arXiv subjects

Xiaohui Chen

Publications and source records attributed to Xiaohui Chen.

At least 19 recordsLinked to original sources

arXiv2026

Central limit theorems and bootstrap for sparse regularized multimarginal optimal transport and barycenters

Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional and multi-sample settings. The unregularized barycenter problem is computationally demanding and suffers severely from the curse of dimensionality, making regularization essential in many applications. While regularized optimal transport methods are widely used, approaches based on entropic penalization tend to overspread mass and may blur the geometric structure of the solution. Motivated by barycenter estimation, we propose a more general methodology based on sparse regularized multimarginal optimal transport (RMOT). Our formulation creates sparse transport plans and is designed to avoid this overspreading effect. We establish consistency, central limit theorems, and bootstrap validity for the optimal potentials and couplings for the empirical RMOT problem. Specializing to sparse regularized barycenters, our results yield a uniform weak limit and bootstrap consistency. Numerical simulations show that sparsity plays a fundamental role in preserving the structure of the solution and avoiding the overspreading behavior typical of entropic regularization.

math.ST↗

arXiv2026

Scene-Conditioned PINN-GNN for Multipath RF Maps: Cross-Scene Generation and In-Scene Completion

Radio frequency (RF) maps provide a compact representation of multipath propagation characteristics and are fundamental to channel modeling, coverage analysis, and environment-aware wireless optimization. This paper proposes a unified RF map construction framework based on a physics-informed neural network (PINN) and a graph neural network (GNN), supporting both cross-scene generation and in-scene completion with 2D and 2.5D environmental representations. The PINN embeds electromagnetic propagation constraints to establish a physically consistent mapping from receiver locations to multipath parameters, including path gain, time of arrival, and angles, while the GNN enforces spatial consistency by modeling correlations among neighboring receivers. To comprehensively evaluate multipath reconstruction quality, we propose a peak-weighted dynamic time warping metric that jointly accounts for amplitude errors and peak delay misalignment in channel impulse responses. Extensive experiments demonstrate that the proposed method consistently outperforms image-based, diffusion-based, and interpolation baselines across both map-level and multipath-level metrics, achieving robust generalization and high-fidelity RF map construction under sparse observations.

eess.SP↗

arXiv2026

Another Look at Log-PCA for Probability Measures: A Dynamical Formulation and Statistical Convergence

This paper is concerned with learning principal variations of random probability measures on $\mathbb{R}^m$ under the Wasserstein geometry. We introduce a new dynamical formulation to interpret the log-PCA, a linearized principal geodesic analysis, as a variational approach. Our differentiable version, termed as the Wasserstein Tangential PCA (WT-PCA), captures the local principal modes of geodesic variations of a (weighted) probability measure on the Wasserstein space via its covariance operator at barycenter. Based on the dynamical perspective and leveraging parallel transport structure of the optimal transport problems, we derive a general statistical convergence rate of the empirical WT-PCA when estimated from data in terms of the 2-Wasserstein distance between the population and empirical barycenter reference measures.

stat.ML↗

arXiv2026

Hierarchical Synthetic Tabular Data Generation: A Hybrid Top-Down and Bottom-Up Framework

Existing approaches for synthetic tabular data generation are based on either purely generative models or LLMs, both of which struggle with data heterogeneity, logical consistency, rare-event coverage, and robustness in low-data regimes. In this paper, we propose a hierarchical hybrid top-down and bottom-up (H-TDBU) framework that decouples semantic structures from stochastic texture. In the top-down path, structure-driven logical constraints and cross-modal alignment rules are constructed, while in the bottom-up path, lightweight tabular generators are used to learn local statistical patterns from real data. The two paths are consolidated in a unified synthesis engine with an iterative feedback loop. We evaluate the framework on weak multimodal financial benchmarks combining tabular and sentiment-text data. Experimental results show that our H-TDBU approach improves train-synthetic-test-real performance over neural baseline methods while preserving semantic consistency. Our results suggest that hierarchical rule-guided synthesis provides an effective mechanism for combining controllability, semantic coherence, and statistical fidelity in synthetic data generation.

cs.LG↗

arXiv2026

A Unified Approach for Computing Wasserstein Barycenters of Discrete and Continuous Measures

