arXiv subjects

Kai Du

Publications and source records attributed to Kai Du.

At least 19 recordsLinked to original sources

arXiv2026

Magnetic quantum defects in a uniaxial antiferromagnetic insulator

Point defects have been successfully utilized in various quantum technologies, serving as quantum qubits for quantum computation, single-photon emitters for quantum communication, and nanoscale sensors for quantum metrology. However, their further development faces key challenges, particularly in discovering and exploring suitable defect-host systems that meet the necessary criteria for quantum applications. Here, using polarization-resolved Raman spectroscopy and terahertz absorption spectroscopy, we discover three distinct chromium-vacancy-induced excitations in the uniaxial antiferromagnetic insulator, Cr$_2$O$_3$. These vacancy-induced excitations have an energy scale of a few tens of millielectronvolts and are twofold degenerate, and the lowest one at 64 $cm^{-1}$ is sharp and sensitive to the external magnetic field along the easy-axis direction, particularly close to the spin-flop regime around 6T, where the mode softens from 64 to 27$cm^{-1}$. Based on the defect supercell first-principles calculations, we interpret the mode at 64 $cm^{-1}$ as a local magnetic excitation of the local moment within the chromium vacancy state. Our results establish that the magnetic defect states in Cr$_2$O$_3$ have potential for quantum applications.

cond-mat.mtrl-sci↗

arXiv2026

Principal Trait Analysis: Towards Deriving "Skills" in Human-AI Collaboration

Large Language Model-powered agents are increasingly used in the workplace via human-artificial intelligence (AI) collaboration. In this new era of work, it is important to understand the kinds of prompting traits that contribute to task success. Moreover, we need to uncover key skills required for modern professionals and inform educators on how to foster these skills among students. Existing guidelines for human-AI collaboration are built from either top-down theory or context-specific observations of human-AI interactions. However, since LLM capabilities are rapidly improving, theory may not be able to explain emerging interaction patterns, and empirical guidelines may become obsolete quickly. In this work, we explore an automated, data-driven approach to uncover patterns, which we term traits, of effective human-AI interaction that are aligned with task outcomes. We propose Principal Trait Analysis, a Principal Component Analysis-inspired algorithm for deriving common traits from patterns in LLM conversations. Our algorithm uses LLM-based processing stages to analyze corpora of human-AI collaborative session traces, deriving common traits across the dataset and scoring each human collaborator's usage style by each trait. The approach also allows domain expertise to be injected during trait discovery and selects the most distinguishing traits to be those that exhibit the highest variance across collaborators. We evaluate PTA on two human-AI collaborative coding datasets, an educational setting (students working with an AI tutor) and a professional setting (developers working with an AI coding agent). We find that PTA-derived traits are significant in explaining collaborator behavior across both settings and can help predict task outcomes. However, whether traits qualify as skills remains to be seen, due to inconclusive results on generalizability and how user traits change over time.

cs.CL↗

arXiv2026

Do Personalized Skills Help Coding Agents? An Empirical Study of Developer Interaction Histories

Large language model (LLM)-powered agents have rapidly evolved from code-completion tools into solvers of complex software engineering tasks. As developers collaborate with coding agents over time, their preferences emerge through repeated interactions and can be used to adapt agent behavior to better meet individual developers' needs. Capturing and reusing these preferences may reduce repeated corrections and improve developer-agent collaboration. Agent skills provide a lightweight mechanism for transferring experience without modifying model parameters. However, existing work primarily focuses on task-specific skills, and it remains unclear whether developer-specific skills distilled from interaction histories can generalize to future tasks. We propose a framework for extracting reusable developer preferences from interaction traces. It first generates personalized skills through rule-based bootstrapping and evidence-grounded refinement, and then evaluates them using a reproducible replay framework with an interactive, trajectory-conditioned LLM-based human developer simulator. We conduct an experiment on 206 real-world developer-agent sessions from 13 developers and compare personalized skills against no-skill, generic-skill, and other-user-skill baselines. Personalized skills provide small and inconsistent improvements over the no-skill baseline, whereas generic skills pooled across developers achieve the largest and most consistent gains. Further analysis suggests that personalized skills become more effective when developer preferences appear frequently, particularly when their histories contain multiple examples relevant to future tasks. These findings provide empirical insights into when developer-specific personalization is effective and demonstrate that broadly transferable procedural knowledge can be more robust than developer-specific preference signals.

