arXiv subjects

Zheng Ma

Publications and source records attributed to Zheng Ma.

At least 109 records · Page 6Linked to original sources

arXiv2022

Asymptotic-Preserving Neural Networks for Multiscale Time-Dependent Linear Transport Equations

In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the network is to resolve the computational challenges of curse-of-dimensionality and multiple scales of the problem. We first show that a standard Physics-Informed Neural Network (PINN) fails to capture the multiscale nature of the problem, hence justifies the need to use Asymptotic-Preserving Neural Networks (APNNs). We show that not all classical AP formulations are fit for the neural network approach. We construct a micro-macro decomposition based neural network, and also build in a mass conservation mechanism into the loss function, in order to capture the dynamic and multiscale nature of the solutions. Numerical examples are used to demonstrate the effectiveness of this APNNs.

math.NA↗

arXiv2022

OpenCalib: A Multi-sensor Calibration Toolbox for Autonomous Driving

Accurate sensor calibration is a prerequisite for multi-sensor perception and localization systems for autonomous vehicles. The intrinsic parameter calibration of the sensor is to obtain the mapping relationship inside the sensor, and the extrinsic parameter calibration is to transform two or more sensors into a unified spatial coordinate system. Most sensors need to be calibrated after installation to ensure the accuracy of sensor measurements. To this end, we present OpenCalib, a calibration toolbox that contains a rich set of various sensor calibration methods. OpenCalib covers manual calibration tools, automatic calibration tools, factory calibration tools, and online calibration tools for different application scenarios. At the same time, to evaluate the calibration accuracy and subsequently improve the accuracy of the calibration algorithm, we released a corresponding benchmark dataset. This paper introduces various features and calibration methods of this toolbox. To our knowledge, this is the first open-sourced calibration codebase containing the full set of autonomous-driving-related calibration approaches in this area. We wish that the toolbox could be helpful to autonomous driving researchers. We have open-sourced our code on GitHub to benefit the community. Code is available at https://github.com/PJLab-ADG/SensorsCalibration.

cs.RO↗

arXiv2022

Unified Chinese License Plate Detection and Recognition with High Efficiency

Recently, deep learning-based methods have reached an excellent performance on License Plate (LP) detection and recognition tasks. However, it is still challenging to build a robust model for Chinese LPs since there are not enough large and representative datasets. In this work, we propose a new dataset named Chinese Road Plate Dataset (CRPD) that contains multi-objective Chinese LP images as a supplement to the existing public benchmarks. The images are mainly captured with electronic monitoring systems with detailed annotations. To our knowledge, CRPD is the largest public multi-objective Chinese LP dataset with annotations of vertices. With CRPD, a unified detection and recognition network with high efficiency is presented as the baseline. The network is end-to-end trainable with totally real-time inference efficiency (30 fps with 640p). The experiments on several public benchmarks demonstrate that our method has reached competitive performance. The code and dataset will be publicly available at https://github.com/yxgong0/CRPD.

cs.CV↗

arXiv2021

MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs

In this paper, we propose a a machine learning approach via model-operator-data network (MOD-Net) for solving PDEs. A MOD-Net is driven by a model to solve PDEs based on operator representation with regularization from data. For linear PDEs, we use a DNN to parameterize the Green's function and obtain the neural operator to approximate the solution according to the Green's method. To train the DNN, the empirical risk consists of the mean squared loss with the least square formulation or the variational formulation of the governing equation and boundary conditions. For complicated problems, the empirical risk also includes a few labels, which are computed on coarse grid points with cheap computation cost and significantly improves the model accuracy. Intuitively, the labeled dataset works as a regularization in addition to the model constraints. The MOD-Net solves a family of PDEs rather than a specific one and is much more efficient than original neural operator because few expensive labels are required. We numerically show MOD-Net is very efficient in solving Poisson equation and one-dimensional radiative transfer equation. For nonlinear PDEs, the nonlinear MOD-Net can be similarly used as an ansatz for solving nonlinear PDEs, exemplified by solving several nonlinear PDE problems, such as the Burgers equation.

math.NA↗

arXiv2021

Self-Secure Capacity-Achieving Feedback Schemes of Gaussian Multiple-Access Wiretap Channels with Degraded Message Sets

