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Zeyu Zheng

Publications and source records attributed to Zeyu Zheng.

At least 19 recordsLinked to original sources
arXiv2026

On Counting Independent Sets in Regular Hypergraphs

Balogh, Bollobás and Narayanan conjectured that among all finite simple $r$-uniform $d$-regular hypergraphs, the number of weak independent sets is maximized by a natural quasi-bipartite construction $H_{r,d}$. We give three types of evidence for this conjecture. For every fixed $r$, we prove the conjectured asymptotic exponential rate whenever the twin quotient has maximum pair codegree $o(d)$. The proof uses the hypergraph container method. For hypergraphs with no cross-edges, the occupancy method gives the sharper error bound $O_r(\log d/d)$. We show that a stronger version of the conjecture in terms of the so-called occupancy fraction is not true, by providing a counterexample for every $r\ge 3$. We also prove exact cases of the conjecture when the hypergraph is $2$-regular. Using an entropy decomposition in the dual edge-cover problem, we settle every odd $r$ and the case $(r,d)=(4,2)$.

math.CO↗
arXiv2026

AdaExplore: Failure-Driven Adaptation and Diversity-Preserving Search for Efficient Kernel Generation

Recent large language model (LLM) agents have shown promise in using execution feedback for test-time adaptation. However, robust self-improvement remains far from solved: most approaches still treat each problem instance independently, without accumulating reusable knowledge. This limitation is particularly pronounced in domain-specific languages such as Triton, which are underrepresented in LLM pretraining data. Their strict constraints and non-linear optimization landscape further make naive generation and local refinement unreliable. We propose AdaExplore, an agent framework that enables self-improvement via accumulated execution feedback for performance-critical kernel code generation through two complementary stages: failure-driven adaptation and diversity-preserving search, jointly improving correctness and optimization performance without additional fine-tuning or external knowledge. In the adaptation stage, the agent synthesizes tasks and converts recurring failures into a reusable memory of validity rules, helping subsequent generations remain within the feasible set. In the search stage, the agent organizes candidate kernels as a tree and alternates between small local refinements and larger structural regeneration, allowing it to explore the optimization landscape beyond local optima. Experiments on kernel runtime optimization benchmarks validate these gains: AdaExplore achieves 3.11x and 1.62x speedups on KernelBench Level-2 and Level-3, respectively, within 100 steps, and continues to improve with additional computation.

cs.CL↗
arXiv2026

Spec2Twin-Chain: Orchestrating Bi-Level Optimization with LLMs for Blockchain Digital Twin Construction

Building a blockchain digital twin largely requires translating domain knowledge and specific system descriptions into a simulator architecture, calibrating its parameters against behavioral evidence, and validating the constructed twin. These steps are commonly performed through application-specific modeling efforts that can be difficult to reuse across systems and downstream decision problems. We consider automating this process through Spec2Twin-Chain, a framework that formulates blockchain digital-twin construction as a bi-level optimization problem. At the upper level, a large language model proposes and revises structurally admissible architectures using system specifications, behavioral evidence, and feedback from evaluated designs. At the lower level, a simulation-based optimizer calibrates the architecture-conditioned parameters under explicit objectives and guardrail constraints. The two levels iterate. The evaluated candidates at lower levels are retained in a global archive and used to guide subsequent proposals at upper levels. We conduct controlled experiments involving twin calibration, feedback-driven recovery, stress analysis, downstream policy optimization, and policy updating. The results demonstrate that the framework can construct behaviorally accurate twins, improve initial designs through iterative feedback, and reuse calibrated twins to support downstream decisions.

cs.AI↗
arXiv2026

Escaping Local Minima Provably in Non-convex Matrix Sensing: A Deterministic Framework via Simulated Lifting