Computing the unregularized Wasserstein barycenter for measure-valued data is a challenging optimization task. Recent algorithms have been tailored to either discrete measures as point clouds or continuous measures discretized on regular grids. In this work, we propose a primal mirror descent algorithm for computing the exact Wasserstein barycenter in the Fisher-Rao geometry. Our algorithm is a unified approach that is flexible enough to simultaneously cover discrete and absolutely continuous input measures, with convergence guarantees in both settings. In particular, when all input measures are discrete, our algorithm, initialized from any probability density, solves a sequence of semi-discrete optimal transport subproblems and produces absolutely continuous iterates that converge to the discrete barycenter. We use synthetic and real data examples to demonstrate the promising result in terms of accuracy and computational cost.

math.OC↗

arXiv2026

Smoothed estimation of Wasserstein barycenters

This paper studies the statistical estimation of exact Wasserstein barycenters. Existing non-asymptotic results for empirical barycenters exhibit a severe curse of dimensionality. Motivated by the semi-dual formulation of the barycenter problem and its associated Sobolev optimization geometry, we develop a smoothness-aware approach that combines density estimation with Sobolev geometric structure to estimate the population barycenter. We establish nonparametric convergence rates for estimating both the barycenter functional and its minimizer, demonstrating how smoothness can substantially improve statistical performance.

math.ST↗

arXiv2026

Breaking the Secret: Economic Interventions for Combating Collusion in Embodied Multi-Agent Systems

Collusion among autonomous agents poses a critical security threat in embodied multi-agent systems (MAS), where coordinated behaviors can deviate from global objectives and lead to real-world consequences. Existing defenses, primarily based on identity control or post-hoc behavior analysis, are insufficient to address such threats in embodied settings due to delayed feedback and noisy observations in physical environments, which make behavioral deviations difficult to detect accurately and in a timely manner. To address this challenge, we propose a mutagenic incentive intervention approach that mitigates collusion by reshaping agents' payoff structures. By rewarding agents who report collusive behavior and penalizing identified participants, the mechanism induces strategic defection and renders collusion unstable. We further design supporting mechanisms, including reporting deposits, smart contract-based reward enforcement, and encrypted communication, to ensure robustness against misuse of the incentive mechanism and retaliation from penalized agents. We implement the proposed approach in both simulated and real-world embodied environments. Experimental results show that our method effectively suppresses collusion by inducing defection, while preserving system efficiency. It achieves performance comparable to the non-collusion baseline and outperforms representative reactive defenses, thereby fulfilling the desired security objectives. These results demonstrate the effectiveness of proactive incentive design as a practical paradigm for securing embodied multi-agent systems.

cs.CR↗

arXiv2026

Hierarchy of discriminative power and complexity in learning quantum ensembles

Distance metrics are central to machine learning, yet distances between ensembles of quantum states remain poorly understood due to fundamental quantum measurement constraints. We introduce a hierarchy of integral probability metrics, termed MMD-$k$, which generalizes the maximum mean discrepancy to quantum ensembles and exhibit a strict trade-off between discriminative power and statistical efficiency as the moment order $k$ increases. For pure-state ensembles of size $N$, estimating MMD-$k$ using experimentally feasible SWAP-test-based estimators requires $\Theta(N^{2-2/k})$ samples for constant $k$, and $\Theta(N^3)$ samples to achieve full discriminative power at $k = N$. In contrast, the quantum Wasserstein distance attains full discriminative power with $\Theta(N^2 \log N)$ samples. These results provide principled guidance for the design of loss functions in quantum machine learning, which we illustrate in the training quantum denoising diffusion probabilistic models.

quant-ph↗

arXiv2026

SpecBridge: Bridging Mass Spectrometry and Molecular Representations via Cross-Modal Alignment

Small-molecule identification from tandem mass spectrometry (MS/MS) remains a bottleneck in untargeted settings where spectral libraries are incomplete. While deep learning offers a solution, current approaches typically fall into two extremes: explicit generative models that construct molecular graphs atom-by-atom, or joint contrastive models that learn cross-modal subspaces from scratch. We introduce SpecBridge, a novel implicit alignment framework that treats structure identification as a geometric alignment problem. SpecBridge fine-tunes a self-supervised spectral encoder (DreaMS) to project directly into the latent space of a frozen molecular foundation model (ChemBERTa), and then performs retrieval by cosine similarity to a fixed bank of precomputed molecular embeddings. Across MassSpecGym, Spectraverse, and MSnLib benchmarks, SpecBridge improves top-1 retrieval accuracy by roughly 20-25% relative to strong neural baselines, while keeping the number of trainable parameters small. These results suggest that aligning to frozen foundation models is a practical, stable alternative to designing new architectures from scratch. The code for SpecBridge is released at https://github.com/HassounLab/SpecBridge.

