arXiv subjects

Zhenhua Wang

Publications and source records attributed to Zhenhua Wang.

At least 19 recordsLinked to original sources

arXiv2026

ScaleSense: Cost-Intelligent Scaling Framework via Learned Resource Estimation in Alibaba AnalyticDB

Cloud-native serverless data warehouses achieve fine-grained elasticity by decoupling storage from compute, yet determining the optimal resource allocation for highly heterogeneous ad-hoc queries remains a formidable industrial challenge. Our analysis of production workloads in Alibaba AnalyticDB exposes a costly ``provisioning trap'': the fear of catastrophic resource depletion drives users to blindly over-provision resources, wasting immense monetary budgets without alleviating non-CPU bottlenecks (e.g., I/O saturation). To break this impasse, we propose ScaleSense, a proactive, query-level resource scaling framework. Specifically, it features a multi-faceted query encoder that jointly models plan topologies and hardware specifications. Crucially, a quantile-based resource predictor estimates multi-dimensional physical footprints, acting as a reliable safety net for optimal resource scaling. An auto-scaling controller then navigates the performance-cost Pareto frontier, dynamically tailoring allocations to specific business priorities without requiring model retraining. Evaluations on over 1.36 million production queries show that ScaleSense achieves state-of-the-art prediction accuracy with good prediction interval coverage. By achieving a 76.7% relative improvement in optimal resource configuration selection over the best baseline, this approach addresses the critical performance-cost trade-off while maintaining low-overhead inference latency, confirming its practical performance in production deployments. Under the performance-optimization policy, ScaleSense satisfies user-defined performance requirements while reducing monetary cost by up to 5.22x.

cs.DB↗

arXiv2026

Existence of Relaxed Equilibrium for Time-Inconsistent Mean Field Games: A Set-Valued Fixed Point Approach

This paper studies the existence of relaxed equilibria for finite-horizon continuous-time time-inconsistent mean field games. We work directly on the product space of relaxed feedback policies and population flows. The policy component is endowed with the stable topology of Young measures, while the population component is restricted to a compact convex set of Wasserstein-continuous flows with uniform moment and time-regularity bounds. For every policy-flow pair, we establish uniform Sobolev and Hölder estimates for the associated auxiliary value function and prove its stability under Young-measure convergence of policies and uniform Wasserstein convergence of population flows. We also establish continuity of the induced population-flow map. The latter requires a duality argument for the Fokker-Planck equations because Young-measure convergence yields only weak-$*$ convergence of the controlled drifts. We then construct a set-valued best-response/consistency map with nonempty compact convex values and apply the Kakutani-Fan-Glicksberg fixed-point theorem. The resulting fixed point satisfies both the equilibrium response condition of the intra-personal game and the mean field consistency condition, , thereby establishing the existence of a relaxed equilibrium

math.OC↗

arXiv2026

Time-Inconsistent MDPs with Entropy Regularization: Equilibrium Existence and Policy Iteration

We study infinite-horizon time-inconsistent Markov decision processes with a countably infinite state space and unbounded reward functions. The reward is allowed to depend explicitly on the initial time and initial state, thereby accommodating general sources of time inconsistency. We seek relaxed feedback equilibria, and our approach is based on entropy regularization and weighted functional analytic methods. With entropy regularization, we characterize a regular relaxed equilibrium through a fixed-point operator. By introducing two weight functions with distinct roles, one controlling the growth of rewards and values and the other defining the ambient weighted space, we construct a compact invariant set under a product topology and apply the Schauder-Tychonoff fixed-point theorem to establish existence of regularized equilibria. Importantly, the invariant set can be chosen uniformly for small entropy weight $λ\in(0,1]$. We then let $λ\to0+$ and show, through compactness, concentration of Gibbs policies, and uniform-integrability arguments, that a subsequential limit is a relaxed equilibrium of the original unregularized problem. We further study a policy iteration algorithm (PIA) for the entropy-regularized equilibrium problem. Under a weighted-discounting structure and sufficiently strong discounting, we establish exponential convergence and uniqueness of the regularized equilibrium in a suitable weighted Banach space. Combining the policy-iteration error with a quantitative soft-max approximation bound, we show that the iterated policies constitute weighted $\varepsilon$-equilibria for the original unregularized problem and derive an explicit regret estimate. A numerical example illustrating the convergence of PIA under strong discounting and a counterexample demonstrating its failure under weak discounting are also provided.