Low-rank matrix sensing is a fundamental yet challenging nonconvex problem whose optimization landscape typically contains numerous spurious local minima, making it difficult for gradient-based optimizers to converge to the global optimum. Recent work has shown that over-parameterization via tensor lifting can convert such local minima into strict saddle points, an insight that also partially explains why massive scaling can improve generalization and performance in modern machine learning. Motivated by this observation, we propose a Simulated Oracle Direction (SOD) escape mechanism that simulates the landscape and escape direction of the over-parametrized space, without resorting to actually lifting the problem, since that would be computationally intractable. In essence, we designed a mathematical framework to project over-parametrized escape directions onto the original parameter space to guarantee a strict decrease of objective value from existing local minima. To the best of our knowledge, this represents the first deterministic framework that could escape spurious local minima with guarantee, especially without using random perturbations or heuristic estimates. Numerical experiments demonstrate that our framework reliably escapes local minima and facilitates convergence to global optima, while incurring minimal computational cost when compared to explicit tensor over-parameterization. We believe this framework has non-trivial implications for nonconvex optimization beyond matrix sensing, by showcasing how simulated over-parameterization can be leveraged to tame challenging optimization landscapes.

cs.LG↗
arXiv2026

The Problem Is the Problem: Towards Scalable Mathematical Discovery

AI systems are increasingly capable of contributing to mathematical research. In research practice, frontier-model reasoning is a limited resource, and expert mathematical review is even more sharply constrained. Allocating these scarce resources well is therefore central to making AI-assisted mathematical discovery efficient. In most current AI-for-math workflows, human effort is concentrated at the beginning and end, in selecting suitable research problems and later reviewing the resulting artifacts. These two stages are becoming bottlenecks for research-level mathematics. We address them by proposing a new human-AI discovery paradigm. The human input is no longer a single problem selected in advance, but a research direction in which the experts have interest and expertise. The system then searches a broad literature corpus for candidate problems in that direction. Inspired by search and recommender systems, we build Find, Attempt, and Recommend (FAR), a literature-to-review cascade that automates the search for suitable problems and focuses human attention on artifacts that have passed several stages of filtering. In a combinatorics pilot, the pipeline starts from 5,245 combinatorics papers, recovers 6,453 candidate conjectures or open problems, and filters them to 4,717 apparently well-posed and still-open conjectures. Subsequent reasoning and automated triage stages surface 598 potential resolutions and select 77 items for author-team review. Among them, we identify many interesting discoveries, including results on conjectures and questions of Davies--Jenssen--Perkins--Roberts, Erdős--Straus, Ikenmeyer--Pak--Panova, and Lund--Saraf--Wolf. These results demonstrate the effectiveness of this new mode of human-AI collaboration for mathematical discovery.

cs.AI↗
arXiv2026

The Oddtown problem modulo a composite number

A family of subsets $\mathcal{A}$ of an $n$-element set is called an $\ell$-Oddtown if the sizes of all sets are not divisible by $\ell$, but the sizes of pairwise intersections are divisible by $\ell$. Berlekamp and Graver showed that when $\ell$ is a prime, the maximum size of an $\ell$-Oddtown is $n$. Babai and Frankl extended this to prime powers, and asked whether the maximum size is still $n$ when $\ell$ is not a prime power, a question that was open even for $\ell=6$. For square-free composite moduli with $ω$ distinct prime factors, the argument of Szegedy gives an upper bound of $ωn-ω\log_2 n$ on the size of an $\ell$-Oddtown. We answer the question of Babai and Frankl in the negative by constructing $\ell$-Oddtowns of size $ωn-o(n)$, which shows that the leading term $ωn$ cannot be improved. We also improve Szegedy's upper bound to $ωn-(2ω+\varepsilon)\log_2 n$ for most $\ell$ and $n$ using a combination of linear algebraic and Fourier-analytic arguments.

math.CO↗
arXiv2026

Variance-Aware Baselines and Adaptive Learning Rates for Reinforcement Learning with Verifiable Rewards

