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Junhao Zhang

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Computer Vision math.AP Distributed, Parallel, and Cluster Computing eess.IV Machine Learning math-ph math.MP physics.soc-ph Quantitative Methods Social and Information Networks

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preprint2026arXiv

Asymptotic stability of steady states for the compressible Navier-Stokes-Riesz system in the presence of vacuum

We consider a one-dimensional physical vacuum free boundary problem on the compressible Navier-Stokes-Riesz system for an attractive Riesz potential $|x|^{2s-1}/(2s-1)$ with $0<s<1/2$. It is proved that for the adiabatic constant $γ$ satisfying $2(1-s)<γ<1+2s/3$ under the additional condition that $3/8<s<1/2$, there exists a unique global-in-time strong solution. Specifically, we establish the Lyapunov-type stability of the compactly supported steady states in the Lagrangian coordinates and we also obtain the time rate of convergence for the strong solution to steady states with the same mass in weighted Sobolev spaces where the weights indicate the behavior of solutions near the vacuum free boundary. The difficulties and challenges in the proof are caused not only by the degeneracy due to the vacuum free boundary but also by the non-local feature of the Riesz potential.

preprint2026arXiv

Runtime-Orchestrated Second-Order Optimization for Scalable LLM Training

Second-order methods offer an attractive path toward more sample-efficient LLM training, but their practical use is often blocked by the systems cost of maintaining and updating large matrix-based optimizer states. We introduce \textbf{Asteria}, a runtime system designed to remove this bottleneck by separating second-order optimization logic from the critical GPU training path. Rather than keeping all preconditioner state on the accelerator, Asteria dynamically distributes optimizer state across GPU memory, CPU memory, and optional NVMe storage according to architectural constraints and runtime pressure. It further uses training hooks to prepare shadow states in advance, allowing expensive inverse-root computations to proceed asynchronously on the host while GPU computation continues. For distributed training, Asteria employs a bounded-staleness protocol that limits synchronization frequency while preserving optimizer effectiveness through topology-aware coordination. We evaluate Asteria on both memory-constrained and distributed training settings. On a DGX Spark platform with a single GB10 GPU and 128GB unified memory, Asteria supports second-order training for a 1B-parameter language model. On multi-node GH200 systems, it lowers visible optimizer overhead, reduces recurring latency spikes, accelerates convergence in wall-clock time, and maintains the optimization advantages of SOAP and KL-Shampoo in a 7B-parameter language model. Our results suggest that second-order LLM training can be made practical not by simplifying the optimizer alone, but by rethinking how optimizer state, background computation, and distributed synchronization are managed at the runtime level.

preprint2022arXiv

Detecting Schizophrenia with 3D Structural Brain MRI Using Deep Learning

Schizophrenia is a chronic neuropsychiatric disorder that causes distinct structural alterations within the brain. We hypothesize that deep learning applied to a structural neuroimaging dataset could detect disease-related alteration and improve classification and diagnostic accuracy. We tested this hypothesis using a single, widely available, and conventional T1-weighted MRI scan, from which we extracted the 3D whole-brain structure using standard post-processing methods. A deep learning model was then developed, optimized, and evaluated on three open datasets with T1-weighted MRI scans of patients with schizophrenia. Our proposed model outperformed the benchmark model, which was also trained with structural MR images using a 3D CNN architecture. Our model is capable of almost perfectly (area under the ROC curve = 0.987) distinguishing schizophrenia patients from healthy controls on unseen structural MRI scans. Regional analysis localized subcortical regions and ventricles as the most predictive brain regions. Subcortical structures serve a pivotal role in cognitive, affective, and social functions in humans, and structural abnormalities of these regions have been associated with schizophrenia. Our finding corroborates that schizophrenia is associated with widespread alterations in subcortical brain structure and the subcortical structural information provides prominent features in diagnostic classification. Together, these results further demonstrate the potential of deep learning to improve schizophrenia diagnosis and identify its structural neuroimaging signatures from a single, standard T1-weighted brain MRI.

preprint2022arXiv

Global Regularity for A Radiation Hydrodynamics Model with Viscosity and Thermal Conductivity

In this paper, we study the global wellposedness of a radiation hydrodynamics model with viscosity and thermal conductivity. It is now well-understood that, unlike the compressible Euler equations whose smooth solutions must blow up in finite time no matter how small and how smooth the initial data is, the dissipative structure of such a radiation hydrodynamics model can indeed guarantee that its one-dimensional Cauchy problem admits a unique global smooth solution provided that the initial data is sufficiently small, while for large initial data, even if the heat conductivity is taken into account but the viscosity effect is ignored, shock type singularities must appear in finite time for smooth solutions of the Cauchy problem of one-dimensional radiation hydrodynamics model with thermal conductivity and zero viscosity. Thus a natural question is, if effects of both the viscosity and the thermal conductivity are considered, does the one-dimensional radiation hydrodynamics model with viscosity and thermal conductivity exist a unique global large solution? We give an affirmative answer to this problem and show in this paper that the initial-boundary value problem to the radiation hydrodynamics model in an one-dimensional periodic box T = R/Z with viscosity and thermal conductivity does exist a unique global smooth solution for any large initial data. The main ingredient in our analysis is to introduce some delicate estimates, especially an improved estimate on the absolute temperature and a pointwise estimate between the absolute temperature, the specific volume, and the first-order spatial derivative of the macro radiation flux, to deduce the desired positive lower and upper bounds on the density and the absolute temperature.

preprint2021arXiv

Learning Geometry-Disentangled Representation for Complementary Understanding of 3D Object Point Cloud

In 2D image processing, some attempts decompose images into high and low frequency components for describing edge and smooth parts respectively. Similarly, the contour and flat area of 3D objects, such as the boundary and seat area of a chair, describe different but also complementary geometries. However, such investigation is lost in previous deep networks that understand point clouds by directly treating all points or local patches equally. To solve this problem, we propose Geometry-Disentangled Attention Network (GDANet). GDANet introduces Geometry-Disentangle Module to dynamically disentangle point clouds into the contour and flat part of 3D objects, respectively denoted by sharp and gentle variation components. Then GDANet exploits Sharp-Gentle Complementary Attention Module that regards the features from sharp and gentle variation components as two holistic representations, and pays different attentions to them while fusing them respectively with original point cloud features. In this way, our method captures and refines the holistic and complementary 3D geometric semantics from two distinct disentangled components to supplement the local information. Extensive experiments on 3D object classification and segmentation benchmarks demonstrate that GDANet achieves the state-of-the-arts with fewer parameters. Code is released on https://github.com/mutianxu/GDANet.

preprint2015arXiv

On the relationship between Gaussian stochastic blockmodels and label propagation algorithms

The problem of community detection receives great attention in recent years. Many methods have been proposed to discover communities in networks. In this paper, we propose a Gaussian stochastic blockmodel that uses Gaussian distributions to fit weight of edges in networks for non-overlapping community detection. The maximum likelihood estimation of this model has the same objective function as general label propagation with node preference. The node preference of a specific vertex turns out to be a value proportional to the intra-community eigenvector centrality (the corresponding entry in principal eigenvector of the adjacency matrix of the subgraph inside that vertex's community) under maximum likelihood estimation. Additionally, the maximum likelihood estimation of a constrained version of our model is highly related to another extension of label propagation algorithm, namely, the label propagation algorithm under constraint. Experiments show that the proposed Gaussian stochastic blockmodel performs well on various benchmark networks.