arXiv subjects
Publications and source records attributed to Peng Gao.
In this paper, we apply the resonance method to exhibit large values at the central point of the family of quadratic Hecke $L$-functions with prime-related moduli of the Gaussian field under the generalized Riemann hypothesis.
Fiber lasers and amplifiers offer attractive alternatives to conventional solid-state systems. However, generation of high-energy ultrashort laser pulses in fibers faces challenges due to the complex interplay of multiple nonlinear effects arising due to pulse confinement within a small fiber core and also limitations imposed by the gain bandwidth of the available active fibers. The discovery of self-similar amplification and gain-managed nonlinear amplification (GMNA) pulse propagation regimes in fibers with normal dispersion suggests that these challenges can be turned into an advantage. Here we show that pulses generated in the GMNA regime are, in fact, the realization of the idealized similariton-type pulses in realistic fibers with limited gain bandwidth. Our analytical and numerical results show how one should shape the fiber gain as a function of propagation length to achieve constant peak power similariton-like pulses with steadily increasing energy, the pulse bandwidth exceeding the gain bandwidth, and the nearly linear frequency chirp allowing for efficient pulse compression to its Fourier limit. Absent Raman nonlinearities, these pulses can reach $μ$J level energies in standard single-mode fibers, representing a tenfold increase in pulse energy compared to the best currently available nonlinear amplifiers. Our results have significant implications for the fundamental understanding of nonlinear wave dynamics and for the advancement of fiber laser technology, supporting the reliable generation of high-energy pulses for practical use in areas such as micromachining, metrology, and bioimaging.
We present Lunima-OmniLV (abbreviated as OmniLV), a universal multimodal multi-task framework for low-level vision that addresses over 100 sub-tasks across four major categories: image restoration, image enhancement, weak-semantic dense prediction, and stylization. OmniLV leverages both textual and visual prompts to offer flexible and user-friendly interactions. Built on Diffusion Transformer (DiT)-based generative priors, our framework supports arbitrary resolutions -- achieving optimal performance at 1K resolution -- while preserving fine-grained details and high fidelity. Through extensive experiments, we demonstrate that separately encoding text and visual instructions, combined with co-training using shallow feature control, is essential to mitigate task ambiguity and enhance multi-task generalization. Our findings also reveal that integrating high-level generative tasks into low-level vision models can compromise detail-sensitive restoration. These insights pave the way for more robust and generalizable low-level vision systems.
In this paper, we apply the resonator method to exhibit large values at the central point of the families of cubic and quartic Dirichlet $L$-functions of prime moduli under the generalized Riemann hypothesis.
Numerical simulation of dynamic wetting processes remains challenging due to the multiscale feature of the moving contact line. This paper presents a finite element method for two- or three-dimensional dynamic wetting problems within the framework of the lubrication equation and the precursor film model. By reconstructing the disjoining pressure formulation, a mesoscopic precursor film model is implemented to enable a relatively thick precursor film to reproduce the intermediate-region interfacial behavior of a physically thin precursor film. The proposed model reduces the requirement for excessive spatial resolution near the contact line, thereby significantly reducing the computational cost while preserving the macroscopic flow dynamics. This method does not incorporate any moving boundary and easily handles topological changes. Its capability and accuracy are validated through various simulations, including the spreading, retraction, sliding, and coalescence of drops, as well as the breakup of liquid ridges. Numerical results (with the mesoscopic precursor film model adopted) show good agreement with the available exact solutions and asymptotic theories.
In this paper, we study the long-time behavior of the viscous conservation law equation on the whole real line, subject to a white-in-time force and arbitrarily small damping and viscosity constants. We establish polynomial mixing rates in two settings: (a) a general super-quadratic flux with hyperviscous dissipation, where the growth of the nonlinearity is controlled by the order of hyperviscosity, and the force is sufficiently non-degenerate on a generic L2-basis; and (b) a general quadratic flux with standard second-order dissipation, and the force is non-degenerate on some unconditional basis. Both settings include the classical Burgers-type nonlinearity. The proof is based on an abstract polynomial coupling criterion developed in arXiv:2408.00592 and a Foiaş--Prodi estimate.
