In this work, we rigorously investigate the robustness of graph neural fractional-order differential equation (FDE) models. This framework extends beyond traditional graph neural (integer-order) ordinary differential equation (ODE) models by implementing the time-fractional Caputo derivative. Utilizing fractional calculus allows our model to consider long-term memory during the feature updating process, diverging from the memoryless Markovian updates seen in traditional graph neural ODE models. The superiority of graph neural FDE models over graph neural ODE models has been established in environments free from attacks or perturbations. While traditional graph neural ODE models have been verified to possess a degree of stability and resilience in the presence of adversarial attacks in existing literature, the robustness of graph neural FDE models, especially under adversarial conditions, remains largely unexplored. This paper undertakes a detailed assessment of the robustness of graph neural FDE models. We establish a theoretical foundation outlining the robustness characteristics of graph neural FDE models, highlighting that they maintain more stringent output perturbation bounds in the face of input and graph topology disturbances, compared to their integer-order counterparts. Our empirical evaluations further confirm the enhanced robustness of graph neural FDE models, highlighting their potential in adversarially robust applications.

Point cloud registration is a crucial technique in 3D computer vision with a wide range of applications. However, this task can be challenging, particularly in large fields of view with dynamic objects, environmental noise, or other perturbations. To address this challenge, we propose a model called PosDiffNet. Our approach performs hierarchical registration based on window-level, patch-level, and point-level correspondence. We leverage a graph neural partial differential equation (PDE) based on Beltrami flow to obtain high-dimensional features and position embeddings for point clouds. We incorporate position embeddings into a Transformer module based on a neural ordinary differential equation (ODE) to efficiently represent patches within points. We employ the multi-level correspondence derived from the high feature similarity scores to facilitate alignment between point clouds. Subsequently, we use registration methods such as SVD-based algorithms to predict the transformation using corresponding point pairs. We evaluate PosDiffNet on several 3D point cloud datasets, verifying that it achieves state-of-the-art (SOTA) performance for point cloud registration in large fields of view with perturbations. The implementation code of experiments is available at https://github.com/AI-IT-AVs/PosDiffNet.

The utilization of multi-modal sensor data in visual place recognition (VPR) has demonstrated enhanced performance compared to single-modal counterparts. Nonetheless, integrating additional sensors comes with elevated costs and may not be feasible for systems that demand lightweight operation, thereby impacting the practical deployment of VPR. To address this issue, we resort to knowledge distillation, which empowers single-modal students to learn from cross-modal teachers without introducing additional sensors during inference. Despite the notable advancements achieved by current distillation approaches, the exploration of feature relationships remains an under-explored area. In order to tackle the challenge of cross-modal distillation in VPR, we present DistilVPR, a novel distillation pipeline for VPR. We propose leveraging feature relationships from multiple agents, including self-agents and cross-agents for teacher and student neural networks. Furthermore, we integrate various manifolds, characterized by different space curvatures for exploring feature relationships. This approach enhances the diversity of feature relationships, including Euclidean, spherical, and hyperbolic relationship modules, thereby enhancing the overall representational capacity. The experiments demonstrate that our proposed pipeline achieves state-of-the-art performance compared to other distillation baselines. We also conduct necessary ablation studies to show design effectiveness. The code is released at: https://github.com/sijieaaa/DistilVPR

We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process. We demonstrate analytically that oversmoothing can be mitigated in this setting. Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs. The code is available at \url{https://github.com/zknus/ICLR2024-FROND}.

Point cloud registration is a fundamental technique in 3-D computer vision with applications in graphics, autonomous driving, and robotics. However, registration tasks under challenging conditions, under which noise or perturbations are prevalent, can be difficult. We propose a robust point cloud registration approach that leverages graph neural partial differential equations (PDEs) and heat kernel signatures. Our method first uses graph neural PDE modules to extract high-dimensional features from point clouds by aggregating information from the 3-D point neighborhood, thereby enhancing the robustness of the feature representations. Then, we incorporate heat kernel signatures into an attention mechanism to efficiently obtain corresponding keypoints. Finally, a singular value decomposition (SVD) module with learnable weights is used to predict the transformation between two point clouds. Empirical experiments on a 3-D point cloud dataset demonstrate that our approach not only achieves state-of-the-art performance for point cloud registration but also exhibits better robustness to additive noise or 3-D shape perturbations.

