arXiv subjects

Xiaobo Liu

Publications and source records attributed to Xiaobo Liu.

At least 37 records · Page 2Linked to original sources

arXiv2025

A scaling and recovering algorithm for the matrix $φ$-functions

A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $φ$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential equations. The algorithm initially scales the input matrix down by a nonnegative integer power of two, and then evaluates the $[m/m]$ diagonal Padé approximant to $φ_p$, where $p$ is the largest index of interest. The remaining $[m+p{-}j/m]$ Padé approximants to $φ_j$, $0 \le j < p$, are obtained implicitly via a recurrence relation. The effect of scaling is subsequently recovered using the double-argument formula. A rigorous backward error analysis, based on the $[m+p/m]$ Padé approximant to the exponential, enables sharp bounds on the relative backward errors. These bounds are expressed in terms of the sequence $\|A^k\|^{1/k}$, which can be much smaller than $\|A\|$ for nonnormal matrices. The scaling parameter and the degrees of the Padé approximants are selected to minimize the overall computational cost, which benefits from the sharp bounds and the optimal evaluation schemes for diagonal Padé approximants. Furthermore, if the input matrix is (quasi-)triangular, the algorithm exploits its structure in the recovering phase. Numerical experiments demonstrate the superiority of the proposed algorithm over existing alternatives in both accuracy and efficiency.

math.NA↗

arXiv2025

Bridging Foundation Models and Efficient Architectures: A Modular Brain Imaging Framework with Local Masking and Pretrained Representation Learning

Functional connectivity (FC) derived from resting-state fMRI plays a critical role in personalized predictions such as age and cognitive performance. However, applying foundation models(FM) to fMRI data remains challenging due to its high dimensionality, computational complexity, and the difficulty in capturing complex spatiotemporal dynamics and indirect region-of-interest (ROI) interactions. To address these limitations, we propose a modular neuroimaging framework that integrates principles from FM with efficient, domain-specific architectures. Our approach begins with a Local Masked Autoencoder (LMAE) for pretraining, which reduces the influence of hemodynamic response function (HRF) dynamics and suppresses noise. This is followed by a Random Walk Mixture of Experts (RWMOE) module that clusters features across spatial and temporal dimensions, effectively capturing intricate brain interactions. Finally, a state-space model (SSM)-based predictor performs downstream task inference. Evaluated on the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) dataset, our framework achieved mean absolute errors (MAEs) of 5.343 for age prediction and 2.940 for fluid intelligence, with Pearson correlation coefficients (PCCs) of 0.928 and 0.887, respectively-outperforming existing state-of-the-art methods. Visualization of expert distribution weights further enhances interpretability by identifying key brain regions. This work provides a robust, interpretable alternative to LLM-based approaches for fMRI analysis, offering novel insights into brain aging and cognitive function.

q-bio.NC↗

arXiv2025

A Federated Learning Framework for Handling Subtype Confounding and Heterogeneity in Large-Scale Neuroimaging Diagnosis

Computer-aided diagnosis (CAD) systems play a crucial role in analyzing neuroimaging data for neurological and psychiatric disorders. However, small-sample studies suffer from low reproducibility, while large-scale datasets introduce confounding heterogeneity due to multiple disease subtypes being labeled under a single category. To address these challenges, we propose a novel federated learning framework tailored for neuroimaging CAD systems. Our approach includes a dynamic navigation module that routes samples to the most suitable local models based on latent subtype representations, and a meta-integration module that combines predictions from heterogeneous local models into a unified diagnostic output. We evaluated our framework using a comprehensive dataset comprising fMRI data from over 1300 MDD patients and 1100 healthy controls across multiple study cohorts. Experimental results demonstrate significant improvements in diagnostic accuracy and robustness compared to traditional methods. Specifically, our framework achieved an average accuracy of 74.06\% across all tested sites, showcasing its effectiveness in handling subtype heterogeneity and enhancing model generalizability. Ablation studies further confirmed the importance of both the dynamic navigation and meta-integration modules in improving performance. By addressing data heterogeneity and subtype confounding, our framework advances reliable and reproducible neuroimaging CAD systems, offering significant potential for personalized medicine and clinical decision-making in neurology and psychiatry.

cs.LG↗

arXiv2025

Comorbidity-Informed Transfer Learning for Neuro-developmental Disorder Diagnosis

