arXiv subjects

Zhen Liu

Publications and source records attributed to Zhen Liu.

At least 37 records · Page 2Linked to original sources

arXiv2026

A subquadratic bound for generalized Turán numbers of odd cycles

For a graph $H$ and a family of graphs $\mathcal F$, let $\text{ex}(n,H,\mathcal F)$ denote the maximum number of copies of $H$ in an $\mathcal F$-free graph on $n$ vertices. For every integer $i\ge 3$, let $C_i$ denote the cycle of length $i$. For $r\ge 3$, set $\mathscr {C}_r=\{C_3,C_4,\ldots,C_r\},$ and set $\mathscr {C}_2=\varnothing$. In this paper, we prove that, for all integers $l>k\ge 2$, $$ \text{ex}(n,C_{2k+1},\mathscr {C}_{2k}\cup\{C_{2l+1}\}) =O_{k,l} \left(n^{2-\frac{1}{k(k+1)(l-k)}}\ \ \right). $$ Together with the known upper bounds for the number of triangles in $C_{2l+1}$-free graphs, this confirms a conjecture of Gerbner, Győri, Methuku, and Vizer.

math.CO↗

arXiv2026

Z Boson Radiative Decay $Z\to μ^+ μ^- γ$ at the LHC

We study the radiative decay of the $Z$ boson, $Z \to μ^+μ^-γ$, at the LHC, providing both Standard Model (SM) precision analysis and new physics projections. With detailed analysis of Run-2 and future HL-LHC performances, we demonstrate that this decay mode can be measured with a statistical precision at the sub-percentage level. From existing Run-1 data, we extract $\text{Br}^\text{fid}(Z \to μμγ) = (3.34 \pm 0.016)\times 10^{-4}$. We further explore the sensitivity of this channel to axion-like particles (ALPs) and to an anomalous $U(1)_X$ gauge boson coupled to the muon. Both scenarios feature resonant structures in the dimuon invariant mass spectrum within the $Z \to a/X + γ\to μ^+μ^-γ$ final state. Our results show that the radiative $Z$ decay provides a clean and statistically powerful probe of such leptophilic new physics, extending the current collider reach for ALPs and anomalous gauge forces down to $g_X \sim \mathcal{O}(10^{-3})$. This study highlights the potential of rare electroweak gauge boson decays as precision tests of the SM and sensitive probes of new interactions at the LHC.

hep-ph↗

arXiv2026

Sharp asymptotics for triangle independence and covering numbers

For a graph $G$, let $α_1(G)$ be the maximum size of an edge set containing at most one edge from every triangle, and let $τ_1(G)$ be the minimum size of an edge set meeting every triangle. Erdős, Gallai, and Tuza proved that $α_1(G)+τ_1(G)=Ω(m^{2/3})$ for every $m$-edge graph and asked for the optimal asymptotic constant. We prove $$\lim_{m\to\infty} \min_{G,\,|E(G)|=m} \frac{α_1(G) + τ_1(G)}{m^{2/3}} = \frac{3}{2},$$ thereby establishing that the sharp constant is $3/2$ and solving the problem.

math.CO↗

arXiv2026

Mean Field Stackelberg Game for Production and Carbon Emission Reduction with State Reflections

Global warming, driven by anthropogenic carbon emissions with transboundary pollution characteristics and irreversible damage, poses an existential threat to human society. This paper develops a novel two-level Stackelberg game with mean field interaction of controls and common noise which integrates hierarchical decision-making under a state-reflected emission dynamics. A central regulator (leader) adjusts product prices to guide $n$ heterogeneous competing regions (followers) while enforcing a hard emission cap via a reflection mechanism that models emergency reductions through a local time process. We establish the existence of an approximate Stackelberg equilibrium and perform sensitivity analysis via Monte Carlo simulations.

math.OC↗

arXiv2026

GraphIR: Architecture-Level Search States for LLM-Guided Neural Architecture Evolution

