Xi Han

Jingwei Zhang, Anh Tien Nguyen, Xi Han et al.

Efficiently modeling large 2D contexts is essential for various fields including Giga-Pixel Whole Slide Imaging (WSI) and remote sensing. Transformer-based models offer high parallelism but face challenges due to their quadratic complexity for handling long sequences. Recently, Mamba introduced a selective State Space Model (SSM) with linear complexity and high parallelism, enabling effective and efficient modeling of wide context in 1D sequences. However, extending Mamba to vision tasks, which inherently involve 2D structures, results in spatial discrepancies due to the limitations of 1D sequence processing. On the other hand, current 2D SSMs inherently model 2D structures but they suffer from prohibitively slow computation due to the lack of efficient parallel algorithms. In this work, we propose 2DMamba, a novel 2D selective SSM framework that incorporates the 2D spatial structure of images into Mamba, with a highly optimized hardware-aware operator, adopting both spatial continuity and computational efficiency. We validate the versatility of our approach on both WSIs and natural images. Extensive experiments on 10 public datasets for WSI classification and survival analysis show that 2DMamba improves up to 2.48% in AUC, 3.11% in F1 score, 2.47% in accuracy and 5.52% in C-index. Additionally, integrating our method with VMamba for natural imaging yields 0.5 to 0.7 improvements in mIoU on the ADE20k semantic segmentation dataset, and 0.2% accuracy improvement on ImageNet-1K classification dataset. Our code is available at https://github.com/AtlasAnalyticsLab/2DMamba.

Xi Han, Fei Hou, Hong Qin

Numerical solvers of Partial Differential Equations (PDEs) are of fundamental significance to science and engineering. To date, the historical reliance on legacy techniques has circumscribed possible integration of big data knowledge and exhibits sub-optimal efficiency for certain PDE formulations, while data-driven neural methods typically lack mathematical guarantee of convergence and correctness. This paper articulates a mathematically rigorous neural solver for linear PDEs. The proposed UGrid solver, built upon the principled integration of U-Net and MultiGrid, manifests a mathematically rigorous proof of both convergence and correctness, and showcases high numerical accuracy, as well as strong generalization power to various input geometry/values and multiple PDE formulations. In addition, we devise a new residual loss metric, which enables unsupervised training and affords more stability and a larger solution space over the legacy losses.

Jingwei Zhang, Xi Han, Hong Qin et al.

Mamba, a State Space Model (SSM) that accelerates training by recasting recurrence as a parallel scan, has recently emerged as a linearly-scaling alternative to self-attention. Because of its unidirectional nature, each state in Mamba only has information of its previous states and is blind to states after. Current Mamba-based computer-vision methods typically overcome this by augmenting Mamba's global forward scan with a global backward scan, forming a bi-directional scan to restore a full receptive field. However, this operation doubles the computational load, eroding much of the efficiency advantage that originally Mamba have. To eliminate this extra scans, we introduce LBMamba, a locally bi-directional SSM block that embeds a lightweight locally backward scan inside the forward scan and executes it in per-thread registers. Building on LBMamba, we present LBVim, a backbone that alternates scan directions every two layers to recover a global receptive field without extra backward sweeps. We validate our approach on both natural images and whole slide images (WSIs) and show that it constantly offers a superior performance-throughput trade-off. Under the same throughput, LBVim achieves 0.8% to 1.6% higher top-1 accuracy on the ImageNet-1K classification dataset, 0.6% to 2.7% higher mIoU on the ADE20K semantic segmentation dataset, 0.9% higher APb and 1.1% higher APm on the COCO detection dataset. Our method also boosts the accuracy of four SOTA Mamba models, namely VMamba, LocalVim, PlainMamba and Adventurer, by 0.5% to 3.4%. We integrate LBMamba into the SOTA pathology multiple instance learning (MIL) model, MambaMIL, which is unidirectional. Experiments on 3 public WSI classification datasets show that our method achieves a relative improvement of up to 3.06% better AUC, 3.39% better F1, 1.67% better accuracy. Our code is available at https://github.com/cvlab-stonybrook/LBMamba.

Alexander Benanti, Xi Han, Hong Qin

Numerical techniques for solving partial differential equations (PDEs) are integral for many fields across science and engineering. Such techniques usually involve solving large, sparse linear systems, where preconditioning methods are critical. In recent years, neural methods, particularly graph neural networks (GNNs), have demonstrated their potential through accelerated convergence. Nonetheless, to extract connective structures, existing techniques aggregate discretized system matrices into graphs, and suffer from rank inflation and a suboptimal convergence rate. In this paper, we articulate NeuraLSP, a novel neural preconditioner combined with a novel loss metric that leverages the left singular subspace of the system matrix's near-nullspace vectors. By compressing spectral information into a fixed low-rank operator, our method exhibits both theoretical guarantees and empirical robustness to rank inflation, affording up to a 53% speedup. Besides the theoretical guarantees for our newly-formulated loss function, our comprehensive experimental results across diverse families of PDEs also substantiate the aforementioned theoretical advances.

Xi Han, Jingwei Zhang, Dimitris Samaras et al.

The neural operator (NO) framework has emerged as a powerful tool for solving partial differential equations (PDEs). Recent NOs are dominated by the Transformer architecture, which offers NOs the capability to capture long-range dependencies in PDE dynamics. However, existing Transformer-based NOs suffer from quadratic complexity, lack geometric rigor, and thus suffer from sub-optimal performance on regular grids. As a remedy, we propose the Geometric Mamba Neural Operator (GeoMaNO) framework, which empowers NOs with Mamba's modeling capability, linear complexity, plus geometric rigor. We evaluate GeoMaNO's performance on multiple standard and popularly employed PDE benchmarks, spanning from Darcy flow problems to Navier-Stokes problems. GeoMaNO improves existing baselines in solution operator approximation by as much as 58.9%.

Jiaxi Ying, Xi Han, Rui Zhou et al.

We tackle the network topology inference problem by utilizing Laplacian constrained Gaussian graphical models, which recast the task as estimating a precision matrix in the form of a graph Laplacian. Recent research \cite{ying2020nonconvex} has uncovered the limitations of the widely used $\ell_1$-norm in learning sparse graphs under this model: empirically, the number of nonzero entries in the solution grows with the regularization parameter of the $\ell_1$-norm; theoretically, a large regularization parameter leads to a fully connected (densest) graph. To overcome these challenges, we propose a graph Laplacian estimation method incorporating the $\ell_0$-norm constraint. An efficient gradient projection algorithm is developed to solve the resulting optimization problem, characterized by sparsity and Laplacian constraints. Through numerical experiments with synthetic and financial time-series datasets, we demonstrate the effectiveness of the proposed method in network topology inference.

Song-Hai Zhang, Ruilong Li, Xin Dong et al.

The standard approach to image instance segmentation is to perform the object detection first, and then segment the object from the detection bounding-box. More recently, deep learning methods like Mask R-CNN perform them jointly. However, little research takes into account the uniqueness of the "human" category, which can be well defined by the pose skeleton. Moreover, the human pose skeleton can be used to better distinguish instances with heavy occlusion than using bounding-boxes. In this paper, we present a brand new pose-based instance segmentation framework for humans which separates instances based on human pose, rather than proposal region detection. We demonstrate that our pose-based framework can achieve better accuracy than the state-of-art detection-based approach on the human instance segmentation problem, and can moreover better handle occlusion. Furthermore, there are few public datasets containing many heavily occluded humans along with comprehensive annotations, which makes this a challenging problem seldom noticed by researchers. Therefore, in this paper we introduce a new benchmark "Occluded Human (OCHuman)", which focuses on occluded humans with comprehensive annotations including bounding-box, human pose and instance masks. This dataset contains 8110 detailed annotated human instances within 4731 images. With an average 0.67 MaxIoU for each person, OCHuman is the most complex and challenging dataset related to human instance segmentation. Through this dataset, we want to emphasize occlusion as a challenging problem for researchers to study.