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Tuan Pham

Publications and source records attributed to Tuan Pham.

At least 19 recordsLinked to original sources
arXiv2026

Extreme principal minors of Wishart and deformed GOE matrices

We study the laws of large numbers for the largest eigenvalues among all principal minors of Wishart matrices and deformed GOE matrices. We propose a new method based on identifying the deterministic sets to which the random sets formed by suitably normalized principal minors converge in Hausdorff distance, thereby reducing the original extreme-value problems to finite-dimensional convex optimization problems. We demonstrate the effectiveness of this method in regimes not covered by the existing second-moment arguments in \cite{cai2021asymptotic,hu2023extreme}. For deformed GOE matrices with fixed minor size \(k\), we determine the limit for every diagonal variance \(a>0\) and identify a phase transition at \(a=2\). Above the transition, the limiting constant satisfies an explicit recursion with no close-form expression, and the optimizers exhibit a nested hierarchical structure, thereby resolving the case left open in \cite{cai2021asymptotic}. For Wishart matrices with general sub-Gaussian entries and fixed \(k\), we characterize the limit through an entropy-constrained deterministic convex set. When the entries are standard Gaussian, we solve the resulting optimization problem explicitly and obtain the exact value of the limiting constant.

math.PR↗
arXiv2026

Exact detection threshold of the packing test

Using Poisson approximation techniques, we derive the detection threshold of the packing test in \cite{Jiang13} when testing spherical uniformity under high-dimensional Fisher--von Mises--Langevin (FvML) and Watson alternatives. Our result rigorously confirms the empirical observation that the packing test is strictly suboptimal for testing uniformity in these two popular models. In the high-dimensional FvML model, its detection threshold is precisely \(\kappa=\Theta\lb p^{3/4}/(\log n)^{1/4}\rb\). In the high-dimensional Watson model, its detection threshold is \(p-2\kappa=\Theta(\sqrt{p\log n})\), or equivalently \(\kappa=p/2-\Theta(\sqrt{p\log n})\). The non-null limiting distributions of the packing test under these two models are derived. We show that the limiting scalings of the largest squared inner product undergo a discontinuous phase transition in the Watson model, whereas no analogous phenomenon occurs in the FvML model.

math.ST↗
arXiv2026

Maximum of sparsely equicorrelated Gaussian fields and applications

We investigate the extreme values of a sparse and equicorrelated Gaussian field on a triangle: the correlations on every vertical or horizontal line are all equal to a parameter $r \in [0,1/2]$ and are zero everywhere else. This problem is closely linked with various problems in high-dimensional statistics and extreme-value theory. We identify the threshold for $r$ at which the standard Gumbel law breaks down. Our result is based on a subtle application of the Chen-Stein method for Poisson approximation. As applications, we discuss the implication of our results on multiple testing and resolve several questions that were left open in \cite{heiny2024maximum}, \cite{tang2022asymptotic} and \cite{Jiang19}.

math.PR↗
arXiv2026

Bridging the Semantic Chasm: Synergistic Conceptual Anchoring for Generalized Few-Shot and Zero-Shot OOD Perception

This manuscript presents a pioneering Synergistic Neural Agents Network (SynerNet) framework designed to mitigate the phenomenon of cross-modal alignment degeneration in Vision-Language Models (VLMs) when encountering Out-of-Distribution (OOD) concepts. Specifically, four specialized computational units - visual perception, linguistic context, nominal embedding, and global coordination - collaboratively rectify modality disparities via a structured message-propagation protocol. The principal contributions encompass a multi-agent latent space nomenclature acquisition framework, a semantic context-interchange algorithm for enhanced few-shot adaptation, and an adaptive dynamic equilibrium mechanism. Empirical evaluations conducted on the VISTA-Beyond benchmark demonstrate that SynerNet yields substantial performance augmentations in both few-shot and zero-shot scenarios, exhibiting precision improvements ranging from 1.2% to 5.4% across a diverse array of domains.

