arXiv subjects

Jun Liao

Publications and source records attributed to Jun Liao.

At least 19 recordsLinked to original sources

arXiv2026

Thompson's Conjecture for Finite Simple Groups of Lie Type over Small Fields

We prove that every finite simple group of Lie type over a field of order at most 8 contains a conjugacy class whose square is the whole group. Together with the previously established cases, our results complete the proof of Thompson's conjecture. We explicitly construct the required class, address all low-rank identifications, and provide the precise computational certificates used in the exceptional character calculations.

math.GR↗

arXiv2026

Block-exoticity of reduction simple fusion systems on $S(n,p)$

In this paper, we prove that for $p\geq 13$ and $5\leq n\leq p-3$, every reduction simple fusion system on the finite $p$-group $S(n,p)$ is block-exotic. Furthermore, we establish the block-exoticity of three infinite families of reduction simple exotic fusion systems.

math.RT↗

arXiv2026

MoWorld: A Flash World Model

The future of World Models depends not only on scaling model capability, but also on scaling practicality and inference efficiency. High-frame-rate inference enables responsive perception, planning, and control in real-world autonomous systems. To this end, we present MoWorld, a cost-effective yet high-performance Flash World Model with an end-to-end framework spanning data generation, pre-training, distillation, and efficient inference, enabling up to 50 FPS real-time interaction with cinematic visual quality without the need of high-end GPUs. To enable large-scale real-world deployment, MoWorld jointly optimizes model capability and cost throughout the entire development pipeline. Specifically, unlike existing approaches that primarily rely on large-scale video corpora, MoWorld is built upon a scalable 3D-native data engine accumulated from our large-scale 3D vision and generative modeling pipeline, enabling the efficient construction of geometrically consistent training data across diverse real-world and synthetic environments. Based on this foundation, a curriculum cross-frame pre-training strategy for stable and scalable World Model learning, an efficient denoising-step distillation algorithm to reduce diffusion training cost, and a mixed-precision parallel inference framework for low-cost real-time deployment. MoWorld is the first real-time interactive World Model built on the Neural Processing Unit (NPU) and can achieves up to 50 FPS in such the devices, enabling practical and efficient deployment at scale. Comprehensive evaluations demonstrate that MoWorld achieves leading performance; notably, its average inference cost is only 30\%-50\% of that of existing World Models, providing a practical foundation for large-scale real-world applications of World Models. We also demonstrate diverse applications of MoWorld.

cs.CV↗

arXiv2026

Catalyst4D: High-Fidelity 3D-to-4D Scene Editing via Dynamic Propagation

Recent advances in 3D scene editing using NeRF and 3DGS enable high-quality static scene editing. In contrast, dynamic scene editing remains challenging, as methods that directly extend 2D diffusion models to 4D often produce motion artifacts, temporal flickering, and inconsistent style propagation. We introduce Catalyst4D, a framework that transfers high-quality 3D edits to dynamic 4D Gaussian scenes while maintaining spatial and temporal coherence. At its core, Anchor-based Motion Guidance (AMG) builds a set of structurally stable and spatially representative anchors from both original and edited Gaussians. These anchors serve as robust region-level references, and their correspondences are established via optimal transport to enable consistent deformation propagation without cross-region interference or motion drift. Complementarily, Color Uncertainty-guided Appearance Refinement (CUAR) preserves temporal appearance consistency by estimating per-Gaussian color uncertainty and selectively refining regions prone to occlusion-induced artifacts. Extensive experiments demonstrate that Catalyst4D achieves temporally stable, high-fidelity dynamic scene editing and outperforms existing methods in both visual quality and motion coherence.

cs.CV↗

arXiv2025

Heterogeneous Multisource Transfer Learning via Model Averaging for Positive-Unlabeled Data

Positive-Unlabeled (PU) learning presents unique challenges due to the lack of explicitly labeled negative samples, particularly in high-stakes domains such as fraud detection and medical diagnosis. To address data scarcity and privacy constraints, we propose a novel transfer learning with model averaging framework that integrates information from heterogeneous data sources - including fully binary labeled, semi-supervised, and PU data sets - without direct data sharing. For each source domain type, a tailored logistic regression model is conducted, and knowledge is transferred to the PU target domain through model averaging. Optimal weights for combining source models are determined via a cross-validation criterion that minimizes the Kullback-Leibler divergence. We establish theoretical guarantees for weight optimality and convergence, covering both misspecified and correctly specified target models, with further extensions to high-dimensional settings using sparsity-penalized estimators. Extensive simulations and real-world credit risk data analyses demonstrate that our method outperforms other comparative methods in terms of predictive accuracy and robustness, especially under limited labeled data and heterogeneous environments.