Large language models (LLMs) enable neural architecture search (NAS) directly over executable neural network programs. However, code-level flexibility does not provide the architecture state needed for effective mutation: LLMs must infer tensor dependencies, editable components, and compatibility constraints from implementation details. To address this representation mismatch, we propose GraphIR, an architecture-aware intermediate representation that supplements executable programs with a mutation-aligned candidate state. GraphIR organizes each candidate through three complementary views: a computation skeleton describing tensor flow, a mutation surface exposing editable modules and operations, and a validity envelope capturing interface contracts, propagated shapes, and downstream dependencies. To evaluate our method, we construct NAS-Dependency, a 120-question benchmark covering six complementary dependency-reasoning dimensions. The diagnostic shows that GraphIR is particularly effective at identifying exact producer occurrences, tracing dependency propagation, and diagnosing interface and failure risks. Across six downstream benchmarks including CLRS, GraphIR achieves the best overall search performance while maintaining comparable model size and favorable end-to-end NAS efficiency when integrated into OpenEvolve. These results show that a mutation-oriented architecture state provides an effective interface between executable neural programs and LLM-guided architecture evolution.

cs.LG↗

arXiv2026

The maximum number of paths of even length in a planar graph

For graphs $G$ and $H$, let $N(G,H)$ be the number of unlabeled, not necessarily induced copies of $H$ in $G$, and let $f(n,H)$ be the maximum of $N(G,H)$ over all $n$-vertex planar graphs $G$. Ghosh, Győri, Martin, Paulos, Salia, Xiao and Zamora conjectured that, for every fixed integer $\ell\ge 2$, \[ f(n,P_{2\ell+1}) =4\ell\left(\frac{n}{\ell}\right)^{\ell+1}+O(n^\ell). \] We prove the conjecture, including the stated error term. Along the way, we also settle the Cox--Martin optimization conjecture.

math.CO↗

arXiv2026

Overcoming the Weakest-Link Effect in LLM-Driven Program Optimization via Heterogeneous Edit Recombination

Large language models (LLMs) are increasingly used to solve complex problems by searching over program space, offering a general paradigm for scientific problems that can be naturally represented and solved as programs. Despite recent progress, identifying effective optimization directions for a candidate program remains challenging. By analogy with automatic differentiation, existing methods typically guide the search using a textual ``gradient'': a first-order update direction expressed as textual edits. Such gradients are inferred either from previously evaluated programs or from LLM-generated feedback on the implicit program-score mapping. However, these estimates become increasingly unreliable as the program--score mapping grows more complex, limiting their practical utility. We argue that explicit gradients are not essential for effective program optimization. Leveraging their prior knowledge, LLMs can propose plausible atomic edits directly from the current program, thereby enabling a zeroth-order optimization strategy. However, zeroth-order search suffers from a \textit{weakest-link effect}: when a bundle of edits is accepted or rejected as a whole, a single harmful edit can negate the benefits of all remaining edits. To address this issue, we introduce HERO, a program optimizer that prompts an LLM to generate diverse, non-overlapping atomic edits and then systematically selects and composes them into coherent program improvements using evaluator scores. We evaluate HERO across algorithmic problems, strategy games, the design of LLM-based agentic systems, and robotic path planning. Across these domains, HERO consistently discovers higher-scoring programs and converges substantially faster than prior LLM-based optimizers, while consuming fewer tokens.

cs.LG↗

arXiv2026

Extreme Volatility Warning under Label Scarcity via Multi-Source Anomaly Fusion

Early warning of extreme market volatility is central to financial risk management, but actionable events are rare, nonstationary, and often triggered by exogenous information shocks. In our CSI~300 setting, only $\sim$80 positive samples are observed across 791 training days, making heavily supervised multi-source models unstable. We first analyze a 100K-parameter hierarchical text-signal fusion model (HTSF) and find that added parameterization hurts in this low-label regime. Motivated by this failure, we propose \textbf{AAMSF} (Anomaly-Augmented Multi-Signal Fusion), a semisupervised framework that combines Isolation Forest anomaly scores over market indicators, GDELT events, Chinese financial news, and English media with lightweight Ridge score fusion. We further introduce \textbf{T-AAMSF}, a temporal extension for multi-day anomaly accumulation. On CSI~300 (2018--2023), AAMSF achieves test AUC-ROC \textbf{0.680}, outperforming the strongest unsupervised baseline (0.630) and neural baseline (0.588), while T-AAMSF improves PR-AUC to 0.291. Ablations reveal strong source asymmetry: GDELT and domestic financial news provide complementary risk signals, whereas English media consistently reduces performance, and learned weighting is unreliable under validation noise. These results suggest an empirical design principle for label-scarce financial risk warning: robust anomaly geometry and source reliability can matter more than supervised representation capacity.