cs.CV↗
arXiv2026

Qubit-parity interference despite unknown interaction phases

Quantum interference between interacting systems is fundamental to basic science and quantum technology, but it typically requires precise control of the interaction phases of lasers or microwave generators. Can interference be observed if those interaction phases are stable but unknown, usually prohibitive for complex state without active control? Here, we answer this question by experimentally preparing a Schr\"odinger-cat-like state of an internal qubit and a motional oscillator of a trapped $^{40}$Ca$^{+}$ ion, and its robustness to such uncontrolled phase. By applying alternating red and blue sideband pulses, we enforce a strict qubit-parity correlation and interference inherently insensitive to stable but unknown phases of the driving laser. For this qubit-parity interference, we use a minimal two-pulse interferometric sequence to demonstrate characteristic visibilities of $20\%$ and $40\%$, which approach the theoretical visibility limit, providing a scalable coherence witness without full state tomography for high-dimensional states.

quant-ph↗
arXiv2025

UMAMI: Unifying Masked Autoregressive Models and Deterministic Rendering for View Synthesis

Novel view synthesis (NVS) seeks to render photorealistic, 3D-consistent images of a scene from unseen camera poses given only a sparse set of posed views. Existing deterministic networks render observed regions quickly but blur unobserved areas, whereas stochastic diffusion-based methods hallucinate plausible content yet incur heavy training- and inference-time costs. In this paper, we propose a hybrid framework that unifies the strengths of both paradigms. A bidirectional transformer encodes multi-view image tokens and Plucker-ray embeddings, producing a shared latent representation. Two lightweight heads then act on this representation: (i) a feed-forward regression head that renders pixels where geometry is well constrained, and (ii) a masked autoregressive diffusion head that completes occluded or unseen regions. The entire model is trained end-to-end with joint photometric and diffusion losses, without handcrafted 3D inductive biases, enabling scalability across diverse scenes. Experiments demonstrate that our method attains state-of-the-art image quality while reducing rendering time by an order of magnitude compared with fully generative baselines.

cs.CV↗
arXiv2025

Time-uniform concentration bounds for iterative algorithms

We develop a new framework for deriving time-uniform concentration bounds for the output of stochastic sequential algorithms satisfying certain recursive inequalities akin to those defining the almost-supermartingale processes introduced by \cite{robbins1971convergence}. Our approach is of wide applicability, and can be deployed in settings in which exponential supermartingale processes, required by prevailing methodologies for anytime-valid concentration inequalities, are not readily available. Our results can be viewed as quantitative versions of the classical Robbins-Siegmund Lemma. We demonstrate the effectiveness of our method by providing new and optimal time-uniform concentration bounds for Oja's algorithm for streaming PCA, stochastic gradient descent, and stochastic approximations.

math.ST↗
arXiv2025

Convergence and Stability Analysis of Self-Consuming Generative Models with Heterogeneous Human Curation

Self-consuming generative models have received significant attention over the last few years. In this paper, we study a self-consuming generative model with heterogeneous preferences that is a generalization of the model in Ferbach et al. (2024). The model is retrained round by round using real data and its previous-round synthetic outputs. The asymptotic behavior of the retraining dynamics is investigated across four regimes using different techniques including the nonlinear Perron--Frobenius theory. Our analyses improve upon that of Ferbach et al. (2024) and provide convergence results in settings where the well-known Banach contraction mapping arguments do not apply. Stability and non-stability results regarding the retraining dynamics are also given.

stat.ML↗
arXiv2025

GeoDiff: Geometry-Guided Diffusion for Metric Depth Estimation

We introduce a novel framework for metric depth estimation that enhances pretrained diffusion-based monocular depth estimation (DB-MDE) models with stereo vision guidance. While existing DB-MDE methods excel at predicting relative depth, estimating absolute metric depth remains challenging due to scale ambiguities in single-image scenarios. To address this, we reframe depth estimation as an inverse problem, leveraging pretrained latent diffusion models (LDMs) conditioned on RGB images, combined with stereo-based geometric constraints, to learn scale and shift for accurate depth recovery. Our training-free solution seamlessly integrates into existing DB-MDE frameworks and generalizes across indoor, outdoor, and complex environments. Extensive experiments demonstrate that our approach matches or surpasses state-of-the-art methods, particularly in challenging scenarios involving translucent and specular surfaces, all without requiring retraining.