The Schalkwijk-Kailath (SK) scheme, which achieves the capacity of the point-to-point white Gaussian channel with feedback, is secure by itself and also achieves the secrecy capacity of the Gaussian wiretap channel with feedback, i.e., the SK scheme is a self-secure capacity-achieving (SSCA) feedback scheme for the Gaussian wiretap channel. For the multi-user wiretap channels, recently, it has been shown that Ozarow's capacity-achieving feedback scheme for the two-user Gaussian multiple-access channel (GMAC) is the SSCA feedback scheme for the two-user Gaussian multiple-access wiretap channel (GMAC-WT). In this paper, first, we propose a capacity-achieving feedback scheme for the two-user GMAC with degraded message sets (GMAC-DMS), and show that this scheme is the SSCA feedback scheme for the two-user GMAC-WT with degraded message sets (GMAC-WT-DMS). Next, we extend the above scheme to the two-user GMAC-DMS with noncausal channel state information at the transmitters (NCSIT), and show that the extended scheme is capacity-achieving and also a SSCA feedback scheme for the two-user GMAC-WT-DMS with NCSIT. Finally, we derive outer bounds on the secrecy capacity regions of the two-user GMAC-WT-DMS with or without NCSIT, and numerical results show the rate gains by the feedback.

cs.IT↗

arXiv2021

Unsupervised domain adaptation via coarse-to-fine feature alignment method using contrastive learning

Previous feature alignment methods in Unsupervised domain adaptation(UDA) mostly only align global features without considering the mismatch between class-wise features. In this work, we propose a new coarse-to-fine feature alignment method using contrastive learning called CFContra. It draws class-wise features closer than coarse feature alignment or class-wise feature alignment only, therefore improves the model's performance to a great extent. We build it upon one of the most effective methods of UDA called entropy minimization to further improve performance. In particular, to prevent excessive memory occupation when applying contrastive loss in semantic segmentation, we devise a new way to build and update the memory bank. In this way, we make the algorithm more efficient and viable with limited memory. Extensive experiments show the effectiveness of our method and model trained on the GTA5 to Cityscapes dataset has boost mIOU by 3.5 compared to the MinEnt algorithm. Our code will be publicly available.

cs.CV↗

arXiv2021

Network Pruning via Resource Reallocation

Channel pruning is broadly recognized as an effective approach to obtain a small compact model through eliminating unimportant channels from a large cumbersome network. Contemporary methods typically perform iterative pruning procedure from the original over-parameterized model, which is both tedious and expensive especially when the pruning is aggressive. In this paper, we propose a simple yet effective channel pruning technique, termed network Pruning via rEsource rEalLocation (PEEL), to quickly produce a desired slim model with negligible cost. Specifically, PEEL first constructs a predefined backbone and then conducts resource reallocation on it to shift parameters from less informative layers to more important layers in one round, thus amplifying the positive effect of these informative layers. To demonstrate the effectiveness of PEEL , we perform extensive experiments on ImageNet with ResNet-18, ResNet-50, MobileNetV2, MobileNetV3-small and EfficientNet-B0. Experimental results show that structures uncovered by PEEL exhibit competitive performance with state-of-the-art pruning algorithms under various pruning settings. Our code is available at https://github.com/cardwing/Codes-for-PEEL.

cs.CV↗

arXiv2021

Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks

Why heavily parameterized neural networks (NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle (LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that low frequency dominance of target functions is the key condition for the non-overfitting of NNs and is verified by experiments. Furthermore, through an ideal two-layer NN, we unravel how detailed microscopic NN training dynamics statistically gives rise to a LFP model with quantitative prediction power.

cs.LG↗

arXiv2021

Automatic Minimisation of Masking in Multitrack Audio using Subgroups

The iterative process of masking minimisation when mixing multitrack audio is a challenging optimisation problem, in part due to the complexity and non-linearity of auditory perception. In this article, we first propose a multitrack masking metric inspired by the MPEG psychoacoustic model. We investigate different audio processing techniques to manipulate the frequency and dynamic characteristics of the signal in order to reduce masking based on the proposed metric. We also investigate whether or not automatically mixing using subgrouping is beneficial or not to perceived quality and clarity of a mix. Evaluation results suggest that our proposed masking metric when used in an automatic mixing framework can be used to reduce inter-channel auditory masking as well as improve the perceived quality and perceived clarity of a mix. Furthermore, our results suggest that using subgrouping in an automatic mixing framework can be used to improve the perceived quality and perceived clarity of a mix.

