arXiv subjects

Ming Xu

Publications and source records attributed to Ming Xu.

At least 127 records · Page 7Linked to original sources

arXiv2022

Randers and $(α,β)$ equigeodesics for some compact homogeneous manifolds

A smooth curve on $G/H$ is called a Riemannian equigeodesic if it is a homogeneous geodesic for all $G$-invariant Riemannian metrics on $G/H$. With the $G$-invariant Riemannian metric replaced by other classes of $G$-invariant metrics, we can similarly define Finsler equigeodesic, Randers equigeodesic, $(α,β)$ equigeodesic, etc. In this paper, we study Randers and $(α,β)$ equigeodesics. For a compact homogeneous manifold, we prove Randers and $(α,β)$ equigeodesics are equivalent, and find a criterion for them. Using this criterion we can classify the equigeodesics on many compact homogeneous manifolds which permit non-Riemannian homogeneous Randers metrics, including four classes of homogeneous spheres.

math.DG↗

arXiv2022

Neuro-Symbolic Learning: Principles and Applications in Ophthalmology

Neural networks have been rapidly expanding in recent years, with novel strategies and applications. However, challenges such as interpretability, explainability, robustness, safety, trust, and sensibility remain unsolved in neural network technologies, despite the fact that they will unavoidably be addressed for critical applications. Attempts have been made to overcome the challenges in neural network computing by representing and embedding domain knowledge in terms of symbolic representations. Thus, the neuro-symbolic learning (NeSyL) notion emerged, which incorporates aspects of symbolic representation and bringing common sense into neural networks (NeSyL). In domains where interpretability, reasoning, and explainability are crucial, such as video and image captioning, question-answering and reasoning, health informatics, and genomics, NeSyL has shown promising outcomes. This review presents a comprehensive survey on the state-of-the-art NeSyL approaches, their principles, advances in machine and deep learning algorithms, applications such as opthalmology, and most importantly, future perspectives of this emerging field.

cs.CV↗

arXiv2022

On the girth cycles of the bipartite graph $D(k,q)$

For integer $k\geq2$ and prime power $q$, the algebraic bipartite graph $D(k,q)$ proposed by Lazebnik and Ustimenko (1995) is meaningful not only in extremal graph theory but also in coding theory and cryptography. This graph is $q$-regular, edge-transitive and of girth at least $k+4$. For its exact girth $g=g(D(k,q))$, Füredi et al. (1995) conjectured $g=k+5$ for odd $k$ and $q\geq4$. This conjecture was shown to be valid in 2016 when $(k+5)/2$ is the product of an arbitrary factor of $q-1$ and an arbitrary power of the characteristic of $\mathbb{F}_q$. In this paper, we determine all the girth cycles of $D(k,q)$ for $3\leq k\leq 5$, $q>3$, and those for $3\leq k\leq8$, $q=3$.

math.CO↗

arXiv2022

3D Random Occlusion and Multi-Layer Projection for Deep Multi-Camera Pedestrian Localization

Although deep-learning based methods for monocular pedestrian detection have made great progress, they are still vulnerable to heavy occlusions. Using multi-view information fusion is a potential solution but has limited applications, due to the lack of annotated training samples in existing multi-view datasets, which increases the risk of overfitting. To address this problem, a data augmentation method is proposed to randomly generate 3D cylinder occlusions, on the ground plane, which are of the average size of pedestrians and projected to multiple views, to relieve the impact of overfitting in the training. Moreover, the feature map of each view is projected to multiple parallel planes at different heights, by using homographies, which allows the CNNs to fully utilize the features across the height of each pedestrian to infer the locations of pedestrians on the ground plane. The proposed 3DROM method has a greatly improved performance in comparison with the state-of-the-art deep-learning based methods for multi-view pedestrian detection.

cs.CV↗

arXiv2022

Improving Worst Case Visual Localization Coverage via Place-specific Sub-selection in Multi-camera Systems