Reinforcement learning with verifiable rewards (RLVR) has emerged as an effective paradigm for post-training large language models, yet the design of its baselines and learning-rate schedules remains largely heuristic. This limits our understanding of the statistical properties of policy-gradient estimators and their interaction with optimization dynamics. In this work, we develop a theoretical framework for variance-aware baseline design and adaptive learning-rate selection in RLVR. Under a KL-regularized policy-optimization setting, we establish the unbiasedness of the resulting gradient estimator, derive exact variance expressions including the KL cross-covariance, and obtain an optimization-loss upper bound that enables principled reasoning about learning dynamics. Building on these results, we prove convergence guarantees and derive an adaptive learning-rate schedule governed by the signal-to-noise ratio (SNR) of the policy gradient. We further show that the variance-optimal baseline is a gradient-weighted estimator of the KL-regularized reward, providing a principled alternative to commonly used reward-based baselines. These results lead to two complementary improvements: a variance-optimal baseline and an SNR-adaptive learning-rate rule. Experiments on Qwen3-4B-Base show that each component independently improves policy-optimization performance. The learning-rate rule can also be naturally integrated with existing policy optimization methods to yield further gains, while combining it with the variance-optimal baseline gives the full Optimal Baseline and Learning-Rate Policy Optimization (OBLR-PO) method and achieves the strongest overall performance.

stat.ML↗
arXiv2026

Preventing Learning Stagnation in PPO by Scaling to 1 Million Parallel Environments

An agent's performance stagnating at a suboptimal level is a common problem in deep on-policy RL. Focusing on PPO, we show that plateaus in certain regimes arise not because of known exploration, capacity, or optimisation challenges, but because sample-based estimates of the loss eventually become poor proxies for the true objective over the course of training. Looking deeper, PPO alternates between sampling rollouts from several parallel environments online using the current policy (which we call the "outer loop") and performing repeated minibatch SGD steps against this offline dataset (the "inner loop"). In our work, we abstract away the inner loop, and conceptually model the outer loop as standard stochastic optimisation. The step size is then controlled by the regularisation strength towards the previous policy and the gradient noise by the number of samples collected between policy update steps. This framing predicts that, much like in SGD, if the outer step size is too large relative to the noise, updates become uninformative and lead to the policy thrashing around a local optimum instead of converging. Recasting PPO in this light makes it clear that there are two ways to address this particular type of learning stagnation: either reduce the step size or increase the number of samples collected between updates. We validate the predictions of our model and conclude that increasing the number of parallel environments is a simple way to avoid these plateaus by simultaneously altering both these factors. Applying our analysis and scaling PPO to more than 1M parallel environments enables monotonic performance improvement up to one trillion transitions and leads to vastly superior performance compared to prior baselines in a complex open-ended domain.

cs.LG↗
arXiv2026

Experimental Designs for Multi-Item Multi-Period Inventory Control

Randomized experiments, or A/B testing, are the gold standard for evaluating interventions, yet they remain underutilized in inventory management. This study addresses this gap by analyzing A/B testing strategies in multi-item, multi-period inventory systems with lost sales and capacity constraints. We examine two canonical experimental designs--switchback experiments and item-level randomization--and show that both suffer from systematic bias due to interference: temporal carryover in switchbacks and cannibalization across items under capacity constraints. Under mild conditions, we characterize the direction of this bias in different scenarios. Motivated by two-sided randomization, we propose a pairwise design over items and time and analyze its bias properties. Controlled stochastic simulations verify the theoretical predictions, and trace-driven experiments on real-world fresh-retail data show that the same mechanisms persist in realistic environments with stockout substitution.

stat.ME↗
arXiv2026

3D-DefectBench: A Controlled Factorial Study of Vision-Language Model Evaluation Pipelines for Fine-Grained 3D Generation Defects