Enterprise networks remain vulnerable to Advanced Persistent Threats (APTs), where adversaries gain an initial foothold and move laterally across the network, accumulating access permissions hop by hop to reach critical targets. Existing network defenses cannot track user movement at the process level across the network; instead, they grant ambient trust to all processes within a host. As a result, once a host is compromised, malicious processes inherit the victim's permissions, thereby expanding the attacker's access scope and enabling further lateral movement. To address this gap, we present NetZone, an in-network access control that confines each user process to a fixed access scope that persists as the user moves across the network. NetZone introduces a new abstraction, called AccessScope, which represents a lightweight access capability bound to the user's processes. Each AccessScope encodes the set of hosts a user identity is authorized to access and is embedded in the process's outgoing network traffic for validation before reaching its destination. As users pivot across hosts, AccessScope propagates with their traffic, rebinds to the receiving process, and persists across hosts. This ensures that regardless of network location, the user's processes are consistently governed by their bound AccessScope and their access permissions remain unchanged. To handle the high volume of network traffic generated by processes, we develop a data-plane co-design that integrates programmable switches with eBPF. NetZone employs a set of in-network optimizations and lightweight AccessScope persistence techniques to inspect the embedded AccessScope on the fly, enabling line-rate processing of high traffic volumes with negligible latency overhead. Our extensive evaluations show that NetZone can effectively defend against sophisticated attack scenarios without introducing noticeable overhead.
Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic families of Dirichlet and Hecke L-functions of primerelated moduli of imaginary quadratic number fields of class number one under the generalized Riemann hypothesis. As corollaries, we evaluate asymptotically the first moment of central values as well as the one-level density of the families of L-functions under consideration.
Cyber threat intelligence (CTI) is foundational to modern cyber defense, yet much of it resides in unstructured reports whose volume and heterogeneity far exceed manual analysis, motivating research on automatically constructing knowledge graphs from CTI reports. However, existing approaches mainly extract partial information within a single report, leaving the cross-source setting unexplored, where the same threat is given unrelated names. Our key insight is that attack behaviors, once mapped to MITRE ATT&CK (a standardized catalog of attack techniques), can anchor the rest of a report. Attack behaviors are the adversarial actions a report describes, while contextual entities (e.g., threat actors, campaigns, and affected products) and Indicators of Compromise (IoCs; e.g., IP addresses) are their participants and traces. Attaching them to these anchors places every per-report graph in one canonical space. We realize this insight in BEACON, an LLM-driven framework for cross-source CTI knowledge graph construction. Its first stage extracts each report into a graph under a propose-then-verify paradigm, grounding candidates in report evidence and official ATT&CK definitions, to suppress LLM misclassification and hallucination. Its second stage merges these graphs with a hierarchical alignment strategy that applies signals in decreasing order of determinism, from character-level and semantic similarity to overlapping technique neighborhoods, iterating as merges pool neighborhoods. No existing benchmark links entities to technique anchors or provides cross-source alignment ground truth. We therefore construct and release two human-annotated datasets from 34 sources: to our knowledge the largest for report-level CTI extraction (8,395 elements) and the first for cross-source consolidation (3,487). On them, BEACON outperforms all baselines by at least 23% and 9%, respectively.
