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Ping He

Publications and source records attributed to Ping He.

At least 19 recordsLinked to original sources
arXiv2026

Exchange graphs and $g$-vectors of surface rigid algebras

We classify the connected components of support $τ$-tilting graphs of surface rigid algebras associated with partial tagged triangulations of punctured marked surfaces with nonempty boundary. For a connected algebra, the graph is disconnected if and only if the algebra is weakly symmetric, has at least two simple modules, and has Cartan rank one. In this case, it has exactly two connected components. For every nonzero $τ$-rigid pair over a connected surface rigid algebra, the graph of $τ$-tilting completions is connected. More generally, we classify the completion components for an arbitrary surface rigid algebra and a fixed $τ$-rigid pair. For partial tagged triangulations with all endpoints at punctures, we express the Cartan matrix and $g$-vectors by signed endpoint data. We prove that $τ$-tilting finiteness is equivalent to positive definiteness of the Cartan matrix. In the finite case, we determine the primitive $g$-vector ray generators in endpoint coordinates. Trees give type A, and a criterion on the original partial tagged triangulation distinguishes types D and C in the unicyclic case.

math.RT↗
arXiv2026

FlashDiff: Efficient Regional Execution and Scheduling for Diffusion Model Serving

Diffusion models have become the central backbone for modern image, video, and audio generation, but their efficient service remains a challenge. Unlike autoregressive decoding, diffusion inference repeatedly updates high-dimensional spatial or temporal latents over many denoising steps. This all-region execution pattern makes generation latency high and limits serving throughput. Existing multi-GPU parallelization methods can reduce per-step computation, but often introduce substantial activation exchange overhead, causing communication to offset or even outweigh the benefits of parallel execution. This paper presents FlashDiff, a diffusion serving system that improves inference efficiency through adaptive regional execution and scheduling. FlashDiff is based on the observation that diffusion refinement is not uniform across latent regions or denoising steps: different regions often stabilize at different rates, while neighboring steps exhibit strong temporal correlation. FlashDiff leverages these properties to selectively execute only regions that require further refinement and to reallocate the resulting compute slack across concurrent serving requests. FlashDiff consists of three mechanisms. First, it decomposes the latent representation into coherent execution regions using early-stage attention signals, preserving semantic structure while exposing fine-grained parallelism. Second, it uses a lightweight runtime controller to estimate region activity and bypass low-impact updates when further refinement is unlikely to affect output quality. Third, it applies an affinity-aware online scheduler that co-locates dependent regions, balances residual load across GPUs, and reuses reclaimed compute capacity to improve serving efficiency. Across real-world image, video, and audio workloads, FlashDiff reduces end-to-end serving latency by 30-97% and improves throughput by 1.2-2.2x.

cs.DC↗
arXiv2026

Automated Discovery of Physically Interpretable Subgrid Length Scales for Detached Eddy Simulation via Agentic AI

Traditional turbulence-model development relies heavily on expert knowledge and is time-consuming. This study develops an agentic AI framework, DEScover (automated Discovery of DES closures), to explore subgrid length scales for detached eddy simulation (DES). The user provides only a modeling idea: the length scale is the grid width normal to the local vortex axis. Four large language model (LLM) agents then propose, review, implement, and evaluate candidate formulations and generate scripts for CFD simulations. The Discovery Agent infers the vortex axis from various vortex-identification methods. The candidates are tested on four cases spanning canonical and engineering flows: a flat plate, a backward-facing step, a free shear layer, and an iced airfoil. For all test cases, the best candidate consistently outperforms the standard length scale based on the maximum cell size. Its accuracy is similar to, or slightly better than, that of the expert-designed shear-layer-adapted length scale. Each agentic discovery run takes about 25 minutes on average, excluding the CFD simulations. These results show that LLM-based reasoning can significantly accelerate the discovery of physically interpretable turbulence models and reduce reliance on manual expert formulation.

physics.flu-dyn↗
arXiv2026

OT-MeanFlow3D: Bridging Optimal Transport and Meanflow for Efficient 3D Point Cloud Generation