Automated evaluation is essential for scaling generative 3D systems, where exhaustive human review is costly and slow. However, the reliability of an automated judge depends on the entire evaluation pipeline, not only the underlying vision-language model (VLM), but also how assets are rendered, what visual evidence is provided, how the task is specified, and how human reference labels are constructed. We introduce 3D-DefectBench, a benchmark and framework for systematic analysis of VLM-based 3D defect detection pipelines. It complements holistic ratings and pairwise preferences with nine fine-grained binary defects spanning geometry, texture, and prompt adherence, providing actionable diagnostics for generator development and judge evaluation. Using a balanced factorial design, we vary four pipeline factors, VLM, camera protocol, visual input, and prompt schema, across 84 inference designs and approximately 3.2 million scored defect decisions, followed by staged validation on a broader set of frontier models. Model choice is the largest determinant of agreement with human labels, but the remaining factors also affect performance, interact with model selection, and can change the best configuration. Within the evaluated design space, a compact six-view RGB protocol performs comparably to denser multi-view settings and inputs augmented with depth or surface normals, making it a strong cost-effective default. Under this standardized pipeline, the best of 12 VLM judges still lag behind trained human labelers, while texture agreement drops sharply when expert-consensus labels are replaced by noisier silver labels. These findings show that automated judges should be evaluated as complete pipelines and calibrated across human reference regimes, rather than benchmarked only as standalone models. We release labels, prompts, predictions, and Croissant metadata on Hugging Face.

cs.CV↗
arXiv2026

ClawArena-Team: Benchmarking Subagent Orchestration and Dynamic Workflows in Language-Model Agents

Production large language-model (LLM) agents are increasingly deployed not as lone problem-solvers but as managers: a main model creates specialized subagents, delegates work, and orchestrates their parallel, asynchronous returns through dynamic workflows. Whether one model can actually run such a team is largely unmeasured: existing benchmarks score a policy's own task-solving or a fixed multi-agent system's emergent behavior, but none isolate the management ability of the single LLM acting as leader. We introduce ClawArena-Team, a benchmark of 41 multi-turn, multimodal, multi-directory scenarios spanning 258 evaluation rounds and 72 staged updates that measures this management ability. The main agent is deliberately constrained: it natively perceives only text and directly accesses only part of the workspace. It commands a fixed, locally served subagent pool, so score differences reflect management skill, not raw capability. All scoring is execution-based with no LLM judge: an overall score -- the Subagent-Management Score (SMS) -- multiplies task correctness by a least-privilege and modality-routing factor. Across twelve proprietary, community-hosted, and self-hosted models, experiments show that the management bottleneck is privilege granting rather than perception (no model exceeds 50% workspace-permission precision); that cost and management quality are decoupled (API cost spans over 100 times while the overall score spans under 4 times, with the cheapest open models on the Pareto frontier); and that most leaderboard scores cluster within a 9.9-point band while orchestration behaviors diverge by more than an order of magnitude. Code is available at https://github.com/aiming-lab/ClawArena.

cs.AI↗
arXiv2026

HERO: Improving the Reliability and Sensitivity of Generative Model Evaluation Using Historical Data

Reliable generative AI models critically rely on expert human annotations to evaluate output quality, yet these "gold" labels are expensive to collect and limited in quantity. Organizations thus often turn to collecting vast but noisy "silver" labels from crowdsourced workers or vendor annotators as proxies for gold labels. Because gold remains the evaluation target, naively aggregating noisy silver labels may introduce bias, and estimators built on sparsely observed gold labels may have high variance to resolve the model performance gaps that guide practical decisions. Model evaluation has become an ongoing operational practice rather than a one-time exercise, with evaluation rounds repeating across model versions, releases, and content domains. A natural question is whether the previous historical evaluation data can be used to improve each new round of evaluation. We introduce HERO (History Enhanced RObust model evaluation), a novel framework that uses historical data to suppress bias (improve reliability) and reduce variance (improve sensitivity) in model performance evaluation. HERO calibrates silver labelers' performance learned from historical gold annotations, and stabilizes the resulting estimator by anchoring it to covariate information measured with high precision in the historical data. HERO can be broadly applied across multiple common evaluation tasks, and remains valid when only a subset of historical labelers appears in the current round. We establish conditions under which the bias and variance reductions hold, showcase HERO's performance in simulation studies, and demonstrate its effectiveness on real-world model evaluation benchmarking datasets.