cs.LG↗

arXiv2026

AutoNeural: Co-Designing Vision-Language Models for NPU Inference

While Neural Processing Units (NPUs) offer high theoretical efficiency for edge AI, state-of-the-art Vision--Language Models (VLMs) tailored for GPUs often falter on these substrates. We attribute this hardware-model mismatch to two primary factors: the quantization brittleness of Vision Transformers (ViTs) and the I/O-bound nature of autoregressive attention mechanisms, which fail to utilize the high arithmetic throughput of NPUs. To bridge this gap, we propose AutoNeural, an NPU-native VLM architecture co-designed for integer-only inference. We replace the standard ViT encoder with a MobileNetV5-style backbone utilizing depthwise separable convolutions, which ensures bounded activation distributions for stable INT4/8/16 quantization. Complementing this, our language backbone integrates State-Space Model (SSM) principles with Transformer layers, employing efficient gated convolutions to achieve linear-time complexity. This hybrid design eliminates the heavy memory I/O overhead of Key-Value caching during generation. Our approach delivers substantial efficiency gains, reducing quantization error of vision encoder by up to 7x and end-to-end latency by 14x compared to conventional baselines. The AutoNeural also delivers 3x decoding speed and 4x longer context window than the baseline. We validate these improvements via a real-world automotive case study on the Qualcomm SA8295P SoC, demonstrating real-time performance for cockpit applications. Our results highlight that rethinking model topology specifically for NPU constraints is a prerequisite for robust multi-modal edge intelligence.

cs.CL↗

arXiv2026

Toward Active Object Detection for UAVs in the Wild: A Large-Scale Dataset, Benchmark and Method

Object detection is a fundamental component in numerous Unmanned Aerial Vehicle (UAV) applications, yet it has long been plagued by hindrances like occlusion or target pixel scarcity. Active Object Detection (AOD) provides a novel paradigm to address these challenges via active vision, while UAV-based AOD research remains scarce due to the lack of high-quality datasets and benchmarks for algorithm development and evaluation. To fill this gap, this paper presents ATRNet-LUDO, the first large-scale real-world dataset for UAV-Ground Active Object Detection (UGAOD). It contains 121,000 multi-view panoramic multi-target aerial images and 1.21 million local single-target slices, covering 10 vehicle targets across 40 scenarios. It enables the construction of diverse training and testing environments for UAV agent interaction and active observation policy learning. Based on this dataset, we establish a comprehensive evaluation benchmark for AOD policy learning methods. Most existing AOD policies rely on Deep Reinforcement Learning (DRL) but suffer from poor generalization. Evaluations on our benchmark reveal a significant generalization gap between training and testing performance, highlighting an urgent need for solutions. To this end, we leverage the Joint Embedding Predictive Architecture (JEPA) to construct a world model that enhances state representation learning, and propose AOD-JEPA by incorporating AOD-specific prior knowledge. Extensive experiments validate its effectiveness and superiority. We hope ATRNet-LUDO and the benchmark will advance research in the UGAOD field. The dataset and code are soon available at https://github.com/Leo000ooo/LUDO_dataset.

cs.CV↗

arXiv2026

Physically Motivated Ansatz for Open Fermionic Systems on Quantum Computer

Determining non-equilibrium steady states (NESS) of open fermionic systems is a fundamental problem akin to finding ground states of closed systems. To address this, variational quantum algorithms can be used to solve the Lindblad master equation, much like the Schrödinger equation, yet ansatz design for NESS remains challenging. Existing approaches rely mostly on hardware-efficient ansätze (HEA), which suffer from the barren plateau problem. Here, we introduce a physically motivated ansatz named NE-UCC. Numerical simulations demonstrate that NE-UCC reliably converges to the steady state even in strongly correlated regimes far from equilibrium, reducing the infidelity by up to ten orders of magnitude compared to HEA. Furthermore, NE-UCC facilitates the exploration of excited eigenmodes with specific symmetries.

