arXiv subjects

Yakun Wang

Publications and source records attributed to Yakun Wang.

At least 19 recordsLinked to original sources

arXiv2026

Zero-Flow Two-Sample Tests

We propose a new approach to two-sample testing for deciding whether two sets of samples are drawn from the same distribution. The test is built on a statistical discrepancy based on the zero-flow criterion, termed zero-flow discrepancy (ZFD). We prove the validity of ZFD and propose a practical testing procedure, termed the zero-flow two-sample test (ZF2ST). The key idea is to learn how samples from the two distributions are locally misaligned and use the resulting directional pattern as evidence of distributional difference. By separating witness learning from hypothesis evaluation, ZF2ST can use flexible neural networks while maintaining valid statistical calibration. We develop both regression-based and power-maximized approaches for learning the witness. Experiments on synthetic and image datasets demonstrate that ZF2ST can achieve strong testing power for structured distributional changes while maintaining well-calibrated type-I error.

cs.LG↗

arXiv2026

Charge radii of calcium isotopes within relativistic configuration-interaction density functional theory

The charge radii of calcium isotopes are investigated within the framework of relativistic configuration-interaction density functional (ReCD) theory. The ReCD theory microscopically incorporates beyond-mean-field correlations through rotational symmetry restoration and configuration mixing among quasiparticle excited states, and treats even-even and odd-$A$ isotopes on the same footing. It is found that beyond-mean-field correlations significantly soften the potential energy surfaces of calcium isotopes and shift the energy minima from nearly spherical mean-field solutions to deformed shapes. The quadrupole deformation parameters predicted by the ReCD theory show much better agreement with the available experimental data than the mean-field results, supporting the reliability of the calculated potential energy surfaces and highlighting the important role of beyond-mean-field correlations. Owing to the sensitive dependence of charge radii on nuclear deformation, the charge radii obtained within the ReCD framework are generally larger than the mean-field predictions. The nearly identical charge radii of $^{40}\mathrm{Ca}$ and $^{48}\mathrm{Ca}$, as well as the unexpectedly large charge radius of $^{52}\mathrm{Ca}$, are well reproduced. Compared with the mean-field calculations, the description of the odd-even staggering is improved, especially for the enhanced charge radii of $^{42}\mathrm{Ca}$ and $^{44}\mathrm{Ca}$. It is also worth noting that secondary local minima appear in the ReCD-based potential energy surfaces of the odd-$A$ calcium isotopes $^{41,43,47}\mathrm{Ca}$. The present results suggest that shape mixing between different local minima, which is not fully included in the present calculation, may further improve the description of the pronounced odd-even staggering observed in calcium isotopes.

nucl-th↗

arXiv2026

A scalable linear programming-based framework for data clustering

We extend the linear programming-based algorithm of De Rosa et al~\cite{derKhaWan24} for K-means clustering to two important clustering paradigms: fair K-means clustering and spectral clustering. For fair K-means clustering, we show that widely used notions of group fairness can be incorporated into the partition-matrix formulation of K-means clustering through a linear number of linear inequalities. For spectral clustering, we consider a linear programming relaxation of the minimum ratio-cut problem that fits naturally within the same framework. We complement these formulations with problem-specific initialization and rounding procedures and evaluate the resulting algorithms on a large collection of real-world data sets. Denoting by $n$ the number of data points, our computational results demonstrate that the proposed approach solves $90\%$ of benchmark instances with $n \leq 3000$ to within $1\%$ optimality in at most three hours. This in turn demonstrates the remarkable strength of the proposed LP relaxations in both applications. Moreover, for more than $56\%$ of the instances, the proposed algorithm finds better solutions than those produced by popular fair Lloyd-type and spectral clustering heuristics.

math.OC↗

arXiv2026

Positive and Negative Determinant Strategies in Repeated Games with Behavior-Value Inconsistency

Direct reciprocity, based on the repeated interactions, is a fundamental mechanism to promote cooperation. Zero-determinant (ZD) strategies have opened an avenue for unilateral payoff control. However, previous studies neglect internal costs provided what agents do differ from what agents think, which is crucial for decision making of intelligent agents. Motivated by this, we establish a game theoretical framework by assuming that an individual pays the internal cost if the behavior is inconsistent with the internal thought. We prove that ZD strategy does not exist if the cost via behavior-value inconsistency is present. Instead, we find a new class of repeated strategies that enforce a unilateral payoff control, which is termed as positive/negative determinant strategy. The found strategy allows an individual to enforce an affine combination of two individuals' average payoffs above/below zero. Consequently, a focal individual is able to unilaterally control the opponent's payoff below a given value via negative determinant strategy, and a focal individual is able to get more payoff than the opponent via positive determinant strategy. We also find that the control ability of positive/negative determinant strategies is better off than that of ZD strategies. Our work highlights the importance of inconsistency between the behavior and value on payoff control, which is typically absent in classic ZD strategies.