Place recognition plays a crucial role in the fields of robotics and computer vision, finding applications in areas such as autonomous driving, mapping, and localization. Place recognition identifies a place using query sensor data and a known database. One of the main challenges is to develop a model that can deliver accurate results while being robust to environmental variations. We propose two multi-modal place recognition models, namely PRFusion and PRFusion++. PRFusion utilizes global fusion with manifold metric attention, enabling effective interaction between features without requiring camera-LiDAR extrinsic calibrations. In contrast, PRFusion++ assumes the availability of extrinsic calibrations and leverages pixel-point correspondences to enhance feature learning on local windows. Additionally, both models incorporate neural diffusion layers, which enable reliable operation even in challenging environments. We verify the state-of-the-art performance of both models on three large-scale benchmarks. Notably, they outperform existing models by a substantial margin of +3.0 AR@1 on the demanding Boreas dataset. Furthermore, we conduct ablation studies to validate the effectiveness of our proposed methods.

LiDAR relocalization plays a crucial role in many fields, including robotics, autonomous driving, and computer vision. LiDAR-based retrieval from a database typically incurs high computation storage costs and can lead to globally inaccurate pose estimations if the database is too sparse. On the other hand, pose regression methods take images or point clouds as inputs and directly regress global poses in an end-to-end manner. They do not perform database matching and are more computationally efficient than retrieval techniques. We propose HypLiLoc, a new model for LiDAR pose regression. We use two branched back-bones to extract 3D features and 2D projection features, respectively. We consider multi-modal feature fusion in both Euclidean and hyperbolic spaces to obtain more effective feature representations. Experimental results indicate that HypLiLoc achieves state-of-the-art performance in both outdoor and indoor datasets. We also conduct extensive ablation studies on the framework design, which demonstrate the effectiveness of multi-modal feature extraction and multi-space embedding. Our code is released at: https://github.com/sijieaaa/HypLiLoc

Image matching identifies matching street landmark patches between the images captured by a vehicular camera and those stored in a database. Applications include autonomous driving perception and localization. However, in practical scenarios, challenging conditions such as changing weather, illumination, and dynamic objects result in perturbations of the captured images, leading to inaccurate matching. To achieve robust landmark patch matching, we present a method, named GRAND-Mat, which leverages a neural diffusion over graph embeddings to counteract perturbations. We first extract high-dimensional features of landmark patches using a ResNet. Then, we utilize graph neural diffusion models to aggregate the self and cross-graph information from these features. Furthermore, we apply feature similarity learning to acquire the final matching score. We evaluate the performance of our model on a street scene dataset, which demonstrates state-of-the-art matching performance under additive perturbations.

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at https://github.com/zknus/Hamiltonian-GNN.

Graph neural networks (GNNs) have shown promising results across various graph learning tasks, but they often assume homophily, which can result in poor performance on heterophilic graphs. The connected nodes are likely to be from different classes or have dissimilar features on heterophilic graphs. In this paper, we propose a novel GNN that incorporates the principle of heterophily by modeling the flow of information on nodes using the convection-diffusion equation (CDE). This allows the CDE to take into account both the diffusion of information due to homophily and the ``convection'' of information due to heterophily. We conduct extensive experiments, which suggest that our framework can achieve competitive performance on node classification tasks for heterophilic graphs, compared to the state-of-the-art methods. The code is available at https://github.com/zknus/Graph-Diffusion-CDE.

Graph neural networks (GNNs) are vulnerable to adversarial perturbations, including those that affect both node features and graph topology. This paper investigates GNNs derived from diverse neural flows, concentrating on their connection to various stability notions such as BIBO stability, Lyapunov stability, structural stability, and conservative stability. We argue that Lyapunov stability, despite its common use, does not necessarily ensure adversarial robustness. Inspired by physics principles, we advocate for the use of conservative Hamiltonian neural flows to construct GNNs that are robust to adversarial attacks. The adversarial robustness of different neural flow GNNs is empirically compared on several benchmark datasets under a variety of adversarial attacks. Extensive numerical experiments demonstrate that GNNs leveraging conservative Hamiltonian flows with Lyapunov stability substantially improve robustness against adversarial perturbations. The implementation code of experiments is available at \url{https://github.com/zknus/NeurIPS-2023-HANG-Robustness}.

