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Peng Gao

Publications and source records attributed to Peng Gao.

At least 55 records · Page 3Linked to original sources
arXiv2026

Polynomial mixing for the white-forced hyperviscous Burgers equation on the whole line

Our goal in this paper is to investigate ergodicity of the white-forced hyperviscous Burgers equation on the whole line. Under the assumption that sufficiently many directions of the phase space are stochastically forced, we can prove that the dynamics is attractive toward a unique invariant probability measure with polynomial rate of any power. In order to prove this, we further develop coupling method and establish a sufficiently general criterion for polynomial mixing. The proof of polynomial mixing for the white-forced hyperviscous Burgers equation is obtained by the combination of the coupling criterion and the Foiaş-Prodi estimate of hyperviscous Burgers equation on the whole line.

math.DS↗
arXiv2026

Distribution Matching Distillation Meets Reinforcement Learning

Distribution Matching Distillation (DMD) facilitates efficient inference by distilling multi-step diffusion models into few-step variants. Concurrently, Reinforcement Learning (RL) has emerged as a vital tool for aligning generative models with human preferences. While both represent critical post-training stages for large-scale diffusion models, existing studies typically treat them as independent, sequential processes, leaving a systematic framework for their unification largely unexplored. In this work, we demonstrate that jointly optimizing these two objectives yields mutual benefits: RL enables more preference-aware and controllable distillation rather than uniformly compressing the full data distribution, while DMD serves as an effective regularizer to mitigate reward hacking during RL training. Building on these insights, we propose DMDR, a unified framework that incorporates Reward-Tilted Distribution Matching optimization alongside two dynamic distillation training strategies in the initial stage, followed by the joint DMD and RL optimization in the second stage. Extensive experiments demonstrate that DMDR achieves state-of-the-art visual quality and prompt adherence among few-step generation methods, even surpassing the performance of its multi-step teacher model.

cs.CV↗
arXiv2026

PersonalPlan: Planning Multi-Agent Systems for Personalized Programming Learning

Effective programming education requires personalized instruction adapted to diverse learner backgrounds. However, while LLM-based multi-agent systems (MAS) excel at complex planning, existing planners often lack profile-grounding and pedagogical scaffolding, thereby undermining personalized programming learning. To fill in the gap, we first introduce \textbf{MAP-PPL} (\textbf{M}ulti-\textbf{A}gent \textbf{P}lans for \textbf{P}ersonalized \textbf{P}rogramming \textbf{L}earning), a profile-conditioned multi-agent planning dataset with 3{,}043 query--profile--plan instances from 1{,}730 Stack Overflow question groups and 2{,}738 learner profiles. Each plan specifies agents, subtasks, executable steps, and prerequisite dependencies. Then, we propose \textbf{PersonalPlan}, a two-stage MAS planner that first performs hierarchical SFT with separate LoRA adapters for profile-aware task decomposition and step dependency planning, then applies a Reward-Adaptive GRPO to encourage the model to generate executable, personalized, and pedagogically scaffolded plans. Extensive experiments on MAP-PPL comparing PersonalPlan against frontier LLMs, generic MAS frameworks, and agentic planners demonstrate its superiority. With only 8B and 32B variants, PersonalPlan achieves state-of-the-art plan executability, personalization, and pedagogical quality, effectively orchestrating MAS for agent-student interactions.

cs.MA↗
arXiv2026

High-Fidelity Two-Step Image Generation via Teacher-Aligned End-to-End Distillation

Few-step diffusion distillation has become increasingly mature for 4-8-step generation, yet pushing further to 2 steps remains challenging. In this work, we introduce Z-Image Turbo++, a high-quality 2-step image generation model distilled from the 8-step Z-Image Turbo teacher. Our method addresses the central bottlenecks of increased task difficulty and limited model capacity in 2-step generation through three simple but effective design choices tailored to this regime. First, we propose Distribution-Aligned Adversarial Learning, which uses teacher-generated images rather than external real images as real samples for GAN training, providing a more attainable and informative adversarial target. Second, we adopt Step-Decoupled Parameterization, assigning independent model parameters to the two denoising steps to better match their distinct capacity demands. Third, we perform End-to-End Training with Iterative Regularization, allowing the first step to receive gradients from final image quality while preserving a meaningful intermediate generation through an explicit step-1 loss. Together, these designs substantially narrow the quality gap between 2-step and 8-step generation in both qualitative and quantitative evaluations, highlighting the potential of carefully tailored distillation strategies for improving the quality-efficiency trade-off in few-step generation.