cs.GT↗

arXiv2026

Direct Fisher Score Estimation for Likelihood Maximization

We study the problem of likelihood maximization when the likelihood function is intractable but model simulations are readily available. We propose a sequential, gradient-based optimization method that directly models the Fisher score based on a local score matching technique which uses simulations from a localized region around each parameter iterate. By employing a linear parameterization to the surrogate score model, our technique admits a closed-form, least-squares solution. This approach yields a fast, flexible, and efficient approximation to the Fisher score, effectively smoothing the likelihood objective and mitigating the challenges posed by complex likelihood landscapes. We provide theoretical guarantees for our score estimator, including bounds on the bias introduced by the smoothing. Empirical results on a range of synthetic and real-world problems demonstrate the superior performance of our method compared to existing benchmarks.

stat.ML↗

arXiv2026

Zero-Flow Encoders

Flow-based methods have achieved significant success in various generative modeling tasks, capturing nuanced details within complex data distributions. However, few existing works have exploited this unique capability to resolve fine-grained structural details beyond generation tasks. This paper presents a flow-inspired framework for representation learning. First, we demonstrate that a rectified flow trained using independent coupling is zero everywhere at $t=0.5$ if and only if the source and target distributions are identical. We term this property the \emph{zero-flow criterion}. Second, we show that this criterion can certify conditional independence, thereby extracting \emph{sufficient information} from the data. Third, we translate this criterion into a tractable, simulation-free loss function that enables learning amortized Markov blankets in graphical models and latent representations in self-supervised learning tasks. Experiments on both simulated and real-world datasets demonstrate the effectiveness of our approach. The code reproducing our experiments can be found at: https://github.com/probabilityFLOW/zfe.

stat.ML↗

arXiv2026

Replay-guided Test-time Adaptation for Fault Diagnosis Under Unseen Operating Conditions

In modern industrial systems, machinery frequently operates under dynamic environments with continuously varying loads and speeds. Consequently, deep learning-based fault diagnosis models often suffer from severe performance degradation under unseen operating conditions due to complex data distribution shifts. Since existing methods predominantly rely on static offline training, they lack the capability to dynamically adapt to these continuous variations. To address this issue, an integrated framework combining offline domain generalization (DG) and online test-time adaptation (OTTA) is proposed. Initially, a model with preliminary generalization capability is obtained offline by extracting domain-invariant features via adversarial learning. During the online phase, a dual-memory replay mechanism is developed. By selectively storing high-confidence online pseudo-labeled samples and replaying them with historical offline data, the model facilitates adaptation to changing data distributions and helps reduce forgetting of previously learned knowledge Experiments on a real-world motor dataset show that the proposed approach achieves competitive performance under the considered unseen operating conditions.

eess.SP↗

arXiv2026

Regret Analysis of Guided Diffusion for Black-Box Optimization over Structured Inputs

Guided-diffusion black-box optimization (BO) has shown strong empirical performance on structured design problems such as molecules and crystals, but its regret behavior remains poorly understood. Existing BO regret analyses typically rely on maximum information gain, non-pretrained surrogate models, or exact acquisition maximization -- assumptions that break down in modern diffusion -- BO pipelines, where pretrained diffusion models serve as powerful priors over valid structures and acquisition maximization is replaced by approximate sampling over astronomically large discrete spaces. We develop a first certificate-based expected simple-regret framework for guided-diffusion BO that avoids maximum-information-gain bounds, RKHS assumptions, and exact acquisition maximization. The central quantity in our analysis is mass lift: the increase in probability mass assigned to near-optimal designs relative to the pretrained generator. This view explains how exponential-looking finite-budget convergence and polynomial acceleration can all arise from the same mechanism. We also give practical diagnostics for estimating search exponents from finite candidate pools and a proposal-corrected resampling construction that provides a fully certified sampler instance.