For autonomous vehicles (AVs), visual perception techniques based on sensors like cameras play crucial roles in information acquisition and processing. In various computer perception tasks for AVs, it may be helpful to match landmark patches taken by an onboard camera with other landmark patches captured at a different time or saved in a street scene image database. To perform matching under challenging driving environments caused by changing seasons, weather, and illumination, we utilize the spatial neighborhood information of each patch. We propose an approach, named RobustMat, which derives its robustness to perturbations from neural differential equations. A convolutional neural ODE diffusion module is used to learn the feature representation for the landmark patches. A graph neural PDE diffusion module then aggregates information from neighboring landmark patches in the street scene. Finally, feature similarity learning outputs the final matching score. Our approach is evaluated on several street scene datasets and demonstrated to achieve state-of-the-art matching results under environmental perturbations.

Real-time data transmissions from a vehicle enhance road safety and traffic efficiency by aggregating data in a central server for data analytics. When drivers share their instantaneous vehicular information for a service provider to perform a legitimate task, a curious service provider may also infer private information it has not been authorized for. In this paper, we propose a privacy preservation framework based on the Hilbert Schmidt Independence Criterion (HSIC) to sanitize driving data to protect the vehicle’s trajectory from adversarial inference while ensuring the data is still useful for driver behavior detection. We develop a deep learning model to learn the HSIC sanitizer and demonstrate through two datasets that our approach achieves better utility-privacy trade-offs when compared to three other benchmarks.

Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural networks (GNNs), such as the problems of over-smoothing and bottlenecks, has been investigated but not their robustness to adversarial attacks. In this work, we explore the robustness properties of graph neural PDEs. We empirically demonstrate that graph neural PDEs are intrinsically more robust against topology perturbation as compared to other GNNs. We provide insights into this phenomenon by exploiting the stability of the heat semigroup under graph topology perturbations. We discuss various graph diffusion operators and relate them to existing graph neural PDEs. Furthermore, we propose a general graph neural PDE framework based on which a new class of robust GNNs can be defined. We verify that the new model achieves comparable state-of-the-art performance on several benchmark datasets.

Though deep learning has been applied successfully in many scenarios, malicious inputs with human-imperceptible perturbations can make it vulnerable in real applications. This paper proposes an error-correcting neural network (ECNN) that combines a set of binary classifiers to combat adversarial examples in the multi-class classification problem. To build an ECNN, we propose to design a code matrix so that the minimum Hamming distance between any two rows (i.e., two codewords) and the minimum shared information distance between any two columns (i.e., two partitions of class labels) are simultaneously maximized. Maximizing row distances can increase the system fault tolerance while maximizing column distances helps increase the diversity between binary classifiers. We propose an end-to-end training method for our ECNN, which allows further improvement of the diversity between binary classifiers. The end-to-end training renders our proposed ECNN different from the traditional error-correcting output code (ECOC) based methods that train binary classifiers independently. ECNN is complementary to other existing defense approaches such as adversarial training and can be applied in conjunction with them. We empirically demonstrate that our proposed ECNN is effective against the state-of-the-art white-box and black-box attacks on several datasets while maintaining good classification accuracy on normal examples.

Deep neural networks (DNNs) are well-known to be vulnerable to adversarial attacks, where malicious human-imperceptible perturbations are included in the input to the deep network to fool it into making a wrong classification. Recent studies have demonstrated that neural Ordinary Differential Equations (ODEs) are intrinsically more robust against adversarial attacks compared to vanilla DNNs. In this work, we propose a neural ODE with Lyapunov-stable equilibrium points for defending against adversarial attacks (SODEF). By ensuring that the equilibrium points of the ODE solution used as part of SODEF are Lyapunov-stable, the ODE solution for an input with a small perturbation converges to the same solution as the unperturbed input. We provide theoretical results that give insights into the stability of SODEF as well as the choice of regularizers to ensure its stability. Our analysis suggests that our proposed regularizers force the extracted feature points to be within a neighborhood of the Lyapunov-stable equilibrium points of the SODEF ODE. SODEF is compatible with many defense methods and can be applied to any neural network's final regressor layer to enhance its stability against adversarial attacks.