cs.CV↗
arXiv2025

OmniCast: A Masked Latent Diffusion Model for Weather Forecasting Across Time Scales

Accurate weather forecasting across time scales is critical for anticipating and mitigating the impacts of climate change. Recent data-driven methods based on deep learning have achieved significant success in the medium range, but struggle at longer subseasonal-to-seasonal (S2S) horizons due to error accumulation in their autoregressive approach. In this work, we propose OmniCast, a scalable and skillful probabilistic model that unifies weather forecasting across timescales. OmniCast consists of two components: a VAE model that encodes raw weather data into a continuous, lower-dimensional latent space, and a diffusion-based transformer model that generates a sequence of future latent tokens given the initial conditioning tokens. During training, we mask random future tokens and train the transformer to estimate their distribution given conditioning and visible tokens using a per-token diffusion head. During inference, the transformer generates the full sequence of future tokens by iteratively unmasking random subsets of tokens. This joint sampling across space and time mitigates compounding errors from autoregressive approaches. The low-dimensional latent space enables modeling long sequences of future latent states, allowing the transformer to learn weather dynamics beyond initial conditions. OmniCast performs competitively with leading probabilistic methods at the medium-range timescale while being 10x to 20x faster, and achieves state-of-the-art performance at the subseasonal-to-seasonal scale across accuracy, physics-based, and probabilistic metrics. Furthermore, we demonstrate that OmniCast can generate stable rollouts up to 100 years ahead. Code and model checkpoints are available at https://github.com/tung-nd/omnicast.

cs.LG↗
arXiv2025

Mean-field theory of the general-spin Ising model

Motivated by modelling in physics and other disciplines, such as sociology and psychology, we derive the mean field of the general-spin Ising model from the variational principle of the Gibbs free energy. The general-spin Ising model has $2k+1$ spin values, generated by $-(k-j)/k$, with $j=0,1,2\ldots,2k$, such that for $k=1$ we obtain $-1,0,1$, for example; the Hamiltonian is identical to that of the standard Ising model. The general-spin Ising model exhibits spontaneous magnetisation, similar to the standard Ising model, but with the location translated by a factor depending on the number of categories $2k+1$. We also show how the accuracy of the mean field depends on both the number of nodes and node degree, and that the hysteresis effect decreases and saturates with the number of categories $2k+1$. Monte Carlo simulations confirm the theoretical results.

cond-mat.stat-mech↗
arXiv2025

Asymptotic analysis of high-dimensional uniformity tests under heavy-tailed alternatives

We study the high-dimensional uniformity testing problem, which involves testing whether the underlying distribution is the uniform distribution, given $n$ data points on the $p$-dimensional unit hypersphere. While this problem has been extensively studied in scenarios with fixed $p$, only three testing procedures are known in high-dimensional settings: the Rayleigh test \cite{Cutting-P-V}, the Bingham test \cite{Cutting-P-V2}, and the packing test \cite{Jiang13}. Most existing research focuses on the former two tests, and the consistency of the packing test remains open. We show that under certain classes of alternatives involving projections of heavy-tailed distributions, the Rayleigh test is asymptotically blind, and the Bingham test has asymptotic power equivalent to random guessing. In contrast, we show theoretically that the packing test is powerful against such alternatives, and empirically that its size suffers from severe distortion due to the slow convergence nature of extreme-value statistics. By exploiting the asymptotic independence of these three tests, we then propose a new test based on Fisher's combination technique that combines their strengths. The new test is shown to enjoy all the optimality properties of each individual test, and unlike the packing test, it maintains excellent type-I error control.

math.ST↗
arXiv2025

Detecting non-uniform patterns on high-dimensional hyperspheres

We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven manner. This characterization naturally leads to an Ingster-type distance for quantifying deviations from uniformity, whose asymptotic behavior can be analyzed systematically via Edgeworth-type expansions. Perhaps surprisingly, we show that this distance captures the minimax rates for testing uniformity simultaneously across several high-dimensional parametric models, even in the models where densities with respect to the uniform law do not exist. We then introduce a simple test for spherical uniformity based on this distance and study its detection rates and consistency against various classes of alternatives, both local and non-local. The proposed test is universally consistent in fixed dimensions, minimax-optimal over a variety of high-dimensional parametric models, and consistent against non-local high-dimensional alternatives. This is different from previously studied high-dimensional Sobolev tests and extreme-value-based tests, which are rate-suboptimal or inconsistent against one or more classes of alternatives. We also establish the local asymptotic distribution of the proposed test under the considered classes of alternatives, along with new information lower bounds.