stat.ML↗

arXiv2026

On the power of linear programming for K-means clustering

In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our numerical experiments with both synthetic real-world data sets, the proposed LP relaxation is almost always tight; i.e. its optimal solution is feasible for the original nonconvex problem. To better understand this unexpected behaviour, on the theoretical side, we focus on K-means clustering with two clusters, and we obtain sufficient conditions under which the LP relaxation is tight. We further analyze the sufficient conditions when the input is generated according to a popular stochastic model and obtain recovery guarantees for the LP relaxation. We conclude our theoretical study by constructing a family of inputs for which the LP relaxation is never tight. Denoting by $n$ the number of data points to be clustered, the LP relaxation contains $Ω(n^3)$ inequalities making it impractical for large data sets. To address the scalability issue, by building upon a cutting-plane algorithm together with the GPU implementation of PDLP, a first-order method LP solver, we develop an efficient algorithm that solves the proposed LP and hence the K-means clustering problem, for up to $n \leq 4000$ data points.

math.OC↗

arXiv2026

Infeasibility Aware Large Language Models for Combinatorial Optimization

Large language models (LLMs) are increasingly explored for NP-hard combinatorial optimization problems, but most existing methods emphasize feasible-instance solution generation and do not explicitly address infeasibility detection. We propose an infeasibility-aware framework that combines certifiable dataset construction, supervised fine-tuning, and LLM-assisted downstream search. For the minor-embedding problem, we introduce a new mathematical programming formulation together with provable zero-phase infeasibility screening, which enables scalable construction of training instances labeled either as feasible with structured certificates or as certifiably infeasible. Using training data generated through this exact optimization pipeline, we show that an 8B-parameter LLM can be fine-tuned to jointly perform solution generation and infeasibility detection. We further utilize LLM outputs as warm starts for downstream local search, providing a practical way to accelerate optimization even when the LLM outputs are imperfect. Experiments show that our fine-tuned model improves overall accuracy by up to 30\% over GPT-5.2; meanwhile LLM-guided warm starts provide up to $2\times$ speedup compared with starting from scratch in downstream local search.

cs.AI↗

arXiv2025

Probing Axion via Mössbauer Spectroscopy

We propose using the ultra-narrow 88 keV Mössbauer transition in $^{109}$Ag to search for QCD axion dark matter. The sub-eV axion field oscillates coherently, inducing a time-varying effective $\barθ_{\rm QCD}$ angle. This, in turn, modulates the nuclear binding energy. From existing linewidth measurements, we derive constraints on the $f_a^{-1}$-$m_a$ plane that already surpass other laboratory bounds. We further detail an experimental setup to directly probe this time-dependent signature via precision Mössbauer spectroscopy in the gravitational potential. This Letter demonstrates that this approach can significantly extend search capability and probe a vast, unexplored region of axion parameter space. Particularly, this setup can probe axion masses beyond the reach of existing experiments, such as atomic-clock measurements, offering a powerful new way for exploring higher-mass axion dark matter. The sensitivity has the potential to be further improved with advancing experimental capabilities.

hep-ph↗

arXiv2025

Machine Learning Based Probe Skew Correction for High-frequency BH Loop Measurements

Experimental characterization of magnetic components has grown to be increasingly important to understand and model their behaviours in high-frequency PWM converters. The BH loop measurement is the only available approach to separate the core loss as an electrical method, which, however, is susceptive to the probe phase skew. As an alternative to the regular de-skew approaches based on hardware, this work proposes a novel machine-learning-based method to identify and correct the probe skew, which builds on the newly discovered correlation between the skew and the shape/trajectory of the measured BH loop. A special technique is proposed to artificially generate skewed images from measured waveforms as augmented training sets. A machine learning pipeline is developed with the Convolutional Neural Network (CNN) to treat the problem as an image-based prediction task. The trained model has demonstrated a high accuracy and generalizability in identifying the skew value from a BH loop unseen by the model, which enables the compensation of the skew to yield the corrected core loss value and BH loop.

eess.SP↗

arXiv2025

The stability of bi-polarization on dynamical directed graphs: an emergent game perspective

This paper proposes a co-evolutionary model of directed graphs and three opinions, i.e., conservative$(+)$, neutral$(\odot)$ and liberal$(-)$. Agents update both opinions and social relationships with bias. We find that an emergent game suffices to predict the stability of bi-polarization under a rare opinion updating limit and a large system size limit. The bi-polarization is stable if and only if the emergent game has an internal Nash equilibrium. The necessary and sufficient condition is explained by both risk dominance and evolutionary stability. This game approach facilitates us to reveal the stability of bi-polarization in empirical systems. Our work fosters the understanding of opinion formation for controversial topics, and shows a deep connection between opinion dynamics and evolutionary game theory.

nlin.AO↗

arXiv2025

Guiding Time-Varying Generative Models with Natural Gradients on Exponential Family Manifold