cs.CV↗
arXiv2026

CTIConnect: A Benchmark for Retrieval-Augmented LLMs over Heterogeneous Cyber Threat Intelligence

Cyber Threat Intelligence (CTI) is foundational to modern cybersecurity, enabling organizations to proactively defend against evolving threats. However, the sheer volume and heterogeneity of CTI data, spanning structured knowledge bases (CVE, CWE, CAPEC, MITRE ATT&CK) and unstructured threat reports, far exceed the capacity of manual analysis. The strong contextual understanding and reasoning of Large Language Models (LLMs) have driven growing interest in applying them to CTI tasks. Yet no existing benchmark evaluates LLMs in a retrieval-augmented setting with a proper evaluation harness that grants access to the heterogeneous domain knowledge sources analysts rely on in practice. To address this gap, we present CTIConnect, a benchmark for systematically evaluating retrieval-augmented LLMs across the CTI task landscape. We construct a unified evaluation environment integrating five heterogeneous CTI sources into 1,860 expert-verified QA pairs spanning nine tasks across three categories: Entity Linking, Multi-Document Synthesis, and Entity Attribution. Extensive experiments on ten state-of-the-art LLMs reveal that the cross-source semantic gap manifests differently across task categories, demanding fundamentally different retrieval strategies, and that the performance bottleneck shifts between retrieval infrastructure and evidence utilization depending on the task. Our domain-specific strategies further outperform stronger general-purpose retrieval paradigms (retrieve-then-rerank, IRCoT), showing that closing this gap requires structural interventions rather than generic retrieval improvements. These findings hold across all ten LLMs, remain consistent on the full benchmark, and stay stable under temporal splits spanning 2008-2025. Together, they provide actionable guidance for designing scalable retrieval architectures over heterogeneous CTI ecosystems.

cs.CR↗
arXiv2026

ReciNet: Reciprocal Space-Aware Long-Range Modeling for Crystalline Property Prediction

Predicting properties of crystals from their structures is a fundamental yet challenging task in materials science. Unlike molecules, crystal structures exhibit infinite periodic arrangements of atoms, requiring methods capable of capturing both local and global information effectively. However, current works fall short of capturing long-range interactions within periodic structures. To address this, we leverage \emph{reciprocal space}, the natural domain for periodic crystals, and construct a Fourier series representation from fractional coordinates and reciprocal lattice vectors with learnable filters. Building on this, we introduce the reciprocal space-based geometry network (\textbf{ReciNet}), a novel architecture that integrates geometric GNNs and reciprocal blocks to model short-range and long-range interactions. Experiments on comprehensive benchmarks JARVIS, Materials Project, and MatBench demonstrate that ReciNet achieves outstanding predictive accuracy across a range of crystal property prediction tasks. Additionally, we explore a model extension for multi-property prediction with the mixture-of-experts, which demonstrates high computational efficiency and reveals positive transfer between correlated properties. These findings highlight the potential of our model as a scalable and accurate solution for crystal property prediction.

cs.LG↗
arXiv2026

High moments of random multiplicative functions twisted by Fourier coefficients of modular forms

Let $λ(n)$ denote the Fourier coefficients of a fixed modular form and $h(n)$ a Steinhaus or Rademacher random multiplicative function. In this paper, we determine, under the generalized Riemann hypothesis, the order of magnitude of $\E|\sum_{n \leq x} h(n)λ(n)|^{2q}$ up to factors of size $e^{O(q^2)}$, for all real $x, q$ with $1 \leq q \leq c\log x/\log\log x $ and $c>0$ a small constant.

math.NT↗
arXiv2026

D-OPSD: On-Policy Self-Distillation for Continuously Tuning Step-Distilled Diffusion Models

The landscape of high-performance image generation models is currently shifting from the inefficient multi-step ones to the efficient few-step counterparts (e.g, Z-Image-Turbo and FLUX.2-klein). However, these models present significant challenges for direct continuous supervised fine-tuning. For example, applying the commonly used fine-tuning technique would compromise their inherent few-step inference capability. To address this, we propose D-OPSD, a novel training paradigm for step-distilled diffusion models that enables on-policy learning during supervised fine-tuning. We first find that the modern diffusion models, where the LLM/VLM serves as the encoder, can inherit its encoder's in-context capabilities. This enables us to formulate the training as an on-policy self-distillation process. Specifically, during training, we make the model act as both the teacher and the student with different contexts, where the student is conditioned only on the text feature, while the teacher is conditioned on the multimodal feature of both the text prompt and the target image. Training minimizes the two predicted distributions over the student's own roll-outs. By optimizing on the model's own trajectory and under its own supervision, D-OPSD enables the model to learn new concepts, styles, etc., without sacrificing the original few-step capacity.