stat.ME↗
arXiv2026

VisualClaw: A Real-Time, Personalized Agent for the Physical World

Vision language models are serving as general-purpose interfaces for complex multimodal tasks. However, deployment still faces three gaps: VLMs typically incur high latency and cost when processing dense video frames and long prompts, the agent scaffold remains static after deployment, and standard video-QA benchmarks do not test whether agents can use visual evidence inside tool-using workspaces. We present VisualClaw, a self-evolving multimodal agent built around two principles. First, hybrid encoding reduces deployment cost by filtering less informative streaming frames with a cascaded gate and compressing the text skill bank through hot/cold top-k injection. Second, skill evolution lets the agent learn from failures: retrieved memories condition an evolver as direct concatenated context or as guided evidence, producing skill-bank updates that help future questions. Across 4 video-QA benchmarks with 2 VLMs, VisualClaw cuts per-question API cost by an average -98% versus full-frame upload and by -25.9% over the offline uniform 8 frame baseline, while boosting accuracy in most settings, e.g., an average +3.85% and a peak +15.80% on EgoSchema with Gemini 3 Flash. To address the gap, we curate VisualClawArena, a 200-scenario multimodal agentic benchmark built through a strict five-stage pipeline; models must use video evidence, documents, dynamic updates, and executable checks inside a workspace. On VisualClawArena, the same framework with computer-use agent backends improves macro accuracy by +2.9% for Codex (GPT-5.5) and +3.2% for Claude Code (Sonnet 4.6) over no-evolution baselines, with a -9.5% cost reduction compared to the uniform-sampled baseline. These properties make VisualClaw a natural fit for edge applications, where the cascade reduces a 1-hour streaming session from ~3,600 API uploads down to only 5-20 calls and the self-evolution makes it a perfect personalized assistant.

cs.CV↗
arXiv2026

Experimentation for Different Scheduling Policies on Queues: Mixed Differences-in-Q Estimators Based on Little's Law

In data centers, tasks are dispatched to various servers to evenly distribute the workload. When a data center considers implementing a new scheduling algorithm, it typically conducts an A/B test prior to deployment to assess the real-world impact of this new method. However, a straightforward A/B test might be interfered with so-called ``Markovian'' interference. We utilized the Differences-in-Q estimator, as developed by Farias et al. (2022), and introduced mixed Differences-in-Q estimators grounded in Little's Law. We show that our A/B testing methods significantly reduce bias and variance when testing various scheduling policies. Extensive simulations were conducted under scenarios like non-stationary arrival rates, heterogeneous service rates, and communication delays. These simulations highlight the robustness and efficacy of our A/B testing approach.

stat.ME↗
arXiv2026

DB-3DME: From Dataset to Benchmark for Human-aligned Automatic 3D Mesh Evaluation

Recent advances in 3D generation have led to substantial improvements in realism, controllability, and efficiency, yet the evaluation of 3D assets remains underexplored. Existing evaluation paradigms, including human evaluation, learned metrics, and vision-language models (VLMs) as judges, suffer from limitations in cost, scalability, resolution handling, or task-specific alignment. In this work, we focus on 3D mesh evaluation and introduce DB-3DME, the Dataset and Benchmark for 3D Mesh Evaluation. DB-3DME contains 2,619 synthetic 3D meshes paired with human ratings on Geometry and Prompt Adherence. Using this dataset, we systematically benchmark state-of-the-art VLMs and identify visual encoding of 3D representations as a key factor for human-aligned evaluation performance. Motivated by this finding, we fine-tune an open-weight VLM, Qwen-2.5-VL-7B, for 3D mesh evaluation by adapting the visual encoder while freezing the language model. The fine-tuned model substantially outperforms existing pre-trained VLMs across multiple evaluation dimensions, establishing a new benchmark for automatic 3D mesh evaluation. We publicly release the benchmark dataset on GitHub and Hugging Face to facilitate future research.