cs.LG↗

arXiv2025

OpenPathNet: An Open-Source RF Multipath Data Generator for AI-Driven Wireless Systems

The convergence of artificial intelligence (AI) and sixth-generation (6G) wireless technologies is driving an urgent need for large-scale, high-fidelity, and reproducible radio frequency (RF) datasets. Existing resources, such as CKMImageNet, primarily provide preprocessed and image-based channel representations, which conceal the fine-grained physical characteristics of signal propagation that are essential for effective AI modeling. To bridge this gap, we present OpenPathNet, an open-source RF multipath data generator accompanied by a publicly released dataset for AI-driven wireless research. Distinct from prior datasets, OpenPathNet offers disaggregated and physically consistent multipath parameters, including per-path gain, time of arrival (ToA), and spatial angles, derived from high-precision ray tracing simulations constructed on real-world environment maps. By adopting a modular, parameterized pipeline, OpenPathNet enables reproducible generation of multipath data and can be readily extended to new environments and configurations, improving scalability and transparency. The released generator and accompanying dataset provide an extensible testbed that holds promise for advancing studies on channel modeling, beam prediction, environment-aware communication, and integrated sensing in AI-enabled 6G systems. The source code and dataset are publicly available at https://github.com/liu-lz/OpenPathNet.

eess.SP↗

arXiv2025

Neural Local Wasserstein Regression

We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization, which can be restrictive in approximation capacity and distort geometry in multivariate underlying domains. In this paper, we propose the \emph{Neural Local Wasserstein Regression}, a flexible nonparametric framework that models regression through locally defined transport maps in Wasserstein space. Our method builds on the analogy with classical kernel regression: kernel weights based on the 2-Wasserstein distance localize estimators around reference measures, while neural networks parameterize transport operators that adapt flexibly to complex data geometries. This localized perspective broadens the class of admissible transformations and avoids the limitations of global map assumptions and linearization structures. We develop a practical training procedure using DeepSets-style architectures and Sinkhorn-approximated losses, combined with a greedy reference selection strategy for scalability. Through synthetic experiments on Gaussian and mixture models, as well as distributional prediction tasks on MNIST, we demonstrate that our approach effectively captures nonlinear and high-dimensional distributional relationships that elude existing methods.

stat.ML↗

arXiv2025

Physics-Informed Extreme Learning Machine (PIELM): Opportunities and Challenges

We are delighted to see the recent development of physics-informed extreme learning machine (PIELM) for its higher computational efficiency and accuracy compared to other physics-informed machine learning (PIML) paradigms. Since a comprehensive summary or review of PIELM is currently unavailable, we would like to take this opportunity to share our perspectives and experiences on this promising research direction. We can see that many efforts have been made to solve ordinary/partial differential equations (ODEs/PDEs) characterized by sharp gradients, nonlinearities, high-frequency behavior, hard constraints, uncertainty, multiphysics coupling, and interpretability. Despite these encouraging successes, many pressing challenges remain to be tackled, which also provides opportunities to develop more robust, interpretable, and generalizable PIELM frameworks for scientific and engineering applications.

cs.LG↗

arXiv2025

A Generalized Label Shift Perspective for Cross-Domain Gaze Estimation

Aiming to generalize the well-trained gaze estimation model to new target domains, Cross-domain Gaze Estimation (CDGE) is developed for real-world application scenarios. Existing CDGE methods typically extract the domain-invariant features to mitigate domain shift in feature space, which is proved insufficient by Generalized Label Shift (GLS) theory. In this paper, we introduce a novel GLS perspective to CDGE and modelize the cross-domain problem by label and conditional shift problem. A GLS correction framework is presented and a feasible realization is proposed, in which a importance reweighting strategy based on truncated Gaussian distribution is introduced to overcome the continuity challenges in label shift correction. To embed the reweighted source distribution to conditional invariant learning, we further derive a probability-aware estimation of conditional operator discrepancy. Extensive experiments on standard CDGE tasks with different backbone models validate the superior generalization capability across domain and applicability on various models of proposed method.