In this paper, we propose a multi-level localization algorithm that breaks a centralized localization problem into a cluster-level distributed localization problem, where each cluster is a centralized unit. In contrast to fully distributed localization, the cluster-level distributed scheme results in reduction in contention, communication overheads, convergence time and energy consumption because cluster heads are responsible for the intra cluster positioning on behalf of the whole cluster. To generate a global map, the cluster heads communicate with their direct neighbors to carry out inter-cluster ranging and positioning. The proposed method is suitable for large ad-hoc networks where most agents are low-cost, low-power RF transceivers used for ranging only while some agents are integrated with microcomputers such as Raspberry Pis capable of running intra and inter-cluster localization algorithms. The proposed system can work without anchor nodes and thus it can be deployed in the environments such as urban canyon, inside multi-story buildings, airports, and underground shopping malls where access to anchors or Global Navigation Satellite System (GNSS) is limited or prohibitive. We exploit a hybrid of two well-known methods: multidimensional scaling (MDS) and extended Kalman filtering (EKF) to effectively construct local and global position maps, even in the absence of GNSS information, anchors, or a complete ranging matrix.

Code index modulated multi-carrier M-ary differential chaos shift keying (CIM-MC-M-DCSK) system not only inherits low-power and low-complexity advantages of the conventional DCSK system, but also significantly increases the transmission rate. This feature is of particular importance to Internet of Things (IoT) with trillions of low-cost devices. In particular, for e-health IoT applications, an efficient transmission scheme is designed to solve the challenge of the limited battery capacity for numerous user equipments served by one base station. In this paper, a new multiple-input-single-output simultaneous wireless information and power transfer (MISO-SWIPT) scheme for CIM-MC-M-DCSK system is proposed by utilizing orthogonal characteristic of chaotic signals with different initial values. The proposed system adopts power splitting mode, which is very promising for simultaneously providing energy and transmitting information of the user equipments without any external power supply. In particular, the new system can achieve desirable anti-multipath-fading capability without using channel estimator. Moreover, the analytical bit-error-rate expression of the proposed system is derived over multipath Rayleigh fading channels. Furthermore, the spectral efficiency and energy efficiency of the proposed system are analyzed. Simulation results not only validate the analytical expressions, but also demonstrate the superiority of the proposed system.

We consider a linear dynamical system in which the state vector consists of both public and private states. One or more sensors make measurements of the state vector and sends information to a fusion center, which performs the final state estimation. To achieve an optimal tradeoff between the utility of estimating the public states and protection of the private states, the measurements at each time step are linearly compressed into a lower dimensional space. Under the centralized setting where all measurements are collected by a single sensor, we propose an optimization problem and an algorithm to find the best compression matrix. Under the decentralized setting where measurements are made separately at multiple sensors, each sensor optimizes its own local compression matrix. We propose methods to separate the overall optimization problem into multiple sub-problems that can be solved locally at each sensor. We consider the cases where there is no message exchange between the sensors; and where each sensor takes turns to transmit messages to the other sensors. Simulations and empirical experiments demonstrate the efficiency of our proposed approach in allowing the fusion center to estimate the public states with good accuracy while preventing it from estimating the private states accurately.

We equip an ultra-wideband (UWB) node and a 2D LiDAR sensor a.k.a. 2D laser rangefinder on a mobile robot, and place UWB beacon nodes at unknown locations in an unknown environment. All UWB nodes can do ranging with each other thus forming a cooperative sensor network. We propose to fuse the peer-to-peer ranges measured between UWB nodes and laser scanning information, i.e., range measured between robot and nearby objects/obstacles, for simultaneous localization of the robot, all UWB beacons and LiDAR mapping. The fusion is inspired by two facts: 1) LiDAR may improve UWB-only localization accuracy as it gives a more precise and comprehensive picture of the surrounding environment; 2) on the other hand, UWB ranging measurements may remove the error accumulated in the LiDAR-based SLAM algorithm. Our experiments demonstrate that UWB/LiDAR fusion enables drift-free SLAM in real-time based on ranging measurements only.