Flow-matching models have recently emerged as a powerful framework for generative modeling, including 3D point cloud synthesis. However, their deployment is limited by the need for multiple sequential sampling steps at inference time. MeanFlow enables single-step generation by learning an average velocity field, but its quality depends heavily on the geometry of the training pairs. In this work, we propose an Optimal Transport-enhanced MeanFlow framework (OT-MF3D) for efficient and accurate 3D point cloud generation and completion. Beyond incorporating OT into MeanFlow, our method introduces a latent-conditioned training algorithm that decouples shape-level sampling from point-level matching. This enables exact point-level OT within each conditioned shape while performing shape-level transport in a compact latent space, avoiding the expensive nested OT computation in point-cloud space. Experiments on standard benchmarks show improved generation and completion quality over fast baselines, with substantially reduced training and inference costs compared with diffusion and other flow-based models.

cs.LG↗
arXiv2026

Ideal filtrations and stabilization in alternating HRS tilting

We prove that the realization functors obtained by alternating forward and backward HRS tilts of any torsion pair over a finite-dimensional algebra are equivalences from some step onward. The number of steps is bounded by the lengths of the indecomposable projective modules. The even hearts define an increasing filtration of ideals contained in a square-zero ideal. For a torsion pair induced by a two-term silting complex, we identify the successive layers with Buan-Zhou kernel ideals and compute them by reduction modulo the successive ideals. We also describe the largest quotient over which the complex becomes tilting and determine the exact stabilization index from the two parity heights. We construct algebras for which the HRS height is arbitrarily large, and compute their ideal filtrations.

math.RT↗
arXiv2026

The Missing Primitive: Diagnosing and Repairing Mathematical Reasoning in Large Language Models

While Large Language Models (LLMs) have demonstrated striking capabilities on frontier mathematical problems, it remains unclear whether they possess the structural mathematical understanding underlying their solutions. In this paper, we take a first step toward systematically studying mathematical understanding in LLMs, from diagnosing its distinct capabilities to leveraging these findings to improve post-training. First, we introduce the notion of Mathematical Primitive to probe structural mathematical understanding and propose \hlei{}, a novel benchmark that evaluates mathematical reasoning along four distinct dimensions: Discovery, Generation, Digestion, and Execution. Second, our systematic diagnosis shows that solution accuracy masks distinct capability profiles, primitives unlock substantial latent execution capacity, and Discovery is the dominant bottleneck in mathematical reasoning. Our post-training analysis further shows that discovery-limited failures are particularly amenable to repair. Finally, building on these findings, we introduce \abs{}, a primitive-privileged self-distillation framework that selectively transfers primitive-guided reasoning into the student model. Extensive experiments demonstrate that \abs{} consistently improves mathematical reasoning over baselines across model scales and challenging benchmarks.

cs.LG↗
arXiv2026

Recovering Subtle Cosmological Information with the Zel'dovich-inspired Transform

Extracting cosmological information from nonlinear and non-Gaussian large-scale structure remains a major challenge. We introduce the Zel'dovich-inspired (ZI) transform, a simple one-parameter local nonlinear transform in which $η$ controls the weighting of higher-order information in the transformed density field. For $η\geq3$, the transform can substantially suppress gravitational non-Gaussianity. Using real-space matter density fields from the \textsc{Quijote} suite and Fisher analysis, we find that the joint data vector of three transformed-field power spectra with $\{η=\infty, 6, 3\}$, denoted $P_\mathrm{ZI}$, reduces marginalized errors for all parameters considered. The improvements range from several-fold for some $Λ$CDM parameters to factors of 290 for local primordial non-Gaussianity and 107 for the summed neutrino mass. Tests on independent fiducial simulations yield nearly unbiased parameter estimates. Compared with other state-of-the-art summary statistics, $P_\mathrm{ZI}$ provides tighter cosmological constraints.