stat.ML↗

arXiv2025

Cross-Field Interface-Aware Neural Operators for Multiphase Flow Simulation

Multiphase flow simulation is critical in science and engineering but incurs high computational costs due to complex field discontinuities and the need for high-resolution numerical meshes. While Neural Operators (NOs) offer an efficient alternative for solving Partial Differential Equations (PDEs), they struggle with two core challenges unique to multiphase systems: spectral bias caused by spatial heterogeneity at phase interfaces, and the persistent scarcity of expensive, high-resolution field data. This work introduces the Interface Information Aware Neural Operator (IANO), a novel architecture that mitigates these issues by leveraging readily obtainable interface data (e.g., topology and position). Interface data inherently contains the high-frequency features not only necessary to complement the physical field data, but also help with spectral bias. IANO incorporates an interface-aware function encoding mechanism to capture dynamic coupling, and a geometry-aware positional encoding method to enhance spatial fidelity for pointwise super-resolution. Empirical results across multiple multiphase flow cases demonstrate that IANO achieves significant accuracy improvements (up to $\sim$10\%) over existing NO baselines. Furthermore, IANO exhibits superior generalization capabilities in low-data and noisy settings, confirming its utility for practical, data-efficient $\text{AI}$-based multiphase flow simulations.

physics.flu-dyn↗

arXiv2025

Network Model Averaging Prediction for Latent Space Models by K-Fold Edge Cross-Validation

In complex systems, networks represent connectivity relationships between nodes through edges. Latent space models are crucial in analyzing network data for tasks like community detection and link prediction due to their interpretability and visualization capabilities. However, when the network size is relatively small, and the true latent space dimension is considerable, the parameters in latent space models may not be estimated very well. To address this issue, we propose a Network Model Averaging (NetMA) method tailored for latent space models with varying dimensions, specifically focusing on link prediction in networks. For both single-layer and multi-layer networks, we first establish the asymptotic optimality of the proposed averaging prediction in the sense of achieving the lowest possible prediction loss. Then we show that when the candidate models contain some correct models, our method assigns all weights to the correct models. Furthermore, we demonstrate the consistency of the NetMA-based weight estimator tending to the optimal weight vector. Extensive simulation studies show that NetMA performs better than simple averaging and model selection methods, and even outperforms the "oracle" method when the real latent space dimension is relatively large. Evaluation on collaboration and virtual event networks further emphasizes the competitiveness of NetMA in link prediction performance.

stat.ME↗

arXiv2025

Decomposing and Fusing Intra- and Inter-Sensor Spatio-Temporal Signal for Multi-Sensor Wearable Human Activity Recognition

Wearable Human Activity Recognition (WHAR) is a prominent research area within ubiquitous computing. Multi-sensor synchronous measurement has proven to be more effective for WHAR than using a single sensor. However, existing WHAR methods use shared convolutional kernels for indiscriminate temporal feature extraction across each sensor variable, which fails to effectively capture spatio-temporal relationships of intra-sensor and inter-sensor variables. We propose the DecomposeWHAR model consisting of a decomposition phase and a fusion phase to better model the relationships between modality variables. The decomposition creates high-dimensional representations of each intra-sensor variable through the improved Depth Separable Convolution to capture local temporal features while preserving their unique characteristics. The fusion phase begins by capturing relationships between intra-sensor variables and fusing their features at both the channel and variable levels. Long-range temporal dependencies are modeled using the State Space Model (SSM), and later cross-sensor interactions are dynamically captured through a self-attention mechanism, highlighting inter-sensor spatial correlations. Our model demonstrates superior performance on three widely used WHAR datasets, significantly outperforming state-of-the-art models while maintaining acceptable computational efficiency.

cs.CV↗

arXiv2024

Criteria for nilpotency of fusion systems

Let $p$ be an odd prime and let $\mathcal{F}$ be a fusion system over a finite $p$-group $P$. A fusion system $\mathcal{F}$ is said to be nilpotent if $\mathcal{F}=\mathcal{F}_{P}(P)$. In this paper we provide new criteria for saturated fusion systems $\mathcal{F}$ to be nilpotent, which can be viewed as extension of the $p$-nilpotency theorem of Glauberman and Thompson for fusion systems attributed to Kessar and Linckelmann.