eess.AS↗

arXiv2020

Fourier-domain Variational Formulation and Its Well-posedness for Supervised Learning

A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we propose a Fourier-domain variational formulation for supervised learning problem. This formulation circumvents the difficulty of imposing the constraints of given values on isolated data points in continuum modelling. Under a necessary and sufficient condition within our unified framework, we establish the well-posedness of the Fourier-domain variational problem, by showing a critical exponent depending on the data dimension. In practice, a neural network can be a convenient way to implement our formulation, which automatically satisfies the well-posedness condition.

math.NA↗

arXiv2020

Generation and Structural Characterization of Debye Random Media

In their seminal paper on scattering by an inhomogeneous solid, Debye and coworkers proposed a simple exponentially decaying function for the two-point correlation function of an idealized class of two-phase random media. Such {\it Debye random media}, which have been shown to be realizable, are singularly distinct from all other models of two-phase media in that they are entirely defined by their one- and two-point correlation functions. To our knowledge, there has been no determination of other microstructural descriptors of Debye random media. In this paper, we generate Debye random media in two dimensions using an accelerated Yeong-Torquato construction algorithm. We then ascertain microstructural descriptors of the constructed media, including their surface correlation functions, pore-size distributions, lineal-path function, and chord-length probability density function. Accurate semi-analytic and empirical formulas for these descriptors are devised. We compare our results for Debye random media to those of other popular models (overlapping disks and equilibrium hard disks), and find that the former model possesses a wider spectrum of hole sizes, including a substantial fraction of large holes. Our algorithm can be applied to generate other models defined by their two-point correlation functions, and their other microstructural descriptors can be determined and analyzed by the procedures laid out here.

cond-mat.dis-nn↗

arXiv2020

On the exact computation of linear frequency principle dynamics and its generalization

Recent works show an intriguing phenomenon of Frequency Principle (F-Principle) that deep neural networks (DNNs) fit the target function from low to high frequency during the training, which provides insight into the training and generalization behavior of DNNs in complex tasks. In this paper, through analysis of an infinite-width two-layer NN in the neural tangent kernel (NTK) regime, we derive the exact differential equation, namely Linear Frequency-Principle (LFP) model, governing the evolution of NN output function in the frequency domain during the training. Our exact computation applies for general activation functions with no assumption on size and distribution of training data. This LFP model unravels that higher frequencies evolve polynomially or exponentially slower than lower frequencies depending on the smoothness/regularity of the activation function. We further bridge the gap between training dynamics and generalization by proving that LFP model implicitly minimizes a Frequency-Principle norm (FP-norm) of the learned function, by which higher frequencies are more severely penalized depending on the inverse of their evolution rate. Finally, we derive an \textit{a priori} generalization error bound controlled by the FP-norm of the target function, which provides a theoretical justification for the empirical results that DNNs often generalize well for low frequency functions.

cs.LG↗

arXiv2020

Phase diagram for two-layer ReLU neural networks at infinite-width limit

How neural network behaves during the training over different choices of hyperparameters is an important question in the study of neural networks. In this work, inspired by the phase diagram in statistical mechanics, we draw the phase diagram for the two-layer ReLU neural network at the infinite-width limit for a complete characterization of its dynamical regimes and their dependence on hyperparameters related to initialization. Through both experimental and theoretical approaches, we identify three regimes in the phase diagram, i.e., linear regime, critical regime and condensed regime, based on the relative change of input weights as the width approaches infinity, which tends to $0$, $O(1)$ and $+\infty$, respectively. In the linear regime, NN training dynamics is approximately linear similar to a random feature model with an exponential loss decay. In the condensed regime, we demonstrate through experiments that active neurons are condensed at several discrete orientations. The critical regime serves as the boundary between above two regimes, which exhibits an intermediate nonlinear behavior with the mean-field model as a typical example. Overall, our phase diagram for the two-layer ReLU NN serves as a map for the future studies and is a first step towards a more systematical investigation of the training behavior and the implicit regularization of NNs of different structures.

cs.LG↗

arXiv2020

Predicting permeability via statistical learning on higher-order microstructural information