6-DoF visual localization systems utilize principled approaches rooted in 3D geometry to perform accurate camera pose estimation of images to a map. Current techniques use hierarchical pipelines and learned 2D feature extractors to improve scalability and increase performance. However, despite gains in typical recall@0.25m type metrics, these systems still have limited utility for real-world applications like autonomous vehicles because of their `worst' areas of performance - the locations where they provide insufficient recall at a certain required error tolerance. Here we investigate the utility of using `place specific configurations', where a map is segmented into a number of places, each with its own configuration for modulating the pose estimation step, in this case selecting a camera within a multi-camera system. On the Ford AV benchmark dataset, we demonstrate substantially improved worst-case localization performance compared to using off-the-shelf pipelines - minimizing the percentage of the dataset which has low recall at a certain error tolerance, as well as improved overall localization performance. Our proposed approach is particularly applicable to the crowdsharing model of autonomous vehicle deployment, where a fleet of AVs are regularly traversing a known route.

cs.RO↗

arXiv2022

A Pattern Matching-Based Framework for Quantum Circuit Rewriting

The realization of quantum algorithms relies on specific quantum compilations according to the underlying quantum processors. However, there are various ways to physically implement qubits in different physical devices and manipulate those qubits. These differences lead to different communication methods and connection topologies, with each vendor implementing its own set of primitive gates. Therefore, quantum circuits have to be rewritten or transformed in order to be transplanted from one platform to another. We propose a pattern matching-based framework for rewriting quantum circuits, called QRewriting. It takes advantage of a new representation of quantum circuits using symbol sequences. Unlike the traditional way of using directed acyclic graphs, the new representation allows us to easily identify the patterns that appear non-consecutively but reducible. Then, we convert the problem of pattern matching into that of finding distinct subsequences and propose a polynomial-time dynamic programming-based pattern matching and replacement algorithm. We develop a rule library for basic optimizations and use it to rewrite the Arithmetic and Toffoli benchmarks from the $G_{IBM}$ gate set to the $G_{Sur}$ gate set. Compared with the existing tool PaF, QRewriting obtains an improvement of reducing depths (resp. gate counts) by 29\% (resp. 14\%).

quant-ph↗

arXiv2022

Improving Road Segmentation in Challenging Domains Using Similar Place Priors

Road segmentation in challenging domains, such as night, snow or rain, is a difficult task. Most current approaches boost performance using fine-tuning, domain adaptation, style transfer, or by referencing previously acquired imagery. These approaches share one or more of three significant limitations: a reliance on large amounts of annotated training data that can be costly to obtain, both anticipation of and training data from the type of environmental conditions expected at inference time, and/or imagery captured from a previous visit to the location. In this research, we remove these restrictions by improving road segmentation based on similar places. We use Visual Place Recognition (VPR) to find similar but geographically distinct places, and fuse segmentations for query images and these similar place priors using a Bayesian approach and novel segmentation quality metric. Ablation studies show the need to re-evaluate notions of VPR utility for this task. We demonstrate the system achieving state-of-the-art road segmentation performance across multiple challenging condition scenarios including night time and snow, without requiring any prior training or previous access to the same geographical locations. Furthermore, we show that this method is network agnostic, improves multiple baseline techniques and is competitive against methods specialised for road prediction.

cs.CV↗

arXiv2022

Mixed-UNet: Refined Class Activation Mapping for Weakly-Supervised Semantic Segmentation with Multi-scale Inference

Deep learning techniques have shown great potential in medical image processing, particularly through accurate and reliable image segmentation on magnetic resonance imaging (MRI) scans or computed tomography (CT) scans, which allow the localization and diagnosis of lesions. However, training these segmentation models requires a large number of manually annotated pixel-level labels, which are time-consuming and labor-intensive, in contrast to image-level labels that are easier to obtain. It is imperative to resolve this problem through weakly-supervised semantic segmentation models using image-level labels as supervision since it can significantly reduce human annotation efforts. Most of the advanced solutions exploit class activation mapping (CAM). However, the original CAMs rarely capture the precise boundaries of lesions. In this study, we propose the strategy of multi-scale inference to refine CAMs by reducing the detail loss in single-scale reasoning. For segmentation, we develop a novel model named Mixed-UNet, which has two parallel branches in the decoding phase. The results can be obtained after fusing the extracted features from two branches. We evaluate the designed Mixed-UNet against several prevalent deep learning-based segmentation approaches on our dataset collected from the local hospital and public datasets. The validation results demonstrate that our model surpasses available methods under the same supervision level in the segmentation of various lesions from brain imaging.

eess.IV↗

arXiv2022

Naturally reductive $(α_1, α_2)$ metrics

Let $F$ be a homogeneous $(α_1,α_2)$ metric on the reductive homogeneous manifold $G/H$. Firstly, we characterize the natural reductiveness of $F$ as a local $f$-product between naturally reductive Riemannian metrics. Secondly, we prove the equivalence among several properties of $F$ for its mean Berwald curvature and S-curvature. Finally, we find an explicit flag curvature formula when $F$ is naturally reductive.

