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We introduce Hyper-YOLO, a new object detection method that integrates hypergraph computations to capture the complex high-order correlations among visual features. Traditional YOLO models, while powerful, have limitations in their neck designs that restrict the integration of cross-level features and the exploitation of high-order feature interrelationships. To address these challenges, we propose the Hypergraph Computation Empowered Semantic Collecting and Scattering (HGC-SCS) framework, which transposes visual feature maps into a semantic space and constructs a hypergraph for high-order message propagation. This enables the model to acquire both semantic and structural information, advancing beyond conventional feature-focused learning. Hyper-YOLO incorporates the proposed Mixed Aggregation Network (MANet) in its backbone for enhanced feature extraction and introduces the Hypergraph-Based Cross-Level and Cross-Position Representation Network (HyperC2Net) in its neck. HyperC2Net operates across five scales and breaks free from traditional grid structures, allowing for sophisticated high-order interactions across levels and positions. This synergy of components positions Hyper-YOLO as a state-of-the-art architecture in various scale models, as evidenced by its superior performance on the COCO dataset. Specifically, Hyper-YOLO-N significantly outperforms the advanced YOLOv8-N and YOLOv9-T with 12\% $\text{AP}^{val}$ and 9\% $\text{AP}^{val}$ improvements. The source codes are at ttps://github.com/iMoonLab/Hyper-YOLO.

There are two paradigms in Federated Learning (FL): parallel FL (PFL), where models are trained in a parallel manner across clients; and sequential FL (SFL), where models are trained in a sequential manner across clients. In contrast to that of PFL, the convergence theory of SFL on heterogeneous data is still lacking. To resolve the theoretical dilemma of SFL, we establish sharp convergence guarantees for SFL on heterogeneous data with both upper and lower bounds. Specifically, we derive the upper bounds for strongly convex, general convex and non-convex objective functions, and construct the matching lower bounds for the strongly convex and general convex objective functions. Then, we compare the upper bounds of SFL with those of PFL, showing that SFL outperforms PFL (at least, when the level of heterogeneity is relatively high). Experimental results on quadratic functions and real data sets validate the counterintuitive comparison result., Comment: arXiv admin note: text overlap with arXiv:2311.03154

Action recognition from video data forms a cornerstone with wide-ranging applications. Single-view action recognition faces limitations due to its reliance on a single viewpoint. In contrast, multi-view approaches capture complementary information from various viewpoints for improved accuracy. Recently, event cameras have emerged as innovative bio-inspired sensors, leading to advancements in event-based action recognition. However, existing works predominantly focus on single-view scenarios, leaving a gap in multi-view event data exploitation, particularly in challenges like information deficit and semantic misalignment. To bridge this gap, we introduce HyperMV, a multi-view event-based action recognition framework. HyperMV converts discrete event data into frame-like representations and extracts view-related features using a shared convolutional network. By treating segments as vertices and constructing hyperedges using rule-based and KNN-based strategies, a multi-view hypergraph neural network that captures relationships across viewpoint and temporal features is established. The vertex attention hypergraph propagation is also introduced for enhanced feature fusion. To prompt research in this area, we present the largest multi-view event-based action dataset $\text{THU}^{\text{MV-EACT}}\text{-50}$, comprising 50 actions from 6 viewpoints, which surpasses existing datasets by over tenfold. Experimental results show that HyperMV significantly outperforms baselines in both cross-subject and cross-view scenarios, and also exceeds the state-of-the-arts in frame-based multi-view action recognition., Comment: Accepted by IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI 2024)

There are two categories of methods in Federated Learning (FL) for joint training across multiple clients: i) parallel FL (PFL), where clients train models in a parallel manner; and ii) sequential FL (SFL), where clients train models in a sequential manner. In contrast to that of PFL, the convergence theory of SFL on heterogeneous data is still lacking. In this paper, we establish the convergence guarantees of SFL for strongly/general/non-convex objectives on heterogeneous data. The convergence guarantees of SFL are better than that of PFL on heterogeneous data with both full and partial client participation. Experimental results validate the counterintuitive analysis result that SFL outperforms PFL on extremely heterogeneous data in cross-device settings., Comment: Accepted at NeurIPS 2023. arXiv admin note: text overlap with arXiv:2302.01633