LLM agents increasingly read untrusted content, invoke external tools, access private data, and delegate work to other agents. Harm often arises not from a single unsafe action but from the flow of sensitive data across a sequence of otherwise plausible steps. We present AgentFlow, a flow-centric policy language and runtime enforcement model for specifying where data may travel in agent systems. Policies are defined over labeled runtime edges and constrain which tools may receive sensitive fields, which sinks may receive released data, and what authority may cross delegation boundaries. The language supports flow and path rules, task-scoped capabilities, controlled release, and stateful taint semantics. A runtime reference monitor mediates agent actions, and a bounded SMT-based verifier checks safety properties for a structured policy fragment. We evaluate AgentFlow on multiple agent benchmarks. In our prototype, seven safety properties verify in under 0.5 seconds each, and the verifier catches all seeded unsafe policy variants in our study. On 949 AgentDojo injected cases across four suites, AgentFlow reduces confirmed compromise from 33.0\% to 0.0\% while improving aggregate utility from 46.7\% to 63.3\%. On a 200-case AgentDyn Dailylife benchmark, it reduces confirmed compromise from 73.5\% to 0.0\% while preserving near-baseline utility (44.5\% to 43.5\%). Breadth checks across ASB, InjecAgent, BIPIA, AgentHarm, and MCPTox replays suggest that the configured policies block the benchmark-specified policy-visible attacker flows; in ASB's direct-prompt-injection harness, attack success is 0/1{,}200. These results are preliminary and scoped to the modeled policy-visible agent behaviors and evaluated benchmarks.
Cyber threat intelligence (CTI) is increasingly consumed not by human analysts but by LLM agents that compose multi-step investigations at query time. The harness side of this shift has matured rapidly (planning loops, tool protocols, context management), but the corpus side has not: threat reports and vulnerability databases are still packaged for retrieval-augmented generation, as opaque chunks behind an embedding index. We argue that this substrate, not model capability, is the bottleneck on agentic CTI investigation, and present CTIFoundry, an agent-native corpus scaffold. At build time, CTIFoundry materializes the latent structure of a CTI corpus: a deterministic ontology graph over four authoritative knowledge bases (CVE, CWE, CAPEC, ATT&CK) whose official cross-references become typed, traversable edges; a span-grounded report layer whose canonical, alias-resolved cross-vendor entities index provenance-carrying chunks; and hybrid dense+lexical retrieval surfaces. At query time this structure is exposed through seven typed tools and three procedural skills mounted on a stock open-source agent harness. On the public CTIConnect benchmark, swapping only the action surface lifts the identically-harnessed agent by +0.19 to +0.28 overall F1 across a four-model, two-provider panel: a small model on CTIFoundry surpasses a flagship on the flat substrate, and the gain is not bought with search effort, since on both Claude models the scaffolded agent is more accurate at roughly half the tool calls. An ablation attributes it: typed structure carries the larger share, procedural skills convert structure into discipline, and the two compose super-additively, because skills bind only to structure that exists.
This paper investigates an increasingly important topic in generative modeling: pixel-space diffusion models. Although numerous studies have explored this topic, most focus on small-scale or class-conditional settings. Consequently, a practical recipe for training pixel-space models that rival or exceed well-established latent-space counterparts remains elusive. Through a comprehensive empirical study, we first observe that direct large-scale pre-training in pixel space converges substantially more slowly than in latent space. This observation motivates a latent-to-pixel strategy that acquires generative priors efficiently in latent space and transitions to pixel space during post-training. We then systematically investigate the key design choices governing this transition, including weight initialization, data composition, prediction target, decoder architecture, and noise schedule, and identify a practical recipe that makes the resulting pixel-space models match or outperform their latent-space counterparts while delivering 3.18 to 4.75 times end-to-end inference speedups. We hope that our findings provide useful empirical insights and practical guidelines for future research on pixel-space generation.
Our goal in this paper is to investigate the ergodicity of the white-forced wave equation on the whole line. Assuming that sufficiently many directions of the phase space are stochastically forced, we prove the uniqueness of the stationary measure and polynomial mixing in the dual-Lipschitz metric. The difficulties in our proof are twofold. On the one hand, in contrast to stochastic parabolic equations, the stochastic wave equation lacks both a smoothing effect and a strongly dissipative mechanism. On the other hand, the unboundedness of the whole line leads to a loss of compactness compared with the bounded domain case. To overcome these obstacles, our proof relies on four key ingredients: a new criterion for polynomial mixing established in [21], a novel weighted Foiaş-Prodi estimate for the wave equation on the whole line, weighted energy estimates for the stochastic wave equation, and the irreducibility of the stochastic wave equation.