Optimising probabilistic models is a well-studied field in statistics. However, its connection with the training of generative models remains largely under-explored. In this paper, we show that the evolution of time-varying generative models can be projected onto an exponential family manifold, naturally creating a link between the parameters of a generative model and those of a probabilistic model. We then train the generative model by moving its projection on the manifold according to the natural gradient descent scheme. This approach also allows us to efficiently approximate the natural gradient of the KL divergence without relying on MCMC for intractable models. Furthermore, we propose particle versions of the algorithm, which feature closed-form update rules for any parametric model within the exponential family. Through toy and real-world experiments, we validate the effectiveness of the proposed algorithms. The code of the proposed algorithms can be found at https://github.com/anewgithubname/iNGD.

stat.ML↗

arXiv2025

Smoothness Really Matters: A Simple Yet Effective Approach for Unsupervised Graph Domain Adaptation

Unsupervised Graph Domain Adaptation (UGDA) seeks to bridge distribution shifts between domains by transferring knowledge from labeled source graphs to given unlabeled target graphs. Existing UGDA methods primarily focus on aligning features in the latent space learned by graph neural networks (GNNs) across domains, often overlooking structural shifts, resulting in limited effectiveness when addressing structurally complex transfer scenarios. Given the sensitivity of GNNs to local structural features, even slight discrepancies between source and target graphs could lead to significant shifts in node embeddings, thereby reducing the effectiveness of knowledge transfer. To address this issue, we introduce a novel approach for UGDA called Target-Domain Structural Smoothing (TDSS). TDSS is a simple and effective method designed to perform structural smoothing directly on the target graph, thereby mitigating structural distribution shifts and ensuring the consistency of node representations. Specifically, by integrating smoothing techniques with neighborhood sampling, TDSS maintains the structural coherence of the target graph while mitigating the risk of over-smoothing. Our theoretical analysis shows that TDSS effectively reduces target risk by improving model smoothness. Empirical results on three real-world datasets demonstrate that TDSS outperforms recent state-of-the-art baselines, achieving significant improvements across six transfer scenarios. The code is available in https://github.com/cwei01/TDSS.

cs.LG↗

arXiv2024

Inference in higher-order undirected graphical models and binary polynomial optimization

We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare the strength of the proposed linear programming relaxations theoretically. Finally, we demonstrate the effectiveness of these relaxations by performing a computational study for two important applications, namely, image restoration and decoding error-correcting codes.

math.OC↗

arXiv2024

Optimizing Long-tailed Link Prediction in Graph Neural Networks through Structure Representation Enhancement

Link prediction, as a fundamental task for graph neural networks (GNNs), has boasted significant progress in varied domains. Its success is typically influenced by the expressive power of node representation, but recent developments reveal the inferior performance of low-degree nodes owing to their sparse neighbor connections, known as the degree-based long-tailed problem. Will the degree-based long-tailed distribution similarly constrain the efficacy of GNNs on link prediction? Unexpectedly, our study reveals that only a mild correlation exists between node degree and predictive accuracy, and more importantly, the number of common neighbors between node pairs exhibits a strong correlation with accuracy. Considering node pairs with less common neighbors, i.e., tail node pairs, make up a substantial fraction of the dataset but achieve worse performance, we propose that link prediction also faces the long-tailed problem. Therefore, link prediction of GNNs is greatly hindered by the tail node pairs. After knowing the weakness of link prediction, a natural question is how can we eliminate the negative effects of the skewed long-tailed distribution on common neighbors so as to improve the performance of link prediction? Towards this end, we introduce our long-tailed framework (LTLP), which is designed to enhance the performance of tail node pairs on link prediction by increasing common neighbors. Two key modules in LTLP respectively supplement high-quality edges for tail node pairs and enforce representational alignment between head and tail node pairs within the same category, thereby improving the performance of tail node pairs.

cs.LG↗

arXiv2024

A tale of two emergent games: opinion dynamics in dynamical directed networks

Uni-directional social interactions are ubiquitous in real social networks whereas undirected interactions are intensively studied. We establish a voter model in a dynamical directed network. We analytically obtain the degree distribution of the evolving network at any given time. Furthermore, we find that the average degree is captured by an emergent game. On the other hand, we find that the fate of opinions is captured by another emergent game. Beyond expectation, the two emergent games are typically different due to the unidirectionality of the evolving networks. The Nash equilibrium analysis of the two games facilitates us to give the criterion under which the minority opinion with few disciples initially takes over the population eventually for in-group bias. Our work fosters the understanding of opinion dynamics ranging from methodology to research content.

physics.soc-ph↗