cs.CV↗
arXiv2026

Three-Dimensional Atomic-Scale Structural Transformation in a SrTiO3 Grain Boundary

Grain boundaries (GBs) in complex oxides play critical roles in governing their functional properties, which are intrinsically linked to their three-dimensional (3D) atomic configurations and local chemical environments that can deviate markedly from those of the bulk. However, the 3D atomic structures of GBs remain poorly understood due to the projection limitations of conventional (S)TEM. Here, using multislice electron ptychography, we resolve the 3D atomic structure of a Σ13(510)/[001] tilt GB in SrTiO3 with simultaneous visualization of both cation and oxygen columns. Depth-resolved reconstruction reveals pronounced structural inhomogeneity along the GB, uncovering a transition from the canonical symmetric configuration (STR1) to an asymmetric configuration (STR2) that is hidden in conventional projection imaging. Quantitative analysis of atomic-column intensities demonstrates that these two GB configurations possess distinct local chemical and vacancy distributions. By further mapping the atomic displacement fields, we reveal that the transformation between STR1 and STR2 proceeds via local atomic shuffling at the GB core and collective shear displacement in the adjoining grains, mediated by the step and dislocation character of the junction, respectively. Moreover, analysis of oxygen octahedral rotations reveals a strong dependence on the local atomic structure with pronounced asymmetry around the STR2 region. These findings establish a direct link among the 3D atomic structure, local chemical composition, and lattice order parameters at the GB, underscoring the critical importance of depth-resolved characterization in understanding and engineering GB-mediated functionalities in complex oxides.

cond-mat.mtrl-sci↗
arXiv2026

Nanoscale Thermal Imaging of Dislocation-Mediated Heat Transport

Dislocations in crystalline materials are widely exploited to tailor the thermal conductivity of semiconductors and thermoelectrics, yet a critical gap persists: direct measurement of local thermal resistance at individual buried dislocations, along with its spatial extent, remains elusive due to the limitations of conventional thermal probes. Here, we use in situ scanning transmission electron microscopy-electron energy-loss spectroscopy to map nanoscale temperature distributions across a low-angle SrTiO3 grain boundary with periodic dislocation arrays. Our results reveal a temperature drop of 47 K across the dislocation array. The associated temperature-field distortions are concentrated near the dislocation cores, consistent with stronger local thermal resistance at these discrete sites rather than a uniformly distributed resistance along the array. We further identify a distinct two-scale heat transport characteristic near the dislocation array: core-dominated effects over approximately 4.8-6.2 nm and extended inter-core influences over approximately 10.3-14.3 nm. Atomic-scale structural and vibrational analyses further reveal core-associated atomic reconstruction and localized optical-phonon perturbations, providing a microscopic basis for the stronger local thermal resistance inferred near dislocation cores. These findings quantitatively resolve spatial heterogeneity of dislocation-mediated heat transport, uncover its atomic-scale mechanism, and provide a quantitative basis for defect engineering, guiding the design of high-performance thermoelectrics, semiconductors, high-temperature structural alloys, and other functional crystalline materials.

cond-mat.mtrl-sci↗
arXiv2026

SenseNova-U1: Unifying Multimodal Understanding and Generation with NEO-unify Architecture

Recent large vision-language models (VLMs) remain fundamentally constrained by a persistent dichotomy: understanding and generation are treated as distinct problems, leading to fragmented architectures, cascaded pipelines, and misaligned representation spaces. We argue that this divide is not merely an engineering artifact, but a structural limitation that hinders the emergence of native multimodal intelligence. Hence, we introduce SenseNova-U1, a native unified multimodal paradigm built upon NEO-unify, in which understanding and generation evolve as synergistic views of a single underlying process. We launch two native unified variants, SenseNova-U1-8B-MoT and SenseNova-U1-A3B-MoT, built on dense (8B) and mixture-of-experts (30B-A3B) understanding baselines, respectively. Designed from first principles, they rival top-tier understanding-only VLMs across text understanding, vision-language perception, knowledge reasoning, agentic decision-making, and spatial intelligence. Meanwhile, they deliver strong semantic consistency and visual fidelity, excelling in conventional or knowledge-intensive any-to-image (X2I) synthesis, complex text-rich infographic generation, and interleaved vision-language generation, with or without think patterns. Beyond performance, we show detailed model design, data preprocessing, pre-/post-training, and inference strategies to support community research. Last but not least, preliminary evidence demonstrates that our models extend beyond perception and generation, performing strongly in vision-language-action (VLA) and world model (WM) scenarios. This points toward a broader roadmap where models do not translate between modalities, but think and act across them in a native manner. Multimodal AI is no longer about connecting separate systems, but about building a unified one and trusting the necessary capabilities to emerge from within.