math.ST↗
arXiv2025

Diffusion-Guided Gaussian Splatting for Large-Scale Unconstrained 3D Reconstruction and Novel View Synthesis

Recent advancements in 3D Gaussian Splatting (3DGS) and Neural Radiance Fields (NeRF) have achieved impressive results in real-time 3D reconstruction and novel view synthesis. However, these methods struggle in large-scale, unconstrained environments where sparse and uneven input coverage, transient occlusions, appearance variability, and inconsistent camera settings lead to degraded quality. We propose GS-Diff, a novel 3DGS framework guided by a multi-view diffusion model to address these limitations. By generating pseudo-observations conditioned on multi-view inputs, our method transforms under-constrained 3D reconstruction problems into well-posed ones, enabling robust optimization even with sparse data. GS-Diff further integrates several enhancements, including appearance embedding, monocular depth priors, dynamic object modeling, anisotropy regularization, and advanced rasterization techniques, to tackle geometric and photometric challenges in real-world settings. Experiments on four benchmarks demonstrate that GS-Diff consistently outperforms state-of-the-art baselines by significant margins.

cs.CV↗
arXiv2025

Polarisation in increasingly connected societies

Explanations of polarization often rely on one of the three mechanisms: homophily, bounded confidence, and community-based interactions. Models based on these mechanisms consider the lack of interactions as the main cause of polarization. Given the increasing connectivity in modern society, this explanation of polarization may be insufficient. We aim to show that in involvement-based models, society becomes more polarized as its connectedness increases. To this end, we propose a minimal voter-type model (called I-voter) that incorporates involvement as a key mechanism in opinion formation and study its dependence on network connectivity. We describe the steady-state behaviour of the model analytically, at the mean-field and the moment-hierarchy levels and stress the generality of our findings by considering various extensions and different network topologies.

physics.soc-ph↗
arXiv2025

Lightspeed Geometric Dataset Distance via Sliced Optimal Transport

We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embedding-agnostic approach for dataset comparison that requires no training, is robust to variations in the number of classes, and can handle disjoint label sets. The core innovation is Moment Transform Projection (MTP), which maps a label, represented as a distribution over features, to a real number. Using MTP, we derive a data point projection that transforms datasets into one-dimensional distributions. The s-OTDD is defined as the expected Wasserstein distance between the projected distributions, with respect to random projection parameters. Leveraging the closed form solution of one-dimensional optimal transport, s-OTDD achieves (near-)linear computational complexity in the number of data points and feature dimensions and is independent of the number of classes. With its geometrically meaningful projection, s-OTDD strongly correlates with the optimal transport dataset distance while being more efficient than existing dataset discrepancy measures. Moreover, it correlates well with the performance gap in transfer learning and classification accuracy in data augmentation.

cs.LG↗
arXiv2024

A District-level Ensemble Model to Enhance Dengue Prediction and Control for the Mekong Delta Region of Vietnam

The Mekong Delta Region of Vietnam faces increasing dengue risks driven by urbanization, globalization, and climate change. This study introduces a probabilistic forecasting model for predicting dengue incidence and outbreaks with one to three month lead times, integrating meteorological, sociodemographic, preventive, and epidemiological data. Seventy-two models were evaluated, and an ensemble combining top-performing spatiotemporal, supervised PCA, and semi-mechanistic hhh4 frameworks was developed. Using data from 2004-2022 for training, validation, and evaluation, the ensemble model demonstrated 69% accuracy at a 3-month horizon, outperforming a baseline model. While effective, its performance declined in years with atypical seasonality, such as 2019 and 2022. The model provides critical lead time for targeted dengue prevention and control measures, addressing a growing public health need in the region.

stat.AP↗