math.DG↗

arXiv2022

FedDC: Federated Learning with Non-IID Data via Local Drift Decoupling and Correction

Federated learning (FL) allows multiple clients to collectively train a high-performance global model without sharing their private data. However, the key challenge in federated learning is that the clients have significant statistical heterogeneity among their local data distributions, which would cause inconsistent optimized local models on the client-side. To address this fundamental dilemma, we propose a novel federated learning algorithm with local drift decoupling and correction (FedDC). Our FedDC only introduces lightweight modifications in the local training phase, in which each client utilizes an auxiliary local drift variable to track the gap between the local model parameter and the global model parameters. The key idea of FedDC is to utilize this learned local drift variable to bridge the gap, i.e., conducting consistency in parameter-level. The experiment results and analysis demonstrate that FedDC yields expediting convergence and better performance on various image classification tasks, robust in partial participation settings, non-iid data, and heterogeneous clients.

cs.LG↗

arXiv2022

Sharing Behavior in Ride-hailing Trips: A Machine Learning Inference Approach

Ride-hailing is rapidly changing urban and personal transportation. Ride sharing or pooling is important to mitigate negative externalities of ride-hailing such as increased congestion and environmental impacts. However, there lacks empirical evidence on what affect trip-level sharing behavior in ride-hailing. Using a novel dataset from all ride-hailing trips in Chicago in 2019, we show that the willingness of riders to request a shared ride has monotonically decreased from 27.0% to 12.8% throughout the year, while the trip volume and mileage have remained statistically unchanged. We find that the decline in sharing preference is due to an increased per-mile costs of shared trips and shifting shorter trips to solo. Using ensemble machine learning models, we find that the travel impedance variables (trip cost, distance, and duration) collectively contribute to 95% and 91% of the predictive power in determining whether a trip is requested to share and whether it is successfully shared, respectively. Spatial and temporal attributes, sociodemographic, built environment, and transit supply variables do not entail predictive power at the trip level in presence of these travel impedance variables. This implies that pricing signals are most effective to encourage riders to share their rides. Our findings shed light on sharing behavior in ride-hailing trips and can help devise strategies that increase shared ride-hailing, especially as the demand recovers from pandemic.

cs.LG↗

arXiv2021

Parallel translations for a left invariant spray

In this paper, we study the left invariant spray geometry on a connected Lie group. Using the technique of invariant frames, we find the ordinary differential equations on the Lie algebra describing for a left invariant spray structure the linearly parallel translations along a geodesic and the nonlinearly parallel translations along a smooth curve. In these equations, the connection operator plays an important role. Using linearly parallel translations, we provide alternative interpretations or proofs for some homogeneous curvature formulae. Concerning the nonlinearly ones, we propose two questions in left invariant spray geometry. One question generalizes Landsberg Problem in Finsler geometry, and the other concerns the restricted holonomy group.

math.DG↗

arXiv2021

Submersion and homogeneous spray geometry

We introduce the submersion between two spray structures and propose the submersion technique in spray geometry. Using this technique, as well as global invariant frames on a Lie group, we setup the general theoretical framework for homogeneous spray geometry. We define the spray vector field $η$ and the connection operator $N$ for a homogeneous spray manifold $(G/H,\mathbf{G})$ with a linear decomposition $\mathfrak{g}=\mathfrak{h}+\mathfrak{m}$. These notions generalize their counter parts in homogeneous Finsler geometry. We prove the correspondence between $\mathbf{G}$ and $η$ when the given decomposition is reductive, and that between geodesics on $(G/H,\mathbf{G})$ and integral curves of $-η$. We find the ordinary differential equations on $\mathfrak{m}$ describing parallel translations on $(G/H,\mathbf{G})$, and we calculate the S-curvature and Riemann curvature of $(G/H,\mathbf{G})$, generalizing L. Huang's curvature formulae for homogeneous Finsler manifolds.