cs.SE↗

arXiv2026

BrainPilot: Automating Brain Discovery with Agentic Research

Understanding the brain increasingly depends on integrating evidence across scales, modalities, and disciplines. Addressing a single research question therefore requires a coordinated sequence of operations, from surveying prior work to executing analyses and interpreting results in light of domain knowledge. AI agents promise to accelerate this process, but current agents lack domain expertise in brain science, may fabricate claims, drift during multi-step reasoning, and offer few defined points for expert intervention. These failures are especially costly in brain science, where conclusions feed into downstream scientific claims and depend on laboratory-specific expertise and careful human judgment. We present \textbf{BrainPilot} a \textbf{fully open-source} multi-agent system that accelerates brain science research with traceable logs and agent-verified results. A principal investigator (PI) agent coordinates specialist agents grounded in curated domain knowledge: a unified brain science knowledge base containing 7{,}233 indexed items and a skill library of 72 reusable methodology units across seven research domains. Every major step is recorded in the Graph of Trace, an auditable record that links subgoals, tool use, evidence, and claims and allows researchers to follow and inspect the workflow. An Auditor agent further integrates fabrication checking into the workflow. For evaluation, we run three brain science tasks from Agents' Last Exam, introduce our own benchmark, \textbf{BrainPilotBench-v0}, and present additional end-to-end case studies. Across these evaluations, BrainPilot with an open-source backbone model attains performance comparable to state-of-the-art agent framework with less costs.

cs.AI↗

arXiv2026

Beyond representational alignment with brain-guided language models for robust reasoning

The correspondence between large language models (LLMs) and the neural mechanisms underlying human higher-order cognition remains insufficiently characterized. Given that language and reasoning in the human brain appear dissociable, an open question is whether LLMs align with neural signals from reasoning-related regions and whether such signals can improve them. Here, focusing on deductive reasoning, we show that LLM internal representations are not only partially aligned with task-fMRI activity but can also be directly enhanced by these signals. Using a neural-predictivity metric, we find that LLMs explain a substantial fraction of the explainable variance in reasoning-related regions at the aggregate level, whereas predictivity within specific reasoning types is lower, indicating both alignment and divergence. Building on this, we propose a brain-guided framework: we steer model representations along directions induced by the joint structure of model and brain representations, applying intervention at inference and fine-tuning during training. We demonstrate that task-evoked brain signals can directly enhance LLM reasoning, yielding gains orthogonal to language-only supervision across 10 LLMs (1.5B-72B), with transfer across reasoning types and up to 13\% absolute accuracy gain. Our results advance LLM-brain correspondences from correlation to guidance, establishing a brain-signal-driven pathway toward more robust and cognitively aligned AI.

cs.LG↗

arXiv2026

Schauder estimates and classical solutions of the Dirichlet problem for stochastic parabolic equations

We study second-order stochastic parabolic equations in a cylindrical domain with homogeneous Dirichlet boundary conditions. Under a natural compatibility condition on the gradient-type noise, we establish global Schauder estimates in stochastic H\"older spaces for the Dirichlet problem. The coefficients and free terms are assumed to be H\"older continuous in the spatial variables, while only their boundary traces are required to be H\"older in time. As a consequence, we obtain existence and uniqueness of quasi-classical solutions in stochastic H\"older spaces, and further derive pathwise classical solvability in H\"older classes.

math.PR↗

arXiv2026

Emergence Transformer: Dynamical Temporal Attention Matters

The Transformer, a breakthrough architecture in artificial intelligence, owes its success to the attention mechanism, which utilizes long-range interactions in sequential data, enabling the emergent coherence between large language models (LLMs) and data distributions. However, temporal attention, that is, different forms of long-range interactions in temporal sequences, has rarely been explored in emergence phenomenon of complex systems including oscillatory coherence in quantum, biophysical, or climate systems. Here, by designing dynamical temporal attention (DTA) with time-varying query, key, and value matrices, we propose an Emergence Transformer. This architecture allows each component to interact with its own or its neighbors' past states through dynamical attention kernels, thereby enabling the promotion and/or suppression of the emergent coherence of components. Interestingly, we uncover that neighbor-DTA consistently promotes oscillatory coherence, whereas self-DTA exhibits an optimal attention weight for coherence enhancement, owing to its non-monotonic dependence on network structure. Practically, we demonstrate how DTA reshapes social coherence, suggesting strategies to either enhance agreement or preserve plurality. We further apply DTA to the paradigmatic Hopfield neural network, achieving emergent continual learning without catastrophic forgetting. Together, these results lay a foundation and provide an immediate paradigm for modulating emergence phenomenon in networked dynamics only using DTA.