We are concerned with a privacy-preserving problem in Kalman filter: a sensor releases a set of measurements to fusion center, who has perfect knowledge of the dynamical model, to allow it to estimate the public state, while prevent it from estimating the private state. We propose to linearly transform the original observation into a lower dimensional space before sending them to fusion center. Two privacy-utility tradeoffs are formulated: one concerns only at the current time step and the other concerns over two time steps. The transformation that leads to the optimal tradeoff can be found in closed-form. The privacy (estimation of private state) and utility (estimation of public state) are measured based on recursive Bayesian Cramér-Rao bound.

Despite of the ultra-wideband (UWB) system's robustness against multipath in cluttered environments, a number of challenges remain before UWB localization can be implemented. In particular, non-line-of-sight (NLOS) propagation is especially critical for high-resolution localization systems because non-negligibly positive biases will be introduced in distance measurements, thus degrading the localization performance. Here, based on received and first path powers obtainable from channel impulse response (CIR), we propose a simple but very efficient method to distinguish between NLOS and LOS conditions. Our method needs neither the training data nor the prior knowledge about the environments, thus enabling realtime NLOS identification. Despite the simplicity of our method, the experimental results verify its speediness and highly correct detection rate.

This paper considers the problem of range-based decentralized localization in wireless sensor networks when the impulsive measurement noise is present. We develop a robust localization estimator requiring no a priori knowledge of the noise distribution. The approach to robust localization presented here follows the concept of M-estimation and is implemented in a decentralized manner thus suiting the dynamic nature of wireless networks. The performance of the proposed scheme is verified by simulations.

This paper considers the problem of decentralized, cooperative, and dynamic self-localization in wireless sensor networks. In particular, we are interested in a restrictive but very realistic scenario where few anchors are deployed and each anchor whose location is priori known may only communicate with very few agents (e.g. just one agent) whose location is unknown and to-be-estimated. The lack of agent-to-anchor communication links renders slow estimation convergence thereby demanding more message exchanges among the nodes i.e. agent-to-agent and agent-to-anchor. This urges us to propose an efficient localization method that needs less iterations (i.e. less message exchanges) to achieve a certain accuracy.

This paper is concerned with determining the number of correlated signals between two data sets when the number of samples from these data sets is extremely small. In such a scenario, a principal component analysis (PCA) preprocessing step is commonly performed before applying canonical correlation analysis (CCA). We present a reduced-rank version of the hypothesis test based on the Bartlett-Lawley statistic, which allows jointly determining the required PCA dimension reduction and the number of correlated signals.

This paper proposes a new way to realize a maximum‐SINR beamformer for block‐based cyclically prefixed single‐carrier modulation. Here, SINR stands for ‘signal to interference plus noise’ ratio, at the beamformer output. This spatial beamformer will ‘blindly’ pass the signal‐of‐interest; and this beamformer will ‘blindly’ null any co‐channel interference, any adjacent‐channel interference, any out‐of‐system interference, and/or any spatio‐temporally correlated additive noises. This proposed scheme is made possible by zero‐padding an in sufficient guard interval, which may be shorter than the temporally spreading channel's order. The proposed receiver will first undergo frequency‐domain equalization, to ‘clear’ the data of any signal‐of‐interest's energy in the zero‐padded guard interval, in order to facilitate the estimation of the interference and noise. This interference‐and‐noise estimate will then be eigen‐subtracted from the signal‐and‐interference‐and‐noise dataset by the aforementioned ‘blind’ beamformer in the spatial dimension.

This study extends an algorithm, previously proposed by the present authors, for ‘linear minimum‐mean‐squared error’ estimation of phase noise of (possibly) temporal non‐stationarity, large magnitude, ‘non’‐identical increments that have a Levy distribution, of which the Wiener distribution represents a special case. This estimator‐taps may be pre‐set to any number, may be pre‐computed offline with no matrix inversion, based on the prior knowledge of only the signal‐to‐(additive)‐noise ratio and the phase‐noise's characteristic function. That estimator may be set to various degrees of latency. This is here generalised to allow observables at irregular time‐instants (e.g. because of the irregular placement of pilot symbols in the transmitted waveform), under which the phase‐noise increments become non‐identically distributed. This study handles this more complicated scenario.