cs.CV↗
arXiv2026

LLM-Augmented Digital Twin for Policy Evaluation in Short-Video Platforms

Short-video platforms are closed-loop, human-in-the-loop ecosystems where platform policy, creator incentives, and user behavior co-evolve. This feedback structure makes counterfactual policy evaluation difficult in production, especially for long-horizon and distributional outcomes. The challenge is amplified as platforms deploy AI tools that change what content enters the system, how agents adapt, and how the platform operates. We propose a large language model (LLM)-augmented digital twin for short-video platforms, with a modular four-twin architecture (User, Content, Interaction, Platform) and an event-driven execution layer that supports reproducible experimentation. Platform policies are implemented as pluggable components within the Platform Twin, and LLMs are integrated as optional, schema-constrained decision services (e.g., persona generation, content captioning, campaign planning, trend prediction) that are routed through a unified optimizer. This design enables scalable simulations that preserve closed-loop dynamics while allowing selective LLM adoption, enabling the study of platform policies, including AI-enabled policies, under realistic feedback and constraints.

cs.AI↗
arXiv2026

Hypothesis-Disciplined Multi-Agent Automated Formalization of Asymptotic Statistical Theory

Asymptotic statistical theory is a challenging domain for AI-assisted formalization: its central results mix convergence statements, asymptotic expansions, functional analysis, and regularity conditions that have a large gap from existing infrastructure in Lean 4 formalization. To address these challenges, we propose a hypothesis-disciplined Lean 4 formalization pipeline built from multiple agents: a manager that coordinates seven specialist roles for proof planning, skeleton scaffolding, Mathlib reconnaissance, proof construction, integration, independent review, and audit. The main methodological discipline is the hypothesis-disciplined audit, implemented by the Auditor agent: every main-theorem hypothesis and concept-layer field must be anchored in the source mathematical prose, justified as a Lean encoding adapter, marked as source-implied, or rejected as an unsupported strengthening. Using this workflow, we build a systematic formalization of asymptotic statistical theory, especially the parametric and semi-parametric models' asymptotic distribution and efficiency results. The resulting Lean development is axiom-clean and source-faithful, with Lean-checked and human-audited proofs of core parametric and semi-parametric theorems organized so that theorem-agnostic infrastructure and statistical concept definitions are separated from theorem-specific assembly. The formalization results are available at https://github.com/junwei-lu/Lean-Asymptotic-Statistical-Theory.

cs.AI↗
arXiv2026

AutoResearchClaw: Self-Reinforcing Autonomous Research with Human-AI Collaboration

Automating scientific discovery requires more than generating papers from ideas. Real research is iterative: hypotheses are challenged from multiple perspectives, experiments fail and inform the next attempt, and lessons accumulate across cycles. Existing autonomous research systems often model this process as a linear pipeline: they rely on single-agent reasoning, stop when execution fails, and do not carry experience across runs. We present AutoResearchClaw, a multi-agent autonomous research pipeline built on five mechanisms: structured multi-agent debate for hypothesis generation and result analysis, a self-healing executor with a \textsc{Pivot}/\textsc{Refine} decision loop that transforms failures into information, verifiable result reporting that prevents fabricated numbers and hallucinated citations, human-in-the-loop collaboration with seven intervention modes spanning full autonomy to step-by-step oversight, and cross-run evolution that converts past mistakes into future safeguards. On ARC-Bench, a 25-topic experiment-stage benchmark, AutoResearchClaw outperforms AI Scientist v2 by 54.7%. A human-in-the-loop ablation across seven intervention modes reveals that precise, targeted collaboration at high-leverage decision points consistently outperforms both full autonomy and exhaustive step-by-step oversight. We position AutoResearchClaw as a research amplifier that augments rather than replaces human scientific judgment. Code is available at https://github.com/aiming-lab/AutoResearchClaw.

cs.AI↗