astro-ph.CO↗
arXiv2026

SecProbe: Adaptive Evaluation of Coding Agents on Cybersecurity Vulnerabilities

Assessing cybersecurity vulnerability awareness in coding agents requires evaluations that reveal capability gaps and remain informative as models evolve. Static benchmarks offer fixed coverage and difficulty, while scarce vulnerable repositories and costly expert authoring limit their renewal at scale. We introduce SecProbe, a framework for adaptive evaluation that combines Item Response Theory (IRT) with on-demand synthesis of repository-scale vulnerability-repair tasks. From observed performance, \textsc{SecProbe} estimates agent ability and identifies where additional evidence is most informative, selecting existing tasks or synthesizing new ones accordingly. As one use case, we construct 353 tasks spanning six programming languages and 151 CWE types and evaluate nine frontier models with two agent harnesses. Success rates peak at 28.33\%, highlighting substantial gaps in vulnerability recognition and repair. Compared with random and one-shot baselines, \textsc{SecProbe} achieves comparable agent ability estimates while requiring agents to solve up to 29.5\% fewer tasks. These results support adaptive evaluation as an efficient and discriminative approach to assessing cybersecurity vulnerability awareness.

cs.CR↗
arXiv2026

Long memory score-driven models as approximations for rough Ornstein-Uhlenbeck processes

This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak convergence, under appropriate scaling, to fractional Ornstein-Uhlenbeck processes with Hurst parameter $H < 1/2$. When score-driven models are used to characterize the dynamics of volatility, they serve as discrete-time approximations for rough volatility. We present several examples, including EGARCH($\infty$) whose limits give rise to a new class of rough volatility models. Building on this framework, we develop a GPU-accelerated Monte Carlo scheme based on divide-and-conquer fast Fourier transforms, reducing the computational complexity for each path from $\mathcal{O}(N^2)$ to $\mathcal{O}(N\log^2 N)$ for large-scale rough volatility simulation and option pricing.

math.PR↗
arXiv2026

PhysMiner: An Agentic AI Framework for Automated Flow Component Analysis

Uncovering the physical mechanisms of turbulent flows remains a fundamental challenge in fluid mechanics. In particular, conventional velocity-gradient analysis methods suffer from shear contamination, which hinders accurate identification of the dominant physical mechanisms. This study presents PhysMiner, an automated framework integrating the triple decomposition method of the velocity gradient tensor with large language model-driven reasoning for turbulence-physics discovery. The triple decomposition module automatically decomposes flow fields into rigid rotation, pure shearing, and normal straining components, enabling statistical analysis, contour visualization, vortex-line extraction, and threshold-insensitive vortex identification while eliminating shear contamination. These automated capabilities are validated across five benchmarks, ranging from canonical configurations to complex engineering flows. A discover-physics agent combines flow statistics, spatial structures, and literature-derived knowledge to perform pattern recognition and physical inference, while a review Agent iteratively validates physical consistency to ensure reliable conclusions. A continuously evolving Triple Decomposition Library accumulates statistical knowledge from successfully analyzed flows, enabling cross-case comparison and progressive enhancement of inductive capability. The complete PhysMiner pipeline is validated end-to-end on the periodic hill flow, where the framework autonomously generates turbulence modeling recommendations and derives an improved subgrid-scale model with superior Reynolds-stress predictions. PhysMiner is open to the public and establishes a foundation for long-term collaborative advancement in automated turbulence-physics discovery.

physics.flu-dyn↗
arXiv2026

From Pre-triangulation to Triangulation: Obstructions and Exact Lifting

We give a new equivalent formulation of Verdier's octahedral axiom. An initial square in a pre-triangulated category determines an obstruction in a quotient of ordinary Hom groups. Its vanishing is equivalent to the existence of a good completion, and $\mathrm{TR4}$ is equivalent to this vanishing for the squares associated with composable morphisms. As a consequence, if two pre-triangulations have the same underlying additive category and one is triangulated, then the other satisfies $\mathrm{TR4}$ precisely when their relative inverse Heller comparison admits an exact lift along every short exact sequence in the Freyd category. As applications, we prove that the exotic pre-triangulated category of Díaz Cabrera--Muro is in fact a triangulated category over every algebraically closed field. We construct scalar families for type-$A_{3a-1}$ preprojective algebras over arbitrary fields and for a range of Dynkin preprojective algebras in characteristic two; in each family the zero parameter is the unique triangulated member. The local equations also yield separable descent, including canonical triangulations for non-modular equivariantizations and for the Markman--Mehrotra K3 deformation categories.