math.OC↗

arXiv2026

Equilibrium for Time-inconsistent Mean Field Games: A Systematic Analysis by Entropy Regularization

This paper studies the existence and approximation of equilibria for general time-inconsistent mean field game (MFG) problems in continuous time. To handle the intricate nonlocal equilibrium Hamilton-Jacobi-Bellman (EHJB) system arising from initial-time dependence, such as non-exponential discounting, we develop a vanishing entropy regularization approach. Using entropy regularization, we first characterize the regularized equilibrium through a coupled exploratory equilibrium HJB (EEHJB) equation and a law-dependent stochastic differential equation. By exploiting Schauder fixed-point arguments and tailored parabolic regularity estimates in a suitable functional space involving both value functions and measure flows, we establish the global existence of regularized equilibria under mild assumptions. We then establish convergence as the entropy regularization vanishes. By employing compactness arguments, Young measure techniques, and a duality tool for divergence-form Fokker-Planck equations, we prove that the regularized equilibria converge, up to subsequences, to a mean-field equilibrium of the original MFG. Furthermore, under entropy regularization, we propose a policy iteration algorithm and establish its convergence under short-time-horizon and weak-terminal-interaction conditions.

math.OC↗

arXiv2026

Interval Observer Design Using Observability Decomposition for Detectable Linear Systems

We provide a systematic interval observer design method for detectable linear time-invariant (LTI) systems, where a part of the state is observable from the measured output. An observability-based invertible LTI transformation decomposes the state into two parts. The first part is decoupled from the other and observable from the output, while the second is affected by the first, does not appear in the output, but is detectable. A Sylvester-based LTI interval observer is designed for the first part. For the second part, a Jordan-based linear time-varying interval observer is built, treating the interaction from the first part as inputs with known bounds. The intervals in the original coordinates are constructed either by inverting the decomposition online for the intervals in the transformed coordinates or by directly implementing the observer written in the original coordinates. Academic examples illustrate the interest of our approach.

eess.SY↗

arXiv2026

Equilibrium under Time-Inconsistency: A New Existence Theory by Vanishing Entropy Regularization

This paper develops a framework for establishing the existence of solutions to the equilibrium Hamilton-Jacobi-Bellman (EHJB) equation arising in time-inconsistent stochastic control problems. The time-inconsistency in our setting arises from the initial-time dependence such as the non-exponential discounting. The classical approach typically relates the existence of equilibrium to the classical solution of the EHJB, whose existence is still an open problem under general model assumptions. We resolve this challenge by building on a vanishing entropy regularization approach. Using fixed-point arguments, we first establish the existence of classical solutions to the exploratory equilibrium Hamilton-Jacobi-Bellman Equation (EEHJB) by deriving a series of delicate PDE estimates for the solution and its derivatives. Building on these estimates for the solution of the EEHJB and its derivatives, we then conduct a rigorous convergence analysis under suitable norms as the entropy regularization vanishes. Our main result shows that solutions of the EEHJB converge to a strong solution of the original EHJB, corresponding to the limit of the regularized equilibria. This convergence yields a verification argument ensuring that the limiting relaxed equilibrium indeed constitutes an equilibrium for the original time-inconsistent control problem. We thus establish the well-posedness of the EHJB and the existence of equilibria in diffusion models under time-inconsistency, without resorting to conventional stringent regularity assumptions of the EHJB.

math.OC↗

arXiv2026

SafeLoad: Efficient Admission Control Framework for Identifying Memory-Overloading Queries in Cloud Data Warehouses