cs.AI↗

arXiv2026

Retina gap junctions support the robust perception by warping neural representational geometries along the visual hierarchy

Deep Neural Networks (DNNs) are vulnerable to elaborately designed adversarial noise, although they have achieved extraordinary success in many tasks. Compared with DNNs, the human visual system is highly robust. However, it is unclear how the human visual system defends against adversarial attacks, especially the role of the early visual system and its influence on the brain manifold. Due to retina gap junctions being crucial for the denoising function in the early visual system, we combine a retina gap junction-based filter, G-filter, with DNN as an abstract human visual system model called the biological hybrid model. We adopt this model to study the defense performance of retina gap junctions and their impact on the brain manifold. Compared with other defense methods, the biological hybrid model is more robust and can be further improved by introducing noise during training. Next, we analyze the manifold and its decision boundary of the biological hybrid model from a geometry perspective. The results show that the biological hybrid model has a unique 2D decision boundary with high nonlinearity and a lower curvature of the decision boundary of the manifold compared to other defense methods. The transforming manifold may account for the high robustness of the biological hybrid model. Finally, to dissect G-filter and clarify its internal mechanism, we borrow the Neural Ordinary Differential Equation (ODE) concept and rewrite G-filter into an equivalent recurrent neural network. The results show that the decision boundary of the model's manifold will gradually change with time and eventually reach a steady state, which is modulated by gap junction conductance, revealing the influence of retina gap junctions on the brain manifold is a gradually evolving process.

q-bio.NC↗

arXiv2026

Atomically-sharp magnetic soliton in the square-net lattice EuRhAl$_{4}$Si$_{2}$

Topological spin textures are hallmark manifestations of competing interactions in magnetic matter. Their effective description by nonlinear field theories reflects an energetic frustration that destabilizes uniform order while selecting finite-size, topologically nontrivial configurations as stationary states. Among the most extreme realizations are atomically-sharp domain wall excitations, namely one-dimensional (1D) magnetic solitons, which represent the ultimate scaling limit of magnetic textures. Such solitons may emerge in magnetic systems where effective exchange interactions compete directly with uniaxial magnetic anisotropy. Here we show that the square-net rare earth compound EuRhAl$_{4}$Si$_{2}$ realizes a very susceptible regime where the magnetic anisotropy competes with highly frustrated exchange interactions stabilizing a rare ferrimagnetic $\uparrow\uparrow\downarrow$ state that, under applied magnetic field, supports the formation of atomically-sharp soliton defects. We confirm the bulk response of the 1D magnetic solitons via magnetization and electrical transport measurements. We establish both the zero- and in-field $\uparrow\uparrow\downarrow$ order via neutron diffraction, while magnetic force microscopy visualizes its real-space evolution into a stripe-like array. To elucidate the microscopic origin of the soliton, we relate the Ruderman-Kittel-Kasuya-Yosida (RKKY)-driven exchange interactions and the magnetic anisotropy through density functional theory, and we construct an effective 1D $J_{1}$-$J_{2}$-$K$ model whose atomistic spin dynamics simulations reproduce the observed soliton states as a function of external field. Our results demonstrate that EuRhAl$_{4}$Si$_{2}$ hosts atomically-sharp, field-driven 1D magnetic solitons, providing a new platform for studying 1D topological excitations at the atomic length scale.

cond-mat.str-el↗

arXiv2026

Polar enhancement of optical nonlinearities and domain-driven second harmonic contrast in bismuth telluro-halide van der Waals crystals