math.RT↗
arXiv2026

Visko Orbis 1.0: A Live Model for Real-Time Interactive Long Video Generation

We present Visko Orbis 1.0, a Live Model for real-time, interactive long video generation. Users can change the prompt at any moment during generation, and the update becomes visible in real time. Visko Orbis 1.0 supports long-form text-to-video, image-to-video, and video continuation, with multilingual prompts and prompt switching while generation is in progress. A bounded multi-scale memory preserves subjects, scenes, and style across chunks, sustaining hour-scale rollouts without evident quality or color drift. The generator is factorized causally in time, matching the causal structure of physical dynamics, and is aligned with a latent world-model reward for predictive consistency. Built on a distilled chunk-wise streaming generator and a streaming video upscaler, Visko Orbis 1.0 delivers 4K video generation at 24 FPS in real time, using an optimized GPU serving engine. In quantitative evaluations, Visko Orbis 1.0 achieves the best DOVER aesthetic and technical scores and the best VideoAlign visual and motion quality, and leads three physical-plausibility protocols (VideoPhy-2, Physics-IQ, and VBench-2.0 Physics); in long-form Arena comparisons, it obtains the highest overall-preference and temporal-stability ratings among all the state-of-the-art real-time interactive video generation systems.

cs.CV↗
arXiv2026

Beyond the Payload: How User Invocation Shapes Coding Agent Vulnerability to Repository Poisoning

Coding agents are increasingly used for software engineering tasks, including bootstrapping projects from third-party repositories whose integrity cannot be assumed. Prior work on repository poisoning largely focuses on attacker-controlled injection and disguise, but developers also shape risk through everyday invocation choices: what task to delegate, how to phrase the request, and which skills or rules to supply. We term these user-side choices Prompt-Level Configurations (PLCs) and introduce CIPR (Coding In Poisoned Repos), the first benchmark that systematically varies PLCs in poisoned real-world repositories. CIPR comprises 1,920 instances across 20 repositories, four task types, three social-media-grounded prompt styles, and three skill/rule conditions, and measures attack success rate (ASR) and agent alert rate (AR) using automated runtime and trace-based oracles. Our evaluation reveals two key insights: (1) Vulnerability is highly context-dependent, with task type creating up to a 4.5-fold difference in ASR, with test-execution task forming a silent attack surface (high ASR, low AR). (2) Prompt expression shifts risk indirectly: underspecified prompts reduce ASR by truncating execution depth; noisy prompts exhibit a directional trend toward suppressing alerts by making malicious content less conspicuous. These findings highlight that coding agent vulnerability is not a static property, but a dynamic outcome shaped by everyday user configurations.

cs.CR↗
arXiv2026

Splitting Rules from Kinematic Flow: Local Evolution and Emergent Time

The differential equations satisfied by the wavefunction coefficients of conformally coupled scalars in a power-law cosmology can be recast as an iterative differential system of basis functions. These functions can be encoded within graph tubings and are governed by a set of rules describing how they flow in kinematic space. In this paper, we formulate a set of splitting rules equivalent to the kinematic flow at tree level by reversing the flow direction of graph tubings. Specifically, for any basis function, these rules identify all other basis functions whose total differentials contain it. From the splitting perspective, we uncover deeper physical information captured by graph tubings, such as the formation of singularity structures and the realization of local evolution. In an alternative basis based on time ordering, the splitting processes correspond to the emergence of time integrals. These rules can also be generalized naturally to the $\mathrm{tr}\,ϕ^3$ theory beyond individual graphs, providing a physical interpretation of the structure of the associahedron. This suggests that graph tubings and the kinematic flow may be more fundamental objects than the differential equations, and may have a life of their own.

hep-th↗
arXiv2026

SE(3)-MeanFlow: Few-Step Protein Backbone Generation on Lie Groups

Generative modeling of protein backbones promises the de novo design of proteins with prescribed structural and functional properties. Existing diffusion and flow-matching models produce high-quality backbones on SE(3)^N, but inference requires numerically integrating an ODE over hundreds of network evaluations, each involving a Lie group exponential map - a bottleneck for high-throughput design campaigns. We introduce SE(3)-MeanFlow, a few-step generative framework that extends MeanFlow from Euclidean space to the Lie group geometry of protein frames. Working natively in the Lie algebra so(3) and in R^3, we derive closed-form average-velocity identities for rotations and translations, giving simulation-free training targets. We further introduce an SE(3) alpha-Flow objective that removes the Jacobian-vector product from the rotation branch and serves as a warm-up stage, after which training switches to a small-t stabilized MeanFlow loss that is used for the remainder of pretraining and for rectification-based post-training. In protein backbone generation, SE(3)-MeanFlow matches or exceeds flow-matching baselines that use several times more sampling steps, and its advantage widens in the few-step regime, where rectification lets it lead at every matched budget - at a modest cost in diversity.