Memory overload is a common form of resource exhaustion in cloud data warehouses. When database queries fail due to memory overload, it not only wastes critical resources such as CPU time but also disrupts the execution of core business processes, as memory-overloading (MO) queries are typically part of complex workflows. If such queries are identified in advance and scheduled to memory-rich serverless clusters, it can prevent resource wastage and query execution failure. Therefore, cloud data warehouses desire an admission control framework with high prediction precision, interpretability, efficiency, and adaptability to effectively identify MO queries. However, existing admission control frameworks primarily focus on scenarios like SLA satisfaction and resource isolation, with limited precision in identifying MO queries. Moreover, there is a lack of publicly available MO-labeled datasets with workloads for training and benchmarking. To tackle these challenges, we propose SafeLoad, the first query admission control framework specifically designed to identify MO queries. Alongside, we release SafeBench, an open-source, industrial-scale benchmark for this task, which includes 150 million real queries. SafeLoad first filters out memory-safe queries using the interpretable discriminative rule. It then applies a hybrid architecture that integrates both a global model and cluster-level models, supplemented by a misprediction correction module to identify MO queries. Additionally, a self-tuning quota management mechanism dynamically adjusts prediction quotas per cluster to improve precision. Experimental results show that SafeLoad achieves state-of-the-art prediction performance with low online and offline time overhead. Specifically, SafeLoad improves precision by up to 66% over the best baseline and reduces wasted CPU time by up to 8.09x compared to scenarios without SafeLoad.

cs.DB↗

arXiv2026

Echo State Networks for Spatio-Temporal Area-Level Data

Spatio-temporal area-level datasets play a critical role in official statistics, providing valuable insights for policy-making and regional planning. Accurate modeling and forecasting of these datasets can be extremely useful for policymakers to develop informed strategies for future planning. Echo State Networks (ESNs) are efficient methods for capturing nonlinear temporal dynamics and generating forecasts. However, ESNs lack a direct mechanism to account for the neighborhood structure inherent in area-level data. Ignoring these spatial relationships can significantly compromise the accuracy and utility of forecasts. In this paper, we incorporate approximate graph spectral filters at the input stage of the ESN, thereby improving forecast accuracy while preserving the model's computational efficiency during training. We demonstrate the effectiveness of our approach using Eurostat's tourism occupancy dataset and show how it can support more informed decision-making in policy and planning contexts.

cs.LG↗

arXiv2025

VADTree: Explainable Training-Free Video Anomaly Detection via Hierarchical Granularity-Aware Tree

Video anomaly detection (VAD) focuses on identifying anomalies in videos. Supervised methods demand substantial in-domain training data and fail to deliver clear explanations for anomalies. In contrast, training-free methods leverage the knowledge reserves and language interactivity of large pre-trained models to detect anomalies. However, the current fixed-length temporal window sampling approaches struggle to accurately capture anomalies with varying temporal spans. Therefore, we propose VADTree that utilizes a Hierarchical Granularityaware Tree (HGTree) structure for flexible sampling in VAD. VADTree leverages the knowledge embedded in a pre-trained Generic Event Boundary Detection (GEBD) model to characterize potential anomaly event boundaries. Specifically, VADTree decomposes the video into generic event nodes based on boundary confidence, and performs adaptive coarse-fine hierarchical structuring and redundancy removal to construct the HGTree. Then, the multi-dimensional priors are injected into the visual language models (VLMs) to enhance the node-wise anomaly perception, and anomaly reasoning for generic event nodes is achieved via large language models (LLMs). Finally, an inter-cluster node correlation method is used to integrate the multi-granularity anomaly scores. Extensive experiments on three challenging datasets demonstrate that VADTree achieves state-of-the-art performance in training-free settings while drastically reducing the number of sampled video segments. The code will be available at https://github.com/wenlongli10/VADTree.

cs.CV↗

arXiv2025

Error Estimates and Higher Order Trotter Product Formulas in Jordan-Banach Algebras