math.GR↗

arXiv2023

The kernels of powers of linear operator via Weyr characteristic

The adjoint of a matrix in the Lie algebra associated with a matrix algebra is a fundamental operator, which can be generalized to a more general operator $\varphi_{AB}: X\rightarrow AX-XB$ by two matrices $A$ and $B$. The kernel of the operator is very well-known and it can be found in Gantmacher's book. The formulas for the dimensions of the kernels of arbitrary powers of the operator $\varphi_{AB}$ were given in terms of the Segre characteristics of these two matrices by the second and third authors in this paper and their collaborators. This paper provides an alternative approach to this problem via the Weyr characteristic in a more essential method. We obtain formulas for the dimensions of the kernels of arbitrary powers of the operator in terms of the Weyr characteristics. Furthermore, the basis for kernel of each power of the operator is described explicitly. As a consequence, for arbitrary square matrices $A$ and $B$ over an algebraically closed field, the dimension of the kernel of each power of the operator $\varphi_{A-\lambda I,B}$ for eigenvalues $\lambda$ of $\varphi_{AB}$ can be viewed as a similarity invariant of the operator $\varphi_{AB}$, so we characterise the operator within similarity, which should be of interest to a number of people (including physicists).

math.RA↗

arXiv2022

Multifold Cross-Validation Model Averaging for Generalized Additive Partial Linear Models

Generalized additive partial linear models (GAPLMs) are appealing for model interpretation and prediction. However, for GAPLMs, the covariates and the degree of smoothing in the nonparametric parts are often difficult to determine in practice. To address this model selection uncertainty issue, we develop a computationally feasible model averaging (MA) procedure. The model weights are data-driven and selected based on multifold cross-validation (CV) (instead of leave-one-out) for computational saving. When all the candidate models are misspecified, we show that the proposed MA estimator for GAPLMs is asymptotically optimal in the sense of achieving the lowest possible Kullback-Leibler loss. In the other scenario where the candidate model set contains at least one correct model, the weights chosen by the multifold CV are asymptotically concentrated on the correct models. As a by-product, we propose a variable importance measure to quantify the importances of the predictors in GAPLMs based on the MA weights. It is shown to be able to asymptotically identify the variables in the true model. Moreover, when the number of candidate models is very large, a model screening method is provided. Numerical experiments show the superiority of the proposed MA method over some existing model averaging and selection methods.

stat.ME↗

arXiv2022

On the local rank of fusion systems

In this paper we define the notion of local rank for fusion systems so as to reformulate the Alperin's weight conjecture in the framework of block fusion systems following the work by Knörr and Robinson.

math.GR↗

arXiv2021

Resolution-enhanced parallel coded ptychography for high-throughput optical imaging

Ptychography is an enabling coherent diffraction imaging technique for both fundamental and applied sciences. Its applications in optical microscopy, however, fall short for its low imaging throughput and limited resolution. Here, we report a resolution-enhanced parallel coded ptychography technique achieving the highest numerical aperture and an imaging throughput orders of magnitude greater than previous demonstrations. In this platform, we translate the samples across the disorder-engineered surfaces for lensless diffraction data acquisition. The engineered surface consists of chemically etched micron-level phase scatters and printed sub-wavelength intensity absorbers. It is designed to unlock an optical space with spatial extent (x, y) and frequency content (kx, ky) that is inaccessible using conventional lens-based optics. To achieve the best resolution performance, we also report a new coherent diffraction imaging model by considering both the spatial and angular responses of the pixel readouts. Our low-cost prototype can directly resolve 308-nm linewidth on the resolution target without aperture synthesizing. Gigapixel high-resolution microscopic images with a 240-mm^2 effective field of view can be acquired in 15 seconds. For demonstrations, we recover slow-varying 3D phase objects with many 2π wraps, including optical prism and convex lens. The low-frequency phase contents of these objects are challenging to obtain using other existing lensless techniques. For digital pathology applications, we perform accurate virtual staining by using the recovered phase as attention guidance in a deep neural network. Parallel optical processing using the reported technique enables novel optical instruments with inherent quantitative nature and metrological versatility.

physics.optics↗

arXiv2020

Blind deblurring for microscopic pathology images using deep learning networks

Artificial Intelligence (AI)-powered pathology is a revolutionary step in the world of digital pathology and shows great promise to increase both diagnosis accuracy and efficiency. However, defocus and motion blur can obscure tissue or cell characteristics hence compromising AI algorithms'accuracy and robustness in analyzing the images. In this paper, we demonstrate a deep-learning-based approach that can alleviate the defocus and motion blur of a microscopic image and output a sharper and cleaner image with retrieved fine details without prior knowledge of the blur type, blur extent and pathological stain. In this approach, a deep learning classifier is first trained to identify the image blur type. Then, two encoder-decoder networks are trained and used alone or in combination to deblur the input image. It is an end-to-end approach and introduces no corrugated artifacts as traditional blind deconvolution methods do. We test our approach on different types of pathology specimens and demonstrate great performance on image blur correction and the subsequent improvement on the diagnosis outcome of AI algorithms.