We study, under the Generalized Riemann Hypothesis (GRH), the moments of sums of Fourier coefficients of a fixed holomorphic Hecke eigenform twisted by the quadratic character $χ_{8p}$, where $p$ ranges over odd primes. We establish the correct order of magnitude for the unsmoothed $m$-th moment for all real $m\geq 4$, and a sharp upper bound of order $XY^{m/2}\,\, (\log X)^{m(m-3)/2}\,\,$ for the smoothed $m$-th moment for all integers $m\geq 4$. A matching lower bound for all even integers $m\geq 4$ shows that this bound is optimal.
Modern cloud applications often comprise thousands of microservices whose interactions form complex request paths. Traditional inter-service access control restricts individual service-to-service requests, but fails to prevent multi-hop attacks, where each hop appears legitimate yet the overall path violates security intent. This gap leaves systems exposed to unauthorized access and data exfiltration. In this paper, we present eMicro, a path-aware defense system for microservices that prevents such attacks while remaining efficient and deployable. eMicro enforces real-time multi-hop access control through three key techniques: (1) history-based access control extended to capture service invocation sequences; (2) security policies encoded as efficient deterministic finite automaton (DFA), supporting constant-time lookups and compact label propagation; (3) eBPF-based in-kernel request tracing for transparent, low-overhead enforcement without code changes. Evaluations on DeathStarBench and production cloud traces from Uber, Alibaba, and ByteDance, covering 12 million request workflows and thousands of services, demonstrate the scalability of eMicro. eMicro performs policy checks in 1 microsecond, stores 50 million policies in only 100 MB, and reduces propagation overhead by 90% with negligible runtime impact. These results show that eMicro delivers scalable and efficient protection against multi-hop attacks, making it practical for deployment in large-scale microservice environments.
In this paper, we study the large-time behaviors of the Kuramoto-Sivashinsky equation (KSE) on the 1D torus while being subjected to random perturbation via additive Gaussian noise. It is well-known that under suitable assumptions on the stochastic forcing, the KSE admits a unique invariant probability measure. In this work, we make further progress on the topic of ergodicity by addressing the issue of convergence rate toward equilibrium. In comparison with the previous results, we can prove that the unique invariant probability measure is exponentially attractive and smallness condition of anti-diffusion coefficient is not necessary here. The proof relies on a coupling argument while making use of Lyapunov functions motivated by those of deterministic equations.
We introduce the MiniMax-M2 series, a family of Mixture-of-Experts language models built around the principle that mini activations can unleash maximum real-world intelligence. The flagship M2 contains 229.9B total parameters with only 9.8B activated per token. Designed end-to-end for agentic deployment, the M2 series rests on three components: (i) agent-driven data pipelines producing large-scale, verifiable trajectories across agentic coding and agentic cowork, each grounded in an executable workspace and an artifact-aligned reward; (ii) Forge, a scalable agent-native RL system that adapts to long-horizon agent trajectories, paired with windowed-FIFO scheduling, prefix-tree merging, inference optimization, and a clean training-inference-agent decoupling that supports both white-box and black-box agents; (iii) the latest M2.7 checkpoint takes an early step toward self-evolution -- autonomously debugging training runs and modifying its own scaffold. Across M2 through M2.7, this combination translates a mini-activation footprint into frontier-tier performance on agentic coding, deep search, office-task, and reasoning benchmarks.
In this paper, we evaluate the murmuration density for the family of quadratic Hecke $L$-functions of the Gaussian field under the generalized Riemann hypothesis.