cs.CV↗

arXiv2025

Scalable Second-order Riemannian Optimization for $K$-means Clustering

Clustering is a hard discrete optimization problem. Nonconvex approaches such as low-rank semidefinite programming (SDP) have recently demonstrated promising statistical and local algorithmic guarantees for cluster recovery. Due to the combinatorial structure of the $K$-means clustering problem, current relaxation algorithms struggle to balance their constraint feasibility and objective optimality, presenting tremendous challenges in computing the second-order critical points with rigorous guarantees. In this paper, we provide a new formulation of the $K$-means problem as a smooth unconstrained optimization over a submanifold and characterize its Riemannian structures to allow it to be solved using a second-order cubic-regularized Riemannian Newton algorithm. By factorizing the $K$-means manifold into a product manifold, we show how each Newton subproblem can be solved in linear time. Our numerical experiments show that the proposed method converges significantly faster than the state-of-the-art first-order nonnegative low-rank factorization method, while achieving similarly optimal statistical accuracy.

cs.LG↗

arXiv2025

PINN and GNN-based RF Map Construction for Wireless Communication Systems

Radio frequency (RF) map is a promising technique for capturing the characteristics of multipath signal propagation, offering critical support for channel modeling, coverage analysis, and beamforming in wireless communication networks. This paper proposes a novel RF map construction method based on a combination of physics-informed neural network (PINN) and graph neural network (GNN). The PINN incorporates physical constraints derived from electromagnetic propagation laws to guide the learning process, while the GNN models spatial correlations among receiver locations. By parameterizing multipath signals into received power, delay, and angle of arrival (AoA), and integrating both physical priors and spatial dependencies, the proposed method achieves accurate prediction of multipath parameters. Experimental results demonstrate that the method enables high-precision RF map construction under sparse sampling conditions and delivers robust performance in both indoor and complex outdoor environments, outperforming baseline methods in terms of generalization and accuracy.

eess.SP↗

arXiv2025

Holographic deep thermalization for secure and efficient quantum random state generation

Randomness is a cornerstone of science, underpinning fields such as statistics, information theory, dynamical systems, and thermodynamics. In quantum science, quantum randomness, especially random pure states, plays a pivotal role in fundamental questions like black hole physics and quantum complexity, as well as in practical applications such as quantum device benchmarking and quantum advantage certification. The conventional approach for generating genuine random states, called `deep thermalization', faces significant challenges, including scalability issues due to the need for a large ancilla system and susceptibility to attacks, as demonstrated in this work. We introduce holographic deep thermalization, a secure and hardware-efficient quantum random state generator. By adopting a sequential application of a scrambling-measure-reset process, it continuously trades space with time, and substantially reduces the required ancilla size to as small as a system-size independent constant; At the same time, it guarantees security by removing quantum correlation between the data system and attackers. Thanks to the resource reduction, our circuit-based implementation on IBM Quantum devices achieves genuine $5$-qubit random state generation utilizing only a total of $8$ qubits.

quant-ph↗

arXiv2025

Graph Generative Pre-trained Transformer

Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize adjacency matrix representations, this work revisits an alternative approach that represents graphs as sequences of node set and edge set. We advocate for this approach due to its efficient encoding of graphs and propose a novel representation. Based on this representation, we introduce the Graph Generative Pre-trained Transformer (G2PT), an auto-regressive model that learns graph structures via next-token prediction. To further exploit G2PT's capabilities as a general-purpose foundation model, we explore fine-tuning strategies for two downstream applications: goal-oriented generation and graph property prediction. We conduct extensive experiments across multiple datasets. Results indicate that G2PT achieves superior generative performance on both generic graph and molecule datasets. Furthermore, G2PT exhibits strong adaptability and versatility in downstream tasks from molecular design to property prediction. Code available at https://github.com/tufts-ml/G2PT,

cs.LG↗

arXiv2025

Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization

The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability distributions. Computation of the unregularized barycenter for discretized probability distributions on point clouds is a challenging task when the domain dimension $d > 1$. Most practical algorithms for approximating the barycenter problem are based on entropic regularization. In this paper, we introduce a nearly linear time $O(m \log{m})$ and linear space complexity $O(m)$ primal-dual algorithm, the Wasserstein-Descent $\dot{\mathbb{H}}^1$-Ascent (WDHA) algorithm, for computing the exact barycenter when the input probability density functions are discretized on an $m$-point grid. The key success of the WDHA algorithm hinges on alternating between two different yet closely related Wasserstein and Sobolev optimization geometries for the primal barycenter and dual Kantorovich potential subproblems. Under reasonable assumptions, we establish the convergence rate and iteration complexity of WDHA to its stationary point when the step size is appropriately chosen. Superior computational efficacy, scalability, and accuracy over the existing Sinkhorn-type algorithms are demonstrated on high-resolution (e.g., $1024 \times 1024$ images) 2D synthetic and real data.

stat.ML↗