Neuro-developmental disorders are manifested as dysfunctions in cognition, communication, behaviour and adaptability, and deep learning-based computer-aided diagnosis (CAD) can alleviate the increasingly strained healthcare resources on neuroimaging. However, neuroimaging such as fMRI contains complex spatio-temporal features, which makes the corresponding representations susceptible to a variety of distractions, thus leading to less effective in CAD. For the first time, we present a Comorbidity-Informed Transfer Learning(CITL) framework for diagnosing neuro-developmental disorders using fMRI. In CITL, a new reinforced representation generation network is proposed, which first combines transfer learning with pseudo-labelling to remove interfering patterns from the temporal domain of fMRI and generates new representations using encoder-decoder architecture. The new representations are then trained in an architecturally simple classification network to obtain CAD model. In particular, the framework fully considers the comorbidity mechanisms of neuro-developmental disorders and effectively integrates them with semi-supervised learning and transfer learning, providing new perspectives on interdisciplinary. Experimental results demonstrate that CITL achieves competitive accuracies of 76.32% and 73.15% for detecting autism spectrum disorder and attention deficit hyperactivity disorder, respectively, which outperforms existing related transfer learning work for 7.2% and 0.5% respectively.

cs.LG↗

arXiv2025

A Confounding Factors-Inhibition Adversarial Learning Framework for Multi-site fMRI Mental Disorder Identification

In open data sets of functional magnetic resonance imaging (fMRI), the heterogeneity of the data is typically attributed to a combination of factors, including differences in scanning procedures, the presence of confounding effects, and population diversities between multiple sites. These factors contribute to the diminished effectiveness of representation learning, which in turn affects the overall efficacy of subsequent classification procedures. To address these limitations, we propose a novel multi-site adversarial learning network (MSalNET) for fMRI-based mental disorder detection. Firstly, a representation learning module is introduced with a node information assembly (NIA) mechanism to better extract features from functional connectivity (FC). This mechanism aggregates edge information from both horizontal and vertical directions, effectively assembling node information. Secondly, to generalize the feature across sites, we proposed a site-level feature extraction module that can learn from individual FC data, which circumvents additional prior information. Lastly, an adversarial learning network is proposed as a means of balancing the trade-off between individual classification and site regression tasks, with the introduction of a novel loss function. The proposed method was evaluated on two multi-site fMRI datasets, i.e., Autism Brain Imaging Data Exchange (ABIDE) and ADHD-200. The results indicate that the proposed method achieves a better performance than other related algorithms with the accuracy of 75.56 and 68.92 in ABIDE and ADHD-200 datasets, respectively. Furthermore, the result of the site regression indicates that the proposed method reduces site variability from a data-driven perspective. The most discriminative brain regions revealed by NIA are consistent with statistical findings, uncovering the "black box" of deep learning to a certain extent.

cs.LG↗

arXiv2025

A note on the cross matrices

A cross matrix $X$ can have nonzero elements located only on the main diagonal and the anti-diagonal, so that the sparsity pattern has the shape of a cross. It is shown that $X$ can be factorized into products of matrices that are at most rank-two perturbations to the identity matrix and can be symmetrically permuted to block diagonal form with $2\times 2$ diagonal blocks and, if $n$ is odd, a $1\times 1$ diagonal block. The permutation similarity implies that any well-defined analytic function of $X$ remains a cross matrix. By exploiting these properties, explicit formulae for the determinant, inverse, and characteristic polynomial are derived. It is also shown that the structure of cross matrix can be preserved under matrix factorizations, including the LU, QR, and SVD decompositions.

math.NA↗

arXiv2025

Action of $W$-type operators on Schur functions and Schur Q-functions

In this paper, we investigate a series of W-type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all operators in the W-constraints for tau functions of higher KdV hierarchies which satisfy the string equation. We will give simple uniform formulas for actions of these operators on all ordinary Schur functions and Schur's Q-functions. As applications of such formulas, we will give new simple proofs for Alexandrov's conjecture and Mironov-Morozov's formula, which express the Brézin-Gross-Witten and Kontsevich-Witten tau-functions as linear combinations of Q-functions with simple coefficients respectively.

math-ph↗

arXiv2025

Mixed precision HODLR matrices

Hierarchical matrix computations have attracted significant attention in the science and engineering community as exploiting data-sparse structures can significantly reduce the computational complexity of many important kernels. One particularly popular option within this class is the Hierarchical Off-Diagonal Low-Rank (HODLR) format. In this paper, we show that the off-diagonal blocks of HODLR matrices that are approximated by low-rank matrices can be represented in low precision without degenerating the quality of the overall approximation (with the error growth bounded by a factor of $2$). We also present an adaptive-precision scheme for constructing and storing HODLR matrices, and we prove that the use of mixed precision does not compromise the numerical stability of the resulting HODLR matrix--vector product and LU factorization. That is, the resulting error in these computations is not significantly greater than the case where we use one precision (say, double) for constructing and storing the HODLR matrix. Our analyses further give insight on how one must choose the working precision in HODLR matrix computations relative to the approximation error in order to not observe the effects of finite precision. Intuitively, when a HODLR matrix is subject to a high degree of approximation error, subsequent computations can be performed in a lower precision without detriment. We demonstrate the validity of our theoretical results through a range of numerical experiments.