In quantum computing, Trotter estimates are critical for enabling efficient simulation of quantum systems and quantum dynamics, help implement complex quantum algorithms, and provide a systematic way to control approximate errors. In this paper, we extend the analysis of Trotter-Suzuki approximations, including third and higher orders, to Jordan-Banach algebras. We solve an open problem in our earlier paper on the existence of second-order Trotter formula error estimation in Jordan-Banach algebras. To illustrate our work, we apply our formula to simulate Trotter-factorized spins, and show improvements in the approximations. Our approach demonstrates the adaptability of Trotter product formulas and estimates to non-associative settings, which offers new insights into the applications of Jordan algebra theory to operator dynamics.

quant-ph↗

arXiv2025

Do Large Language Models Truly Grasp Mathematics? An Empirical Exploration From Cognitive Psychology

The cognitive mechanism by which Large Language Models (LLMs) solve mathematical problems remains a widely debated and unresolved issue. Currently, there is little interpretable experimental evidence that connects LLMs' problem-solving with human cognitive psychology.To determine if LLMs possess human-like mathematical reasoning, we modified the problems used in the human Cognitive Reflection Test (CRT). Our results show that, even with the use of Chains of Thought (CoT) prompts, mainstream LLMs, including the latest o1 model (noted for its reasoning capabilities), have a high error rate when solving these modified CRT problems. Specifically, the average accuracy rate dropped by up to 50% compared to the original questions.Further analysis of LLMs' incorrect answers suggests that they primarily rely on pattern matching from their training data, which aligns more with human intuition (System 1 thinking) rather than with human-like reasoning (System 2 thinking). This finding challenges the belief that LLMs have genuine mathematical reasoning abilities comparable to humans. As a result, this work may adjust overly optimistic views on LLMs' progress towards artificial general intelligence.

cs.AI↗

arXiv2025

AIPsychoBench: Understanding the Psychometric Differences between LLMs and Humans

Large Language Models (LLMs) with hundreds of billions of parameters have exhibited human-like intelligence by learning from vast amounts of internet-scale data. However, the uninterpretability of large-scale neural networks raises concerns about the reliability of LLM. Studies have attempted to assess the psychometric properties of LLMs by borrowing concepts from human psychology to enhance their interpretability, but they fail to account for the fundamental differences between LLMs and humans. This results in high rejection rates when human scales are reused directly. Furthermore, these scales do not support the measurement of LLM psychological property variations in different languages. This paper introduces AIPsychoBench, a specialized benchmark tailored to assess the psychological properties of LLM. It uses a lightweight role-playing prompt to bypass LLM alignment, improving the average effective response rate from 70.12% to 90.40%. Meanwhile, the average biases are only 3.3% (positive) and 2.1% (negative), which are significantly lower than the biases of 9.8% and 6.9%, respectively, caused by traditional jailbreak prompts. Furthermore, among the total of 112 psychometric subcategories, the score deviations for seven languages compared to English ranged from 5% to 20.2% in 43 subcategories, providing the first comprehensive evidence of the linguistic impact on the psychometrics of LLM.

cs.CL↗

arXiv2025

Interval Estimation for Bounded Jacobian Nonlinear Systems by Zonotope Analysis

This paper introduces an interval state estimation method for discrete-time bounded Jacobian nonlinear systems allying Luenberger-like observer with zonotope set computation. First, a robust observer is designed to obtain bounded-error and point-estimation with a peak-to-peak performance. This allows one to cope with the unknown but bounded process disturbance and measurement noise. Then, based on the stable dynamics of the observation error, tight interval estimation is obtained by applying zonotope set computation and analysis. To sum up, a comprehensive interval estimation algorithm is proposed by integrating the robust (in the sense of peak-to-peak performance index) point-valued estimate with the feasible zonotope set of the estimation error. Numerical simulation tests are conducted to assess the effectiveness of the proposed approach.