Quantitative structure-property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure facilitates prediction of permeability, a key property that has been extensively studied in material science, geophysics and chemical engineering. In this work, we study the predictability of different structural descriptors via both linear regressions and neural networks. A large data set of 30,000 virtual, porous microstructures of different types is created for this end. We compute permeabilities of these structures using the lattice Boltzmann method, and characterize the pore space geometry using one-point correlation functions (porosity, specific surface), two-point surface-surface, surface-void, and void-void correlation functions, as well as the geodesic tortuosity as an implicit descriptor. Then, we study the prediction of the permeability using different combinations of these descriptors. We obtain significant improvements of performance when compared to a Kozeny-Carman regression with only lowest-order descriptors (porosity and specific surface). We find that combining all three two-point correlation functions and tortuosity provides the best prediction of permeability, with the void-void correlation function being the most informative individual descriptor. Moreover, the combination of porosity, specific surface, and geodesic tortuosity provides very good predictive performance. This shows that higher-order correlation functions are extremely useful for forming a general model for predicting physical properties of complex materials. Additionally, our results suggest that neural networks are superior to the more conventional regression methods for establishing quantitative structure-property relationships.

cond-mat.soft↗

arXiv2020

Fully Decentralized Federated Learning Based Beamforming Design for UAV Communications

To handle the data explosion in the era of internet of things (IoT), it is of interest to investigate the decentralized network, with the aim at relaxing the burden to central server along with keeping data privacy. In this work, we develop a fully decentralized federated learning (FL) framework with an inexact stochastic parallel random walk alternating direction method of multipliers (ISPW-ADMM). Performing more communication efficient and enhanced privacy preservation compared with the current state-of-the-art, the proposed ISPW-ADMM can be partially immune to the impacts from time-varying dynamic network and stochastic data collection, while still in fast convergence. Benefits from the stochastic gradients and biased first-order moment estimation, the proposed framework can be applied to any decentralized FL tasks over time-varying graphs. Thus to further demonstrate the practicability of such framework in providing fast convergence, high communication efficiency, and system robustness, we study the extreme learning machine(ELM)-based FL model for robust beamforming (BF) design in UAV communications, as verified by the numerical simulations.

eess.SP↗

arXiv2020

A Dual Symmetric Gauss-Seidel Alternating Direction Method of Multipliers for Hyperspectral Sparse Unmixing

Since sparse unmixing has emerged as a promising approach to hyperspectral unmixing, some spatial-contextual information in the hyperspectral images has been exploited to improve the performance of the unmixing recently. The total variation (TV) has been widely used to promote the spatial homogeneity as well as the smoothness between adjacent pixels. However, the computation task for hyperspectral sparse unmixing with a TV regularization term is heavy. Besides, the convergence of the primal alternating direction method of multipliers (ADMM) for the hyperspectral sparse unmixing with a TV regularization term has not been explained in details. In this paper, we design an efficient and convergent dual symmetric Gauss-Seidel ADMM (sGS-ADMM) for hyperspectral sparse unmixing with a TV regularization term. We also present the global convergence and local linear convergence rate analysis for this algorithm. As demonstrated in numerical experiments, our algorithm can obviously improve the efficiency of the unmixing compared with the state-of-the-art algorithm. More importantly, we can obtain images with higher quality.

math.NA↗

arXiv2020

Path Integral Based Convolution and Pooling for Graph Neural Networks

Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose a path integral based graph neural networks (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix we call maximal entropy transition (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus providing a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics we propose to boost applications of GNN in physical sciences.

cs.LG↗

arXiv2020

Haar Graph Pooling

Deep Graph Neural Networks (GNNs) are useful models for graph classification and graph-based regression tasks. In these tasks, graph pooling is a critical ingredient by which GNNs adapt to input graphs of varying size and structure. We propose a new graph pooling operation based on compressive Haar transforms -- HaarPooling. HaarPooling implements a cascade of pooling operations; it is computed by following a sequence of clusterings of the input graph. A HaarPooling layer transforms a given input graph to an output graph with a smaller node number and the same feature dimension; the compressive Haar transform filters out fine detail information in the Haar wavelet domain. In this way, all the HaarPooling layers together synthesize the features of any given input graph into a feature vector of uniform size. Such transforms provide a sparse characterization of the data and preserve the structure information of the input graph. GNNs implemented with standard graph convolution layers and HaarPooling layers achieve state of the art performance on diverse graph classification and regression problems.

cs.LG↗