cs.LG↗
arXiv2026

Efficient three-dimensional variational data assimilation of multi-plane PIV data

We perform three-dimensional variational data assimilation (3DVar) using a discrete adjoint approach to optimise the time-averaged momentum equations. The experimental data consist of sparse stereoscopic particle image velocimetry (PIV) measurements collected along $12$ cross-stream planes in the wake of a vehicle-like bluff body at a Reynolds number $Re_L = 5.64 \times 10^5$ based on the streamwise body length. Adjoint localisation is proposed and implemented to reduce the memory footprint of the discrete adjoint method for spatially-varying control variables in 3DVar by confining the control variable space to a user-defined subdomain. Restricting the control variable to $12$ % of the full control space yields a maximum reduction in peak memory of $64$ %, while producing assimilated fields of comparable fidelity with respect to mean velocity and the optimised momentum forcing field. The localised adjoint case improves upon the baseline Spalart--Allmaras turbulence model and recovers the correct asymmetric topology of the complex three-dimensional (3D) recirculation bubble. The assimilated Reynolds shear stress agrees well with the experiment, and the assimilated mean pressure is shown to be physically consistent when correlated with the in-plane vorticity fields. A data efficiency study is also performed, in which the number of planes provided for assimilation is progressively reduced, demonstrating that the data coverage must extend at least to the end of the primary recirculation bubble to adequately constrain the near-wake dynamics. The efficiency that adjoint localisation affords is crucial for assimilating sparse, experimental data for 3D separated flows on fine meshes that can tackle industrial problems of interest.

physics.flu-dyn↗
arXiv2026

Weak Equilibrium Measures and Capacity--Hitting Identities for the Hypoelliptic Third-Order Langevin Diffusion

We construct weak equilibrium measures and weak capacities for the hypoelliptic third-order Langevin diffusion motivated by an accelerated sampling algorithm (Mou et al. (2021) \textit{J. Mach. Learn. Res.}, \textbf{22}(42), 1--41). In this process, the Brownian noise acts only in the highest-order auxiliary variable and reaches the physical variables through a step-three Hörmander chain, so the standard uniformly elliptic boundary-flux theory is not directly applicable at characteristic points of phase-space balls. We prove an elliptic-regularization stability theorem for the corresponding hitting laws and then define the weak equilibrium measure and weak capacity. The proof combines the boundary-hitting stability strategy of Lee--Ramil--Seo (2026, \textit{arXiv:2503.12610v2}) with localized hypoelliptic heat-kernel estimates (Pigato (2022) \textit{Stoch. Process. Appl.}, \textbf{145}, 117--142) adapted to the third-order chain. We obtain the bounded-domain weak capacity--hitting identity and a Lyapunov drift argument in the spirit of Lee--Ramil--Seo that yields positive Harris recurrence and extends the construction to a whole-space weak equilibrium measure, and whole-space capacity--hitting identity.

math.PR↗
arXiv2026

Hybrid Analysis for Secure MCP Tool Use in LLM Agents

The rapid development of large language model (LLM) agents has enabled their broad adoption across diverse real-world tasks. To standardize interactions between LLM agents and external environments, Model Context Protocol (MCP) tools have emerged as a de facto standard and have been widely integrated into these systems. However, the use of MCP tools also introduces new safety risks, as LLM agents can be induced to perform malicious or unauthorized actions. Although prior work has proposed defenses for securing tool use in LLM agents, most methods rely on static analysis, i.e., inspecting prompts and generated outputs, which limits the defense effectiveness and robustness. To address these limitations, we propose MTGuard, a hybrid analysis-based defense framework designed to safeguard the use of MCP tools in LLM agents by leveraging lifecycle-aware static-dynamic co-analysis. Extensive evaluation demonstrates that MTGuard effectively mitigates multiple categories of harmful tool use across different LLM agents while maintaining performance on benign user tasks.

cs.CR↗