eess.IV↗

arXiv2020

LoCEC: Local Community-based Edge Classification in Large Online Social Networks

Relationships in online social networks often imply social connections in the real world. An accurate understanding of relationship types benefits many applications, e.g. social advertising and recommendation. Some recent attempts have been proposed to classify user relationships into predefined types with the help of pre-labeled relationships or abundant interaction features on relationships. Unfortunately, both relationship feature data and label data are very sparse in real social platforms like WeChat, rendering existing methods inapplicable. In this paper, we present an in-depth analysis of WeChat relationships to identify the major challenges for the relationship classification task. To tackle the challenges, we propose a Local Community-based Edge Classification (LoCEC) framework that classifies user relationships in a social network into real-world social connection types. LoCEC enforces a three-phase processing, namely local community detection, community classification and relationship classification, to address the sparsity issue of relationship features and relationship labels. Moreover, LoCEC is designed to handle large-scale networks by allowing parallel and distributed processing. We conduct extensive experiments on the real-world WeChat network with hundreds of billions of edges to validate the effectiveness and efficiency of LoCEC.

cs.SI↗

arXiv2020

Predicting Long-Term Skeletal Motions by a Spatio-Temporal Hierarchical Recurrent Network

The primary goal of skeletal motion prediction is to generate future motion by observing a sequence of 3D skeletons. A key challenge in motion prediction is the fact that a motion can often be performed in several different ways, with each consisting of its own configuration of poses and their spatio-temporal dependencies, and as a result, the predicted poses often converge to the motionless poses or non-human like motions in long-term prediction. This leads us to define a hierarchical recurrent network model that explicitly characterizes these internal configurations of poses and their local and global spatio-temporal dependencies. The model introduces a latent vector variable from the Lie algebra to represent spatial and temporal relations simultaneously. Furthermore, a structured stack LSTM-based decoder is devised to decode the predicted poses with a new loss function defined to estimate the quantized weight of each body part in a pose. Empirical evaluations on benchmark datasets suggest our approach significantly outperforms the state-of-the-art methods on both short-term and long-term motion prediction.

cs.CV↗

arXiv2019

Near-field Fourier ptychography: super-resolution phase retrieval via speckle illumination

Achieving high spatial resolution is the goal of many imaging systems. Designing a high-resolution lens with diffraction-limited performance over a large field of view remains a difficult task in imaging system design. On the other hand, creating a complex speckle pattern with wavelength-limited spatial features is effortless and can be implemented via a simple random diffuser. With this observation and inspired by the concept of near-field ptychography, we report a new imaging modality, termed near-field Fourier ptychography, for tackling high-resolution imaging challenges in both microscopic and macroscopic imaging settings. The meaning of 'near-field' is referred to placing the object at a short defocus distance with a large Fresnel number. In our implementations, we project a speckle pattern with fine spatial features on the object instead of directly resolving the spatial features via a high-resolution lens. We then translate the object (or speckle) to different positions and acquire the corresponding images using a low-resolution lens. A ptychographic phase retrieval process is used to recover the complex object, the unknown speckle pattern, and the coherent transfer function at the same time. In a microscopic imaging setup, we use a 0.12 numerical aperture (NA) lens to achieve a NA of 0.85 in the reconstruction process. In a macroscale photographic imaging setup, we achieve ~7-fold resolution gain using a photographic lens. The final achievable resolution is not determined by the collection optics. Instead, it is determined by the feature size of the speckle pattern. The reported imaging modality can be employed in light, coherent X-ray, and transmission electron imaging systems to increase resolution and provide quantitative absorption and phase contrast of the object.

physics.optics↗

arXiv2018

Axially-shifted pattern illumination for macroscale turbidity suppression and virtual volumetric confocal imaging without axial scanning

Structured illumination has been widely used for optical sectioning and 3D surface recovery. In a typical implementation, multiple images under non-uniform pattern illumination are used to recover a single object section. Axial scanning of the sample or the objective lens is needed for acquiring the 3D volumetric data. Here we demonstrate the use of axially-shifted pattern illumination (asPI) for virtual volumetric confocal imaging without axial scanning. In the reported approach, we project illumination patterns at a tilted angle with respect to the detection optics. As such, the illumination patterns shift laterally at different z sections and the sample information at different z-sections can be recovered based on the captured 2D images. We demonstrate the reported approach for virtual confocal imaging through a diffusing layer and underwater 3D imaging through diluted milk. We show that we can acquire the entire confocal volume in ~1s with a throughput of 420 megapixels per second. Our approach may provide new insights for developing confocal light ranging and detection systems in degraded visual environments.

cs.CV↗