The BiTeX family of polar van der Waals (vdW) semiconductors offers a unique platform for exploring the interplay between polar crystalline structure and nonlinear optical phenomena. Here, we utilize second harmonic generation (SHG) polarimetry to demonstrate giant anisotropic optical nonlinearities in BiTeBr and BiTeI driven by contributions to the crystals' nonlinear polarizability originating from their permanent dipole moment. In addition, using SHG microscopy, we show that BiTeI displays a distinctive SHG spatial texture consisting of thread-like regions of reduced harmonic intensity. These features demark the boundaries between phase and anti-phase polar domains, confirmed via piezoresponse force microscopy and are attributable to disorder-driven restoration of inversion symmetry and concomitant optical interference effects. Our results unveil the power of polarization-resolved SHG microscopy in elucidating the intricate relationship between structure, symmetry, and nonlinear optical responses in polar vdW materials and highlight the promise of BiTeX as a material platform for domain-engineered nanoscale nonlinear photonics.

physics.optics↗

arXiv2025

Propagation of chaos for the Landau equation via microcanonical binary collisions

We develop a fully constructive, conservative, and collision-level realization of Kac's program for the spatially homogeneous Landau equation across the full interaction range, including the Coulomb case. Our model is the microcanonical binary-collision (MBC) process: a reversible pure-jump $N$-particle Markov process that is Landau-native, realizing the grazing-collision mechanism via small conservative rotations of relative velocities. The analysis hinges on two critical structural pillars: a Fisher-information dissipation mechanism that extends the Guill\'en--Silvestre paradigm (Acta Math. 234:315-375, 2025) to a genuinely conservative particle system, yielding robust control of singular configurations, and a quantitative self-averaging principle that enforces a coherent deterministic emergence of the Landau flow from the microscopic dynamics. We prove propagation of chaos in the joint mean-field and grazing-collision limit ($N\to\infty, h\to 0$), identifying any limit point with the unique global solution to the Landau equation. Furthermore, we rigorously derive the Landau master equation as the grazing-collision limit of the MBC process. To the best of our knowledge, this provides the first fully conservative, Landau-native binary-collision model rigorously shown to produce the Landau equation over the entire interaction range.

math.AP↗

arXiv2025

Electrotoroidicity: New Paradigm for Transverse Electromagnetic Responses

The exploration of transverse electromagnetic responses in solids with broken spatial-inversion (I) and/or time-reversal (T) symmetries has unveiled numerous captivating phenomena, including the (anomalous) Hall effect, Faraday rotations, non-reciprocal directional dichroism, and off-diagonal linear magnetoelectricity, all within the framework of magnetotoroidicity. Here, we introduce a novel class of transverse electromagnetic responses originating from electrotoroidicity in ferro-rotational (FR) systems with preserved I and T symmetries, distinct from magnetotoroidicity. We discover a high-order off-diagonal magnetic susceptibility of FR domains and a reduced linear diagonal magnetic susceptibility at FR domain walls in doped ilmenite FeTiO3. The non-trivial "Hall-like" effect of the former corresponds to an anomalous transverse susceptibility in the presence of spontaneous electrotoroidal moments in FR materials. Our findings unveil an emergent type of transverse electromagnetic responses even in I and T symmetry-conserved conditions and illustrate new functionalities of abundant FR materials.

cond-mat.mtrl-sci↗

arXiv2025

Embedding high-resolution touch across robotic hands enables adaptive human-like grasping

Developing robotic hands that adapt to real-world dynamics remains a fundamental challenge in robotics and machine intelligence. Despite significant advances in replicating human hand kinematics and control algorithms, robotic systems still struggle to match human capabilities in dynamic environments, primarily due to inadequate tactile feedback. To bridge this gap, we present F-TAC Hand, a biomimetic hand featuring high-resolution tactile sensing (0.1mm spatial resolution) across 70% of its surface area. Through optimized hand design, we overcome traditional challenges in integrating high-resolution tactile sensors while preserving the full range of motion. The hand, powered by our generative algorithm that synthesizes human-like hand configurations, demonstrates robust grasping capabilities in dynamic real-world conditions. Extensive evaluation across 600 real-world trials demonstrates that this tactile-embodied system significantly outperforms non-tactile-informed alternatives in complex manipulation tasks (p<0.0001). These results provide empirical evidence for the critical role of rich tactile embodiment in developing advanced robotic intelligence, offering new perspectives on the relationship between physical sensing capabilities and intelligent behavior.