quant-ph↗

arXiv2026

Paths of even length with equal-degree endpoints

Addressing a question posed by Erdős and Hajnal, Chen and Ma proved that, for all $n \ge 600$, the complete bipartite graph $K_{n,n+1}$ is the unique graph on $2n+1$ vertices with at least $n^2+n$ edges that contains no two vertices of equal degree joined by a path of length three. In this paper, we extend this result and prove that for every fixed integer $\ell\ge 2$ and sufficiently large $n$, the unique $2n$-vertex graph with at least $(n^2+n)/2$ edges that contains no two vertices of equal degree joined by a path of length $2\ell$ is the half graph $H_n$. This resolves the problem posed by Chen and Ma, as well as a related question of Attwa, Azócar Carvajal, Boyadzhiyska, Pierron, and Taraz concerning paths of even length with equal-degree endpoints.

math.CO↗

arXiv2026

ELVA: Exploring Ranking-Driven Universal Multimodal Retrieval

Leveraging Multimodal Large Language Models (MLLMs) via contrastive learning has become a mainstream paradigm for improving the performance of Universal Multimodal Retrieval (UMR). However, previous works have ignored the grain blindness when adapting the contrastive paradigm into retrieval tasks. Grain blindness refers to the tendency of the model to overlook grain-level information contained in the query, which is crucial for effectively handling complex queries. This stems from contrastive learning treating samples as a binary classification (positive/negative), while ignoring the different information carried by each negative sample. To address this, we argue that negatives should be treated differently according to their similarity to the positive sample, enabling the model to learn distinct grain information from each negative. In this paper, we introduce a simple but effective framework, called ELVA, a novel rule-based RL framework that mitigates grain blindness through ranking-driven MLLMs. 1) Instead of relying on reward models, we extend Reinforcement Learning with Verifiable Rewards (RLVR) to retrieval tasks, allowing the model to explore new ranking behaviors without explicit ranking labels. 2) By utilizing rule-based rewards, our approach jointly optimizes the ranking of negative samples while enlarging the similarity gap between positive and negative. To more precisely measure grain blindness, we further introduce MRBench, a new benchmark specifically designed for multi-grain query scenarios. ELVA achieves state-of-the-art results across standard retrieval benchmarks, and its notable 13.1% improvement on MRBench further demonstrates its effectiveness in alleviating grain blindness.

cs.IR↗

arXiv2026

Structured Progressive Knowledge Activation for LLM-Driven Neural Architecture Search

This paper focuses on a key challenge in Neural Architecture Search (NAS): integrating established architectural knowledge while exploring new designs under expensive evaluations. Large language models (LLMs) are a promising assistant for NAS because they can translate rich architectural and coding priors into executable code edits. However, in practice, seemingly local revisions often propagate into non-local behavioral and performance shifts because a single edit can inadvertently couple multiple interacting functional factors, a phenomenon we refer to as functional entanglement. To make LLM knowledge usable under such entanglement, we propose Structured Progressive Knowledge Activation (SPARK), which activates relevant priors by explicitly selecting the functional factor to modify and conditioning the edit on that factor. This factor-conditioned editing reduces entangled side effects and yields more targeted, reliable architecture modifications. On CLRS-DFS, SPARK achieves a 28.1x sample-efficient architecture evolution speedup and yields a 22.9\% relative improvement in OOD accuracy. Our code is available at https://github.com/AIM-ResearchLab/SPARK.

cs.LG↗

arXiv2026

Modeling Earth-Scale Human-Like Societies with One Billion Agents

Understanding the dynamic evolution of complex social phenomena requires both high-fidelity modeling of human behavior and large-scale simulations. Traditional agent-based models (ABMs) have been employed to study these dynamics, but are constrained by simplified agent behaviors. Recent advances in large language models (LLMs) enable agents to exhibit sophisticated social behaviors, yet face significant scaling challenges. We present Light Society, an agent-based simulation framework that advances both fronts. Light Society formalizes social processes as structured transitions of agent and environment states, governed by a set of LLM-powered simulation operations. Joint algorithmic and system optimizations, particularly a mixture-of-models engine that combines full LLMs with distilled surrogates, enable Light Society to efficiently simulate societies with over one billion agents. Grounded in real-world demographic profiles from the World Values Survey, simulations of Trust Games and opinion diffusion at up to one billion agents demonstrate Light Society's high fidelity and efficiency in modeling diverse social phenomena, providing researchers with a practical foundation for hypothesis testing and the study of emergent collective behaviors at planetary scale.