In many applications, piecewise continuous functions are commonly interpolated over meshes. However, accurate high-order manipulations of such functions can be challenging due to potential spurious oscillations known as the Gibbs phenomena. To address this challenge, we propose a novel approach, Robust Discontinuity Indicators (RDI), which can efficiently and reliably detect both C^{0} and C^{1} discontinuities for node-based and cell-averaged values. We present a detailed analysis focusing on its derivation and the dual-thresholding strategy. A key advantage of RDI is its ability to handle potential inaccuracies associated with detecting discontinuities on non-uniform meshes, thanks to its innovative discontinuity indicators. We also extend the applicability of RDI to handle general surfaces with boundaries, features, and ridge points, thereby enhancing its versatility and usefulness in various scenarios. To demonstrate the robustness of RDI, we conduct a series of experiments on non-uniform meshes and general surfaces, and compare its performance with some alternative methods. By addressing the challenges posed by the Gibbs phenomena and providing reliable detection of discontinuities, RDI opens up possibilities for improved approximation and analysis of piecewise continuous functions, such as in data remap., Comment: 37 pages, 37 figures, submitted to Computational and Applied Mathematics (COAM)

Federated Learning (FL) and Split Learning (SL) are two popular paradigms of distributed machine learning. By offloading the computation-intensive portions to the server, SL is promising for deep model training on resource-constrained devices, yet still lacking of rigorous convergence analysis. In this paper, we derive the convergence guarantees of Sequential SL (SSL, the vanilla case of SL that conducts the model training in sequence) for strongly/general/non-convex objectives on heterogeneous data. Notably, the derived guarantees suggest that SSL is better than Federated Averaging (FedAvg, the most popular algorithm in FL) on heterogeneous data. We validate the counterintuitive analysis result empirically on extremely heterogeneous data.

Numerical integration on spheres, including the computation of the areas of spherical triangles, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We describe a new algorithm, called ARPIST, for accurate and stable integration of functions on spherical triangles. ARPIST is based on an easy-to-implement transformation to the spherical triangle from its corresponding linear triangle via radial projection to achieve high accuracy and efficiency. More importantly, ARPIST overcomes potential instabilities in computing the Jacobian of the transformation, even for poorly shaped triangles that may occur at poles in regular longitude-latitude meshes, by avoiding potential catastrophic rounding errors. We compare our proposed technique with L'Huilier's Theorem for computing the area of spherical triangles, and also compare it with the recently developed LSQST method (J. Beckmann, H.N. Mhaskar, and J. Prestin, GEM - Int. J. Geomath., 5:143-162, 2014) and a radial-basis-function-based technique (J. A. Reeger and B. Fornberg, Stud. Appl. Math., 137:174-188, 2015) for integration of smooth functions on spherical triangulations. Our results show that ARPIST enables superior accuracy and stability over previous methods while being orders of magnitude faster and significantly easier to implement., Comment: 28 pages, 14 figures, submitted to Journal of Computational and Applied Mathematics

This paper investigates bilateral control of teleoperators with closed architecture and subjected to arbitrary bounded time-varying delay. A prominent challenge for bilateral control of such teleoperators lies in the closed architecture, especially in the context not involving interaction force/torque measurement. This yields the long-standing situation that most bilateral control rigorously developed in the literature is hard to be justified as applied to teleoperators with closed architecture. With a new class of dynamic feedback, we propose kinematic and adaptive dynamic controllers for teleoperators with closed architecture, and we show that the proposed kinematic and dynamic controllers are robust with respect to arbitrary bounded time-varying delay. In addition, by exploiting the input-output properties of an inverted form of the dynamics of robot manipulators with closed architecture, we remove the assumption of uniform exponential stability of a linear time-varying system due to the adaptation to the gains of the inner controller in demonstrating stability of the presented adaptive dynamic control. The application of the proposed approach is illustrated by the experimental results using a Phantom Omni and a UR10 robot., Comment: This version is prepared with the consideration of the reviewers' and AE's comments

Perfect state transfer in graphs is a concept arising from quantum physics and quantum computing. Given a graph $G$ with adjacency matrix $A_G$, the transition matrix of $G$ with respect to $A_G$ is defined as $H_{A_{G}}(t) = \exp(-\mathrm{i}tA_{G})$, $t \in \mathbb{R},\ \mathrm{i}=\sqrt{-1}$. We say that perfect state transfer from vertex $u$ to vertex $v$ occurs in $G$ at time $\tau$ if $u \ne v$ and the modulus of the $(u,v)$-entry of $H_{A_G}(\tau)$ is equal to $1$. If the moduli of all diagonal entries of $H_{A_G}(\tau)$ are equal to $1$ for some $\tau$, then $G$ is called periodic with period $\tau$. In this paper we give a few sufficient conditions for NEPS of complete graphs to be periodic or exhibit perfect state transfer., Comment: This is the final version that will appear in Discrete Applied Mathematics