math.DS↗

arXiv2025

Policy Iteration for Exploratory Hamilton--Jacobi--Bellman Equations

We study the policy iteration algorithm (PIA) for entropy-regularized stochastic control problems on an infinite time horizon with a large discount rate, focusing on two main scenarios. First, we analyze PIA with bounded coefficients where the controls applied to the diffusion term satisfy a smallness condition. We demonstrate the convergence of PIA based on a uniform $\mathcal{C}^{2,α}$ estimate for the value sequence generated by PIA, and provide a quantitative convergence analysis for this scenario. Second, we investigate PIA with unbounded coefficients but no control over the diffusion term. In this scenario, we first provide the well-posedness of the exploratory Hamilton--Jacobi--Bellman equation with linear growth coefficients and polynomial growth reward function. By such a well-posedess result we achieve PIA's convergence by establishing a quantitative locally uniform $\mathcal{C}^{1,α}$ estimates for the generated value sequence.

math.OC↗

arXiv2025

Variational Autoencoded Multivariate Spatial Fay-Herriot Models

Small area estimation models are essential for estimating population characteristics in regions with limited sample sizes, thereby supporting policy decisions, demographic studies, and resource allocation, among other use cases. The spatial Fay-Herriot model is one such approach that incorporates spatial dependence to improve estimation by borrowing strength from neighboring regions. However, this approach often requires substantial computational resources, limiting its scalability for high-dimensional datasets, especially when considering multiple (multivariate) responses. This paper proposes two methods that integrate the multivariate spatial Fay-Herriot model with spatial random effects, learned through variational autoencoders, to efficiently leverage spatial structure. Importantly, after training the variational autoencoder to represent spatial dependence for a given set of geographies, it may be used again in future modeling efforts, without the need for retraining. Additionally, the use of the variational autoencoder to represent spatial dependence results in extreme improvements in computational efficiency, even for massive datasets. We demonstrate the effectiveness of our approach using 5-year period estimates from the American Community Survey over all census tracts in California.

stat.ML↗

arXiv2025

Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in Banach Algebras

The Lie-Trotter formula has been a fundamental tool in quantum mechanics, quantum computing, and quantum simulations. The error estimations for the Lie-Trotter product formula play a crucial role in achieving scalability and computational efficiency. In this note, we present two error estimates of Lie-Trotter product formulas, utilizing Jordan product within Banach algebras. Additionally, we introduce two generalized Lie-Trotter formula and provide two explicit estimation formulas. Consequently, the renowned Suzuki symmetrized approximation for the exponentiated sums follows directly from our main Theorem.

quant-ph↗

arXiv2025

Moderate Deviation Principle for Join-The-Shortest-Queue-d Systems

The Join-the-Shortest-Queue-d routing policy is considered for a large system with $n$ servers. Moderate deviation principles (MDP) for the occupancy process and the empirical queue length process are established as $n\to \infty$. Each MDP is formulated in terms of a large deviation principle with an appropriate speed function in a suitable infinite-dimensional path space. Proofs rely on certain variational representations for exponential functionals of Poisson random measures. As a case study, the convergence of rate functions for systems with finite buffer size $K$ to the rate function without buffer is analyzed, as $K \to \infty$.

math.PR↗

arXiv2024

Binomial-tree approximation for time-inconsistent stopping

For time-inconsistent stopping in a one-dimensional diffusion setup, we investigate how to use discrete-time models to approximate the original problem. In particular, we consider the value function $V(\cdot)$ induced by all mild equilibria in the continuous-time problem, as well as the value $V^h(\cdot)$ associated with the equilibria in a binomial-tree setting with time step size $h$. We show that $\lim_{h\rightarrow 0+} V^h \leq V$. We provide an example showing that the exact convergence may fail. Then we relax the set of equilibria and consider the value $V^h_{\varepsilon}(\cdot)$ induced by $\varepsilon$-equilibria in the binomial-tree model. We prove that $\lim_{\varepsilon \rightarrow 0+}\lim_{h \rightarrow 0+}V^h_{\varepsilon} = V$.

math.OC↗