cs.MA↗

arXiv2026

A Multimodal Domain-Adversarial Network for Fragmentation Background Suppression in AMS Heavy Nuclei Measurements

The Alpha Magnetic Spectrometer (AMS) aboard the International Space Station provides high-precision measurements of cosmic-ray nuclei fluxes from charge Z=1 to Z=28 and beyond. With negligible charge confusion from non-interacting nuclei, the precision of nuclei flux measurements is primarily limited by fragmentation backgrounds originating from heavier cosmic rays interacting within detector materials, particularly between tracker Layers 1 and 2 (L1-L2). As AMS extends its measurements to heavier and rarer nuclei, these fragmentation backgrounds become increasingly dominant, necessitating advanced background suppression methods. To address this challenge, we introduce a Multimodal Domain-Adversarial (MDA) neural network designed to effectively suppress these interaction backgrounds. The MDA model fuses heterogeneous data from the silicon tracker and time-of-flight detectors using specialized sub-networks combined via multi-head attention. Crucially, a domain-adversarial training strategy is employed to learn invariant representations, enabling the model, which is trained on Monte Carlo simulations, to be reliably applied to flight data. Using phosphorus (P) as a benchmark, we demonstrate its background suppression capabilities. This approach provides a robust, generalizable framework applicable to the measurement of other rare cosmic-ray nuclei with AMS.

hep-ex↗

arXiv2026

DIPBox: A Multi-scale Testing Framework for Tracking Dataset Regeneration

Training datasets have tremendous proprietary value and are vulnerable to unauthorized copying. Existing defenses mainly focus on tracking individual data points, but pay little attention to the threat of dataset regeneration. Through a measurement study of public tumor datasets, we identify substantial real-world partial-dataset replication, raising concerns about potential license noncompliance. To counter the challenge of tracking previously unknown adversarial regeneration, our key insight is that regeneration that preserves model utility inevitably preserves measurable signals across multiple feature scales. We categorize these dataset features into sample-, set-, and distribution-level features and design four similarity metrics to accurately identify regeneration. Based on these metrics, we develop DIPBox, which to our knowledge is the first testing framework that tracks regeneration suspects via multi-scale similarity testing across a spectrum of defender access settings, from limited to full information. We further provide a learning-theoretic analysis that justifies these multi-scale metrics and formalizes an inherent utility--divergence trade-off, implying fundamental limits on evasive regeneration. Extensive experiments on 16 vision and text base datasets, 320 regenerated datasets, and 590 derived models validate that DIPBox outperforms previous solutions while characterizing its robustness and limits under three adaptive attacks.

cs.CR↗

arXiv2026

New Gauge Forces, Neutron Stars and Schwinger Neutrino Production

We investigate neutrino effects of new long-range forces arising from gauging $B-L$, $L_e-L_{μ/τ}$ or $L_μ-L_τ$ symmetries of the Standard Model. The leptonic potential generated by astronomical bodies, such as the Earth, the Sun or a neutron star, results in the Schwinger pair production of neutrinos charged under the new gauge symmetry. The oppositely charged particles accumulate in the potential well forming a degenerate Fermi gas, while equally charged particles fly away forming a steady flux of neutrinos. We find that, for the $B-L$ and $L_e-L_{μ/τ}$ forces, these effects are too weak to be observable. For the $L_μ-L_τ$ force these effects are significant in neutron stars if the gauge coupling is $g\gtrsim 10^{-18}$. The muonic force changes the element abundances of a neutron star in equilibrium and suppresses its $L_μ-L_τ$ charge. This invalidates the constraint on $g$ from neutron star mergers, at $g\gtrsim 10^{-17}$. Furthermore, for such values of $g$, the neutrino flux produced by the Schwinger effect could potentially be detected from a single young neutron star at a distance of $\simeq 100$ pc, with the typical neutrino energy $E_ν\sim 100$ MeV. A dedicated search for such a signal will reassert the bound $g\lesssim 10^{-18}$.

hep-ph↗