cs.RO↗

arXiv2025

Optimal control of SDEs with merely measurable drift: an HJB approach

We investigate an optimal control problem for a diffusion whose drift and running cost are merely measurable in the state variable. Such low regularity rules out the use of Pontryagin's maximum principle and also invalidates the standard proof of the Bellman principle of optimality. We address these difficulties by analyzing the associated Hamilton-Jacobi-Bellman (HJB) equation. Working in a weak formulation of admissible controls, we first establish the state-equation solvability and Krylov estimates needed to make the control problem well defined. Using PDE techniques together with a policy iteration scheme, we prove that the HJB equation admits a unique strong solution, and this solution coincides with the value function of the control problem. Based on this identification, we establish a verification theorem and recover the Bellman optimality principle without imposing any additional smoothness assumptions. We further investigate a mollification scheme depending on a parameter $\varepsilon > 0$. It turns out that the smoothed value functions $V_{\varepsilon}$ may fail to converge to the original value function $V$ as $\varepsilon \to 0$, and we provide an explicit counterexample. To resolve this, we identify a structural condition on the control set. When the control set is countable, convergence $V_{\varepsilon} \to V$ holds locally uniformly.

math.OC↗

arXiv2025

Topological Magneto-optical Kerr Effect without Spin-orbit Coupling in Spin-compensated Antiferromagnet

The magneto-optical Kerr effect (MOKE), the differential reflection of oppositely circularly polarized light, has traditionally been associated with relativistic spin-orbit coupling (SOC), which links a particle's spin with its orbital motion. In ferromagnets, large MOKE signals arise from the combination of magnetization and SOC, while in certain coplanar antiferromagnets, SOC-induced Berry curvature enables MOKE despite zero net magnetization. Theoretically, large MOKE can also arise in a broader class of magnetic materials with compensated spins, without relying on SOC - for example, in systems exhibiting real-space scalar spin chirality. The experimental verification has remained elusive. Here, we demonstrate such a SOC- and magnetization-free MOKE in the noncoplanar antiferromagnet Co1/3TaS2. Using a Sagnac interferometer microscope, we image domains of scalar spin chirality and their reversal. Our findings establish experimentally a new mechanism for generating large MOKE signals and position chiral spin textures in compensated magnets as a compelling platform for ultrafast, stray-field-immune opto-spintronic applications.

physics.optics↗

arXiv2025

Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation

In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conservative gradient noise. Our approach revolves round introducing a new entropy formulation for stochastic variational inequalities. As a consequence, we obtain a novel well-posedness result for the obstacle problem of deterministic porous medium equations with nonlinear reaction terms.

math.PR↗

arXiv2025

Universal Superconductivity in FeTe and All-Iron-Based Ferromagnetic Superconductor Heterostructures

Ferromagnetism (FM) and superconductivity (SC) are two of the most famous macroscopic quantum phenomena. However, nature normally does not allow SC and FM to coexist without significant degradation. Here, we introduce the first fully iron-based SC/FM heterostructures, composed of Fe(Te,Se) and Fe3GeTe2, and show that in this platform strong FM and high-temperature SC robustly coexist. We subsequently discover that chemical proximity effect from neighboring layers can universally drive the otherwise non-superconducting FeTe films into a SC state. This suggests that the ground state of FeTe is so close to the SC state that it could be driven in and out of the SC state with various other perturbations. Altogether, this shows that Fe-Te-based heterostructures provide a unique opportunity to manipulate magnetism, superconductivity and topological physics, paving the way toward new superconducting technologies.

cond-mat.supr-con↗

arXiv2024

A structure-preserving collisional particle method for the Landau kinetic equation

In this paper, we propose and implement a structure-preserving stochastic particle method for the Landau equation. The method is based on a particle system for the Landau equation, where pairwise grazing collisions are modeled as diffusion processes. By exploiting the unique structure of the particle system and a spherical Brownian motion sampling, the method avoids additional temporal discretization of the particle system, ensuring that the discrete-time particle distributions exactly match their continuous-time counterparts. The method achieves $O(N)$ complexity per time step and preserves fundamental physical properties, including the conservation of mass, momentum and energy, as well as entropy dissipation. It demonstrates strong long-time accuracy and stability in numerical experiments. Furthermore, we also apply the method to the spatially non-homogeneous equations through a case study of the Vlasov--Poisson--Landau equation.

math.NA↗