cs.CV↗
arXiv2026

On the Gauss circle problem over smooth numbers

The Gauss circle problem concerns with the evaluation of $\sum_{n \leq x}r(n)$, where $r(n)$ denotes the number of representations of $n$ as sums of two squares and $x \geq 2$. Let $Ψ_G(x,y)$ denote the sum of $y$-smooth numbers below $x$ weighted by $r(n)$. In this paper, we evaluate $Ψ_G(x,y)$ asymptotically for certain ranges of $x \geq y \geq 2$.

math.NT↗
arXiv2026

Migration and spreading of a droplet driven by a chemical step

The chemical step is an elementary pattern in chemically heterogeneous substrates, featuring two regions of different wettability separated by a sharp border. Within the framework of lubrication theory, we investigate droplet motion and the contact-line dynamics driven by a chemical step, with the contact-line singularity addressed by the Navier slip condition. For both two-dimensional (2D) and three-dimensional (3D) droplets, two successive stages are identified: the migration stage, when the droplet traverses both regions, and the asymmetric spreading stage, when the droplet spreads on the hydrophilic region while being constrained by the border. For 2D droplets, we present a matched asymptotic analysis which agrees with numerical solutions. In the migration stage, a 2D droplet can exhibit translational motion with a constant speed. In the asymmetric spreading stage, the contact line at the droplet rear is pinned at the border. We show that a boundary layer still exists near the pinned contact line, across which the slope is approximately constant, whereas the curvature would diverge in the absence of slip. For 3D droplets, our numerical simulations show that the evolution is qualitatively analogous to the 2D case, while being significantly affected by the lateral flow. At early times, the contact line on the hydrophilic region advances linearly and spreads transversely according to a power law $t^{1/2}$. The droplet length and width exhibit non-monotonic variations due to the lateral flow. Eventually, the droplet detaches from the border and reaches equilibrium at the hydrophilic substrate.

physics.flu-dyn↗
arXiv2026

PRBench: End-to-end Paper Reproduction in Physics Research

AI agents powered by large language models exhibit strong reasoning and problem-solving capabilities, enabling them to assist scientific research tasks such as formula derivation and code generation. However, whether these agents can reliably perform end-to-end reproduction from real scientific papers remains an open question. We introduce PRBench, a benchmark of 30 expert-curated tasks spanning 11 subfields of physics. Each task requires an agent to comprehend the methodology of a published paper, implement the corresponding algorithms from scratch, and produce quantitative results matching the original publication. Agents are provided only with the task instruction and paper content, and operate in a sandboxed execution environment. All tasks are contributed by domain experts from over 20 research groups at the School of Physics, Peking University, each grounded in a real published paper and validated through end-to-end reproduction with verified ground-truth results and detailed scoring rubrics. Using an agentified assessment pipeline, we evaluate a set of coding agents on PRBench and analyze their capabilities across key dimensions of scientific reasoning and execution. The best-performing agent, OpenAI Codex powered by GPT-5.3-Codex, achieves a mean overall score of 34%. All agents exhibit a zero end-to-end callback success rate, with particularly poor performance in data accuracy and code correctness. We further identify systematic failure modes, including errors in formula implementation, inability to debug numerical simulations, and fabrication of output data. Overall, PRBench provides a rigorous benchmark for evaluating progress toward autonomous scientific research.

cs.CL↗
arXiv2026

First Moment of Quadratic Hecke $L$-Functions with Lower Order Term

We evaluate the first moment of the family of primitive quadratic Hecke $L$-functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis and the Lindelöf hypothesis. We obtain asymptotic formulas with secondary main terms and error terms of size that is one quarter of that of the main term.

math.NT↗