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GSM-R is predicted to be obsoleted by 2030, and a suitable successor is needed. Defined by the International Union of Railways (UIC), the Future Railway Mobile Communication System (FRMCS) contains many future use cases with strict requirements. These use cases should ensure regular communication not only in network coverage but also uncovered scenarios. There is still a lack of standards on off-network communication in FRMCS, so this article focuses on off-network communication and intends to provide reference and direction for standardization. We first provide a comprehensive summary and analysis of off-network use cases in FRMCS. Then we give an overview of existing technologies (GSM-R, TETRA, DMR, LTE-V2X, and NR-V2X) that may support off-network communication. In addition, we simulate and evaluate the performance of existing technologies. Simulation results show that it is possible to satisfy the off-network communication requirements in FRMCS with enhancements based on LTE-V2X or NR-V2X. Finally, we give some future research directions to provide insights for industry and academia.

In this paper, we introduce two types of novel Asymptotic-Preserving Convolutional Deep Operator Networks (APCONs) designed to address the multiscale time-dependent linear transport problem. We observe that the vanilla physics-informed DeepONets with modified MLP may exhibit instability in maintaining the desired limiting macroscopic behavior. Therefore, this necessitates the utilization of an asymptotic-preserving loss function. Drawing inspiration from the heat kernel in the diffusion equation, we propose a new architecture called Convolutional Deep Operator Networks, which employ multiple local convolution operations instead of a global heat kernel, along with pooling and activation operations in each filter layer. Our APCON methods possess a parameter count that is independent of the grid size and are capable of capturing the diffusive behavior of the linear transport problem. Finally, we validate the effectiveness of our methods through several numerical examples.

The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that automatic differentiation is not applicable for fractional derivatives, solving fractional diffusion equations using PINNs requires addressing additional challenges. To address this issue, this paper proposes an extension to PINNs called Laplace-based fractional physics-informed neural networks (Laplace-fPINNs), which can effectively solve the forward and inverse problems of fractional diffusion equations. This approach avoids introducing a mass of auxiliary points and simplifies the loss function. We validate the effectiveness of the Laplace-fPINNs approach using several examples. Our numerical results demonstrate that the Laplace-fPINNs method can effectively solve both the forward and inverse problems of high-dimensional fractional diffusion equations.

Mode collapse is still a major unsolved problem in generative adversarial networks. In this work, we analyze the causes of mode collapse from a new perspective. Due to the nonuniform sampling in the training process, some sub-distributions can be missed while sampling data. Therefore, the GAN objective can reach the minimum when the generated distribution is not the same as the real one. To alleviate the problem, we propose a global distribution fitting (GDF) method by a penalty term to constrain generated data distribution. On the basis of not changing the global minimum of the GAN objective, GDF will make it harder to reach the minimum value when the generated distribution is not the same as the real one. Furthermore, we also propose a local distribution fitting (LDF) method to cope with the situation that the real distribution is unknown. Experiments on several benchmarks demonstrate the effectiveness and competitive performance of GDF and LDF.

Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computation cost and storage resources because of the memory effect brought by the convolution integral of time fractional derivative. We propose a Bayesian Inversion with Neural Operator (BINO) to overcome the difficulty in traditional methods as follows. We employ a deep operator network to learn the solution operators for the fractional diffusion equations, allowing us to swiftly and precisely solve a forward problem for given inputs (including fractional order, diffusion coefficient, source terms, etc.). In addition, we integrate the deep operator network with a Bayesian inversion method for modelling a problem by subdiffusion process and solving inverse subdiffusion problems, which reduces the time costs (without suffering from overwhelm storage resources) significantly. A large number of numerical experiments demonstrate that the operator learning method proposed in this work can efficiently solve the forward problems and Bayesian inverse problems of the subdiffusion equation.

Background: Code summarization automatically generates the corresponding natural language descriptions according to the input code. Comprehensiveness of code representation is critical to code summarization task. However, most existing approaches typically use coarse-grained fusion methods to integrate multi-modal features. They generally represent different modalities of a piece of code, such as an Abstract Syntax Tree (AST) and a token sequence, as two embeddings and then fuse the two ones at the AST/code levels. Such a coarse integration makes it difficult to learn the correlations between fine-grained code elements across modalities effectively. Aims: This study intends to improve the model's prediction performance for high-quality code summarization by accurately aligning and fully fusing semantic and syntactic structure information of source code at node/token levels. Method: This paper proposes a Multi-Modal Fine-grained Feature Fusion approach (MMF3) for neural code summarization. We introduce a novel fine-grained fusion method, which allows fine-grained fusion of multiple code modalities at the token and node levels. Specifically, we use this method to fuse information from both token and AST modalities and apply the fused features to code summarization. Results: We conduct experiments on one Java and one Python datasets, and evaluate generated summaries using four metrics. The results show that: 1) the performance of our model outperforms the current state-of-the-art models, and 2) the ablation experiments show that our proposed fine-grained fusion method can effectively improve the accuracy of generated summaries. Conclusion: MMF3 can mine the relationships between crossmodal elements and perform accurate fine-grained element-level alignment fusion accordingly. As a result, more clues can be provided to improve the accuracy of the generated code summaries., Comment: 12 pages, 5 figures

A journal's impact and similarity with rivals is closely related to its competitive intensity. A subject area can be considered as an ecological system of journals, and can then be measured using the competitive intensity concept from plant systems. Based on Journal Citation Reports data from 1997, 2000, 2005, 2010, and 2013, we calculated the mutual citation, cosine similarity, and competitive relationship matrices for mycology journals. We derived the mutual citation network for mycology according to Journal Citation Reports data from 2013. We calculated each journal's competitive pressure, and the competitive intensity for the subject. We found that competitive pressures are very variable among journals. Differences between a journal's absolute and relative influence are related to the competitive pressure. A more powerful journal has lower competitive pressure. New journals have more competitive pressure. If there are no other influences, the competition intensity of a subject will continue to increase. Furthermore, we found that if a subject has more journals, its competitive intensity decreases., Comment: 10 pages, 3 figures

In recent years, vision and language pre-training (VLP) models have advanced the state-of-the-art results in a variety of cross-modal downstream tasks. Aligning cross-modal semantics is claimed to be one of the essential capabilities of VLP models. However, it still remains unclear about the inner working mechanism of alignment in VLP models. In this paper