math.DG↗

arXiv2021

Quantum Circuit Transformation Based on Tabu Search

The goal of quantum circuit transformation is to map a logical circuit to a physical device by inserting additional gates as few as possible in an acceptable amount of time. We present an effective approach called TSA to construct the mapping. It consists of two key steps: one makes use of a combined subgraph isomorphism and completion to initialize some candidate mappings, the other dynamically modifies the mappings by using tabu search-based adjustment. Our experiments show that, compared with state-of-the-art methods GA, SABRE and FiDLS proposed in the literature, TSA can generate mappings with a smaller number of additional gates and it has a better scalability for large-scale circuits.

quant-ph↗

arXiv2021

Probabilistic Appearance-Invariant Topometric Localization with New Place Awareness

Probabilistic state-estimation approaches offer a principled foundation for designing localization systems, because they naturally integrate sequences of imperfect motion and exteroceptive sensor data. Recently, probabilistic localization systems utilizing appearance-invariant visual place recognition (VPR) methods as the primary exteroceptive sensor have demonstrated state-of-the-art performance in the presence of substantial appearance change. However, existing systems 1) do not fully utilize odometry data within the motion models, and 2) are unable to handle route deviations, due to the assumption that query traverses exactly repeat the mapping traverse. To address these shortcomings, we present a new probabilistic topometric localization system which incorporates full 3-dof odometry into the motion model and furthermore, adds an "off-map" state within the state-estimation framework, allowing query traverses which feature significant route detours from the reference map to be successfully localized. We perform extensive evaluation on multiple query traverses from the Oxford RobotCar dataset exhibiting both significant appearance change and deviations from routes previously traversed. In particular, we evaluate performance on two practically relevant localization tasks: loop closure detection and global localization. Our approach achieves major performance improvements over both existing and improved state-of-the-art systems.

cs.RO↗

arXiv2021

PRGC: Potential Relation and Global Correspondence Based Joint Relational Triple Extraction

Joint extraction of entities and relations from unstructured texts is a crucial task in information extraction. Recent methods achieve considerable performance but still suffer from some inherent limitations, such as redundancy of relation prediction, poor generalization of span-based extraction and inefficiency. In this paper, we decompose this task into three subtasks, Relation Judgement, Entity Extraction and Subject-object Alignment from a novel perspective and then propose a joint relational triple extraction framework based on Potential Relation and Global Correspondence (PRGC). Specifically, we design a component to predict potential relations, which constrains the following entity extraction to the predicted relation subset rather than all relations; then a relation-specific sequence tagging component is applied to handle the overlapping problem between subjects and objects; finally, a global correspondence component is designed to align the subject and object into a triple with low-complexity. Extensive experiments show that PRGC achieves state-of-the-art performance on public benchmarks with higher efficiency and delivers consistent performance gain on complex scenarios of overlapping triples.

cs.CL↗

arXiv2021

Isoparametric hypersurfaces induced by navigation in Lorentz Finsler geometry

Using a navigation process with the datum $(F,V)$, in which $F$ is a Finsler metric and the smooth tangent vector field $V$ satisfies $F(-V(x))>1$ everywhere, a Lorentz Finsler metric $\tilde{F}$ can be induced. Isoparametric functions and isoparametric hypersurfaces with or without involving a smooth measure can be defined for $\tilde{F}$. When the vector field $V$ in the navigation datum is homothetic, we prove the local correspondences between isoparametric functions and isoparametric hypersurfaces before and after this navigation process. Using these correspondences, we provide some examples of isoparametric functions and isoparametric hypersurfaces on a Funk space of Lorentz Randers type.

math.DG↗

arXiv2021

Probabilistic Visual Place Recognition for Hierarchical Localization

Visual localization techniques often comprise a hierarchical localization pipeline, with a visual place recognition module used as a coarse localizer to initialize a pose refinement stage. While improving the pose refinement step has been the focus of much recent research, most work on the coarse localization stage has focused on improvements like increased invariance to appearance change, without improving what can be loose error tolerances. In this letter, we propose two methods which adapt image retrieval techniques used for visual place recognition to the Bayesian state estimation formulation for localization. We demonstrate significant improvements to the localization accuracy of the coarse localization stage using our methods, whilst retaining state-of-the-art performance under severe appearance change. Using extensive experimentation on the Oxford RobotCar dataset, results show that our approach outperforms comparable state-of-the-art methods in terms of precision-recall performance for localizing image sequences. In addition, our proposed methods provides the flexibility to contextually scale localization latency in order to achieve these improvements. The improved initial localization estimate opens up the possibility of both improved overall localization performance and modified pose refinement techniques that leverage this improved spatial prior.

cs.CV↗