math.NA↗

arXiv2024

Mixed-Precision Paterson--Stockmeyer Method for Evaluating Polynomials of Matrices

The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing transcendental matrix functions. We derive a mixed-precision version of the Paterson--Stockmeyer method that is particularly useful for evaluating matrix polynomials with scalar coefficients of decaying magnitude. The new method is mainly of interest in the arbitrary precision arithmetic, and it is attractive for high-precision computations. The key idea is to perform computations on data of small magnitude in low precision, and rounding error analysis is provided for the use of lower-than-the-working precisions. We focus on the evaluation of the Taylor approximants of the matrix exponential and show the applicability of our method to the existing scaling and squaring algorithms. We also demonstrate through experiments the general applicability of our method to other problems, such as computing the polynomials from the Padé approximant of the matrix exponential and the Taylor approximant of the matrix cosine. Numerical experiments show our mixed-precision Paterson--Stockmeyer algorithms can be more efficient than its fixed-precision counterpart while delivering the same level of accuracy.

math.NA↗

arXiv2024

Proprioceptive Learning with Soft Polyhedral Networks

Proprioception is the "sixth sense" that detects limb postures with motor neurons. It requires a natural integration between the musculoskeletal systems and sensory receptors, which is challenging among modern robots that aim for lightweight, adaptive, and sensitive designs at a low cost. Here, we present the Soft Polyhedral Network with an embedded vision for physical interactions, capable of adaptive kinesthesia and viscoelastic proprioception by learning kinetic features. This design enables passive adaptations to omni-directional interactions, visually captured by a miniature high-speed motion tracking system embedded inside for proprioceptive learning. The results show that the soft network can infer real-time 6D forces and torques with accuracies of 0.25/0.24/0.35 N and 0.025/0.034/0.006 Nm in dynamic interactions. We also incorporate viscoelasticity in proprioception during static adaptation by adding a creep and relaxation modifier to refine the predicted results. The proposed soft network combines simplicity in design, omni-adaptation, and proprioceptive sensing with high accuracy, making it a versatile solution for robotics at a low cost with more than 1 million use cycles for tasks such as sensitive and competitive grasping, and touch-based geometry reconstruction. This study offers new insights into vision-based proprioception for soft robots in adaptive grasping, soft manipulation, and human-robot interaction.

cs.RO↗

arXiv2024

A Novel Perception Entropy Metric for Optimizing Vehicle Perception with LiDAR Deployment

Developing an effective evaluation metric is crucial for accurately and swiftly measuring LiDAR perception performance. One major issue is the lack of metrics that can simultaneously generate fast and accurate evaluations based on either object detection or point cloud data. In this study, we propose a novel LiDAR perception entropy metric based on the probability of vehicle grid occupancy. This metric reflects the influence of point cloud distribution on vehicle detection performance. Based on this, we also introduce a LiDAR deployment optimization model, which is solved using a differential evolution-based particle swarm optimization algorithm. A comparative experiment demonstrated that the proposed PE-VGOP offers a correlation of more than 0.98 with vehicle detection ground truth in evaluating LiDAR perception performance. Furthermore, compared to the base deployment, field experiments indicate that the proposed optimization model can significantly enhance the perception capabilities of various types of LiDARs, including RS-16, RS-32, and RS-80. Notably, it achieves a 25% increase in detection Recall for the RS-32 LiDAR.

cs.RO↗

arXiv2024

On A Tautological Relation Conjectured By Buryak-Shadrin

Buryak and Shadrin conjectured a tautological relation on moduli spaces of curves $\overline{\mathcal{M}}_{g,n}$ which has the form $B^m_{g, \textbf{d}}=0$ for certain tautological classes $B^m_{g, \textbf{d}}$ where $m \geq 2, n \geq 1$ and $|\textbf{d}| \geq 2g+m-1$. In this paper we prove that this conjecture holds if it is true for the $m=2$ and $|\textbf{d}| = 2g+1$ case. This result reduces the proof of this conjecture to checking finitely many cases for each genus $g$. We will also prove this conjecture for the $g=1$ case.

math.AG↗

arXiv2024

The Application of ChatGPT in Responding to Questions Related to the Boston Bowel Preparation Scale

