. Inverse problems in chaotic dynamics, namely inferring initial conditions from final states, remain largely unsolved because of ill-posedness, non-uniqueness, instability, and potentially chaotic time-reverse dynamics. We address this open problem with Bidirectional Conditional Flow Matching (Bi-CFM), which learns bidirectional mappings between distributions of initial and final states to capture the stochasticity of chaotic evolution and mitigate exponential error accumulation over time. Furthermore, for systems with conservation laws, we extend it to Conservation-constrained Bi-CFM (CBi-CFM). Across the classic Lorenz, Circuit, and high-dimensional Lorenz 96 systems, Bi-CFM improves five distribution-level metrics over baselines while achieving a speedup of more than two orders of magnitude. In the three-body planet-planet scattering problem in planetary dynamics, CBi-CFM better respects conservation laws, with conservation errors comparable to those of the ground truth. Finally, on real observations of globular clusters, collisional million-body systems shaped by $\sim 10^{10}$ years (10 Gyr) of evolution, our method represents an advance in accuracy, establishing a scalable route to solving inverse problems of long-timescale real-world chaotic dynamics.

cs.AI↗

arXiv2026

An Alternative Proof of Dilworth's Theorem via Local Chain Merges

Several elegant proofs of Dilworth's theorem for finite posets already exist in the literature. In this note, we present an alternative inductive proof using a local legal merge lemma on chain ends. By combining this lemma with the bound established by Dilworth's theorem, we observe a direct consequence: every chain decomposition can be transformed into a minimal chain decomposition through a finite sequence of such legal merges

cs.DM↗

arXiv2026

Factor-Aware Mixture-of-Experts with Pretrained Encoder for Combinatorial Generalization

The integration of pretrained encoders with diffusion policies has become a dominant paradigm for visual robotic manipulation. However, it still struggles to generalize across complex environments with varying factors such as lighting and surface textures. To address this, we propose FAME, a framework that integrates a factor-aware mixture-of-experts (MoE) with a pretrained encoder to enhance generalization to environmental variations. FAME follows a three-stage training process: (1) policy warmup, where a diffusion policy is trained on standard-environment data with a frozen encoder; (2) factor-specific adapter training, where lightweight adapters inserted between the frozen encoder and the temporarily frozen policy are trained on customized datasets, each targeting a distinct environmental variation; and (3) joint fine-tuning, where a central router and the warmed policy are trained on mixed data to handle multiple factors jointly. FAME is ``factor-aware'' because the central router softly weights frozen factor-specific adapters as a dense MoE, enabling combinatorial generalization across multiple factors. Evaluations on the Meta-World benchmark show that FAME outperforms diffusion policy baselines by 34%. We further validate FAME in a real-world pick-and-place task using a compact model trained on newly collected data, where FAME achieves a 35% improvement in generalization under real-world variations.

cs.RO↗

arXiv2026

Electric-field-driven magnetic switching and tightly bound interlayer excitons in bilayer CrSBr

Electric field control of magnetic order in two-dimensional (2D) van der Waals magnets is a central goal for low-power spin-based technologies. In the ambient-stable antiferromagnet CrSBr, strong magnetic anisotropy and robust exciton-spin coupling provide a favorable platform, yet deterministic electric field control of its magnetic phases has not been achieved. Here we demonstrate electric-field-driven reversible switching between antiferromagnetic and ferromagnetic states in dual-gated bilayer CrSBr without intentional carrier doping. In parallel, photoluminescence measurements resolve a tightly bound interlayer exciton with an intrinsic dipole moment of only ~1 e angstrom. The electric field dependence of the magnetic phase transition reveals two coexisting mechanisms: a linear magnetoelectric effect in the antiferromagnetic state and an electric-field-modulated interlayer exchange coupling. Their interplay accounts for the asymmetric evolution of the critical magnetic field. Our results establish bilayer CrSBr as a promising 2D material for electrically controlled spin-optoelectronic functionalities.

cond-mat.mes-hall↗

arXiv2026

Ray Antenna Array Enhanced Low-Altitude ISAC: Performance Analysis and Beamforming Design

The low-altitude economy (LAE) heavily relies on aerial vehicles, yet these platforms remain vulnerable to environmental and security risks, necessitating robust airspace monitoring. Integrated sensing and communication (ISAC) as one of the key technologies of 6G provides potential solutions for safe LAE. However, conventional antenna arrays face limitations in cost, scalability, and coverage, especially directly above the base station, due to hardware complexity and degraded angular resolution. By exploiting the recently proposed ray antenna array (RAA), this paper considers a RAA-enhanced low-altitude ISAC system. RAA architecture employs multiple ray-arranged arrays directly connected without phase shifters, significantly reducing hardware costs while supporting flexible beamforming via dynamic ray selection. Moreover, RAA can provide uniform angular resolution and eliminates coverage holes, making it particularly suitable for low-altitude ISAC. In this paper, we formulate an optimization problem for joint ray selection and beamforming to enhance sensing coverage under communication constraints. An efficient alternating optimization algorithm is proposed to solve this problem. Analytical and simulation results demonstrate that RAA achieves higher sensing signal-to-noise ratio compared to traditional arrays, offering a cost-effective and high-performance solution for achieving low-altitude ISAC.

cs.IT↗

arXiv2026

PerceptionDLM: Parallel Region Perception with Multimodal Diffusion Language Models

Multimodal large language models (MLLMs) have achieved remarkable progress in visual understanding tasks. However, most existing MLLMs rely on autoregressive generation, which limits their efficiency for perception tasks that require captioning multiple regions. In this work, we propose PerceptionDLM, a multimodal diffusion language model optimized for efficient parallel region perception. Built upon PerceptionDLM-Base, a strong foundational baseline that achieves state-of-the-art performance among open-source diffusion MLLMs, our architecture fully leverages the parallel decoding nature of DLMs. Specifically, we introduce efficient prompting and structured attention masking to enable simultaneous perception of multiple masked regions, allowing the model to generate region descriptions in parallel at both the sequence and token levels. This design significantly improves inference efficiency compared with existing approaches that process regions sequentially. To systematically evaluate the parallelism property of visual perception capability for DLMs, we construct a new Parallel Detailed Localized Captioning Benchmark (ParaDLC-Bench) by scaling the DLC-Bench to include multiple region masks per image, enabling joint evaluation of both caption quality and inference efficiency. Experiments demonstrate that PerceptionDLM maintains competitive performance in region captioning while achieving substantial speed improvements for multi-region perception tasks. Our results highlight the potential of multimodal diffusion language models for efficient, parallel visual perception. To the best of our knowledge, we are the first to achieve parallel region caption and perception by leveraging the advantages of diffusion language models. Code, models, and datasets are released.

cs.CV↗