Application-specific optical processors have been considered disruptive technologies for modern computing that can fundamentally accelerate the development of artificial intelligence (AI) by offering substantially improved computing performance. Recent advancements in optical neural network architectures for neural information processing have been applied to perform various machine learning tasks. However, the existing architectures have limited complexity and performance; and each of them requires its own dedicated design that cannot be reconfigured to switch between different neural network models for different applications after deployment. Here, we propose an optoelectronic reconfigurable computing paradigm by constructing a diffractive processing unit (DPU) that can efficiently support different neural networks and achieve a high model complexity with millions of neurons. It allocates almost all of its computational operations optically and achieves extremely high speed of data modulation and large-scale network parameter updating by dynamically programming optical modulators and photodetectors. We demonstrated the reconfiguration of the DPU to implement various diffractive feedforward and recurrent neural networks and developed a novel adaptive training approach to circumvent the system imperfections. We applied the trained networks for high-speed classifying of handwritten digit images and human action videos over benchmark datasets, and the experimental results revealed a comparable classification accuracy to the electronic computing approaches. Furthermore, our prototype system built with off-the-shelf optoelectronic components surpasses the performance of state-of-the-art graphics processing units (GPUs) by several times on computing speed and more than an order of magnitude on system energy efficiency.

This paper presents an end-to-end 3D convolutional network named attention-based multi-modal fusion network (AMFNet) for the semantic scene completion (SSC) task of inferring the occupancy and semantic labels of a volumetric 3D scene from single-view RGB-D images. Compared with previous methods which use only the semantic features extracted from RGB-D images, the proposed AMFNet learns to perform effective 3D scene completion and semantic segmentation simultaneously via leveraging the experience of inferring 2D semantic segmentation from RGB-D images as well as the reliable depth cues in spatial dimension. It is achieved by employing a multi-modal fusion architecture boosted from 2D semantic segmentation and a 3D semantic completion network empowered by residual attention blocks. We validate our method on both the synthetic SUNCG-RGBD dataset and the real NYUv2 dataset and the results show that our method respectively achieves the gains of 2.5% and 2.6% on the synthetic SUNCG-RGBD dataset and the real NYUv2 dataset against the state-of-the-art method., Comment: Accepted by AAAI 2020

Data remap between non-matching meshes is a critical step in multiphysics coupling using a partitioned approach. The data fields being transferred often have jumps in function values or derivatives. It is important but very challenging to avoid spurious oscillations (a.k.a. the Gibbs Phenomenon) near discontinuities and at the same time to achieve high-order accuracy away from discontinuities. In this work, we introduce a new approach, called WLS-ENOR, or Weighted-Least-Squares-based Essentially Non-Oscillatory Remap, to address this challenge. Based on the WLS-ENO reconstruction technique proposed by Liu and Jiao (J. Comput. Phys. vol 314, pp 749--773, 2016), WLS-ENOR differs from WLS-ENO and other WENO schemes in that it resolves not only the O(1) oscillations due to C 0 discontinuities, but also the accumulated effect of O(h) oscillations due to C 1 discontinuities. To this end, WLS-ENOR introduces a robust detector of discontinuities and a new weighting scheme for WLS-ENO near discontinuities. We also optimize the weights at smooth regions to achieve superconvergence. As a result, WLS-ENOR is more than fifth-order accurate and highly conservative in smooth regions, while being non-oscillatory and minimally diffusive near discontinuities. We also compare WLS-ENOR with some commonly used methods based on L 2 projection, moving least squares, and radial basis functions.

Developing accurate, transferable, and computationally-efficient interatomic forcefields is key to facilitate the modeling of silicate glasses. However, the high number of forcefield parameters that need to be optimized render traditional parameterization methods poorly efficient or potentially subject to bias. Here, we present a new forcefield parameterization methodology based on ab initio molecular dynamics simulations, Gaussian process regression, and Bayesian optimization. By taking the example of glassy silica, we show that our methodology yields a new interatomic forcefield that offers an unprecedented description of the atomic structure of silica. This methodology offers a new route to efficiently parameterize new empirical interatomic forcefields for silicate glasses with very limited need for intuition.

High-order surface reconstruction is an important technique for CAD-free, mesh-based geometric and physical modeling, and for high-order numerical methods for solving partial differential equations (PDEs) in engineering applications. In this paper, we introduce a novel method for accurate and robust reconstructions of piecewise smooth surfaces from a triangulated surface. Our proposed method extends the Continuous Moving Frames (CMF) and the Weighted Averaging of Local Fittings (WALF) methods (Engrg. Comput. 28 (2012)) in two main aspects. First, it utilizes a Hermite-style least squares approximation to achieve fourth and higher-order accuracy with compact support, even if the input mesh is relatively coarse. Second, it introduces an iterative feature-aware parameterization to ensure high-order accurate, G0 continuous reconstructions near sharp features. We present the theoretical framework of the method and compare it against CMF and WALF in terms of accuracy and stability. We also demonstrate that the use of the Hermite-style reconstruction in the solutions of PDEs using finite element methods (FEM), and show that quartic and sextic FEMs using the high-order reconstructed surfaces produce nearly identical results as using exact geometry while providing additional flexibility., Comment: 27 pages, 16 figures