Background: Colonoscopy, a crucial diagnostic tool in gastroenterology, depends heavily on superior bowel preparation. ChatGPT, a large language model with emergent intelligence which also exhibits potential in medical applications. This study aims to assess the accuracy and consistency of ChatGPT in using the Boston Bowel Preparation Scale (BBPS) for colonoscopy assessment. Methods: We retrospectively collected 233 colonoscopy images from 2020 to 2023. These images were evaluated using the BBPS by 3 senior endoscopists and 3 novice endoscopists. Additionally, ChatGPT also assessed these images, having been divided into three groups and undergone specific Fine-tuning. Consistency was evaluated through two rounds of testing. Results: In the initial round, ChatGPT's accuracy varied between 48.93% and 62.66%, trailing the endoscopists' accuracy of 76.68% to 77.83%. Kappa values for ChatGPT was between 0.52 and 0.53, compared to 0.75 to 0.87 for the endoscopists. Conclusion: While ChatGPT shows promise in bowel preparation scoring, it currently does not match the accuracy and consistency of experienced endoscopists. Future research should focus on in-depth Fine-tuning.

cs.AI↗

arXiv2023

Autoencoding a Soft Touch to Learn Grasping from On-land to Underwater

Robots play a critical role as the physical agent of human operators in exploring the ocean. However, it remains challenging to grasp objects reliably while fully submerging under a highly pressurized aquatic environment with little visible light, mainly due to the fluidic interference on the tactile mechanics between the finger and object surfaces. This study investigates the transferability of grasping knowledge from on-land to underwater via a vision-based soft robotic finger that learns 6D forces and torques (FT) using a Supervised Variational Autoencoder (SVAE). A high-framerate camera captures the whole-body deformations while a soft robotic finger interacts with physical objects on-land and underwater. Results show that the trained SVAE model learned a series of latent representations of the soft mechanics transferrable from land to water, presenting a superior adaptation to the changing environments against commercial FT sensors. Soft, delicate, and reactive grasping enabled by tactile intelligence enhances the gripper's underwater interaction with improved reliability and robustness at a much-reduced cost, paving the path for learning-based intelligent grasping to support fundamental scientific discoveries in environmental and ocean research.

cs.RO↗

arXiv2023

An enhanced motion planning approach by integrating driving heterogeneity and long-term trajectory prediction for automated driving systems

Navigating automated driving systems (ADSs) through complex driving environments is difficult. Predicting the driving behavior of surrounding human-driven vehicles (HDVs) is a critical component of an ADS. This paper proposes an enhanced motion-planning approach for an ADS in a highway-merging scenario. The proposed enhanced approach utilizes the results of two aspects: the driving behavior and long-term trajectory of surrounding HDVs, which are coupled using a hierarchical model that is used for the motion planning of an ADS to improve driving safety.

cs.RO↗

arXiv2023

Jigsaw-based Benchmarking for Learning Robotic Manipulation

Benchmarking provides experimental evidence of the scientific baseline to enhance the progression of fundamental research, which is also applicable to robotics. In this paper, we propose a method to benchmark metrics of robotic manipulation, which addresses the spatial-temporal reasoning skills for robot learning with the jigsaw game. In particular, our approach exploits a simple set of jigsaw pieces by designing a structured protocol, which can be highly customizable according to a wide range of task specifications. Researchers can selectively adopt the proposed protocol to benchmark their research outputs, on a comparable scale in the functional, task, and system-level of details. The purpose is to provide a potential look-up table for learning-based robot manipulation, commonly available in other engineering disciplines, to facilitate the adoption of robotics through calculated, empirical, and systematic experimental evidence.

cs.RO↗

arXiv2022

Traffic Analytics Development Kits (TADK): Enable Real-Time AI Inference in Networking Apps

Sophisticated traffic analytics, such as the encrypted traffic analytics and unknown malware detection, emphasizes the need for advanced methods to analyze the network traffic. Traditional methods of using fixed patterns, signature matching, and rules to detect known patterns in network traffic are being replaced with AI (Artificial Intelligence) driven algorithms. However, the absence of a high-performance AI networking-specific framework makes deploying real-time AI-based processing within networking workloads impossible. In this paper, we describe the design of Traffic Analytics Development Kits (TADK), an industry-standard framework specific for AI-based networking workloads processing. TADK can provide real-time AI-based networking workload processing in networking equipment from the data center out to the edge without the need for specialized hardware (e.g., GPUs, Neural Processing Unit, and so on). We have deployed TADK in commodity WAF and 5G UPF, and the evaluation result shows that TADK can achieve a throughput up to 35.3Gbps per core on traffic feature extraction, 6.5Gbps per core on traffic classification, and can decrease SQLi/XSS detection down to 4.5us per request with higher accuracy than fixed pattern solution.

cs.NI↗

arXiv2022

Q-Polynomial expansion for Brezin-Gross-Witten tau-function

In this paper, we prove a conjecture of Alexandrov that the generalized Brezin-Gross-Witten tau-functions are hypergeometric tau functions of BKP hierarchy after re-scaling. In particular, this shows that the original BGW tau-function, which has enumerative geometric interpretations, can be represented as a linear combination of Schur Q-polynomials with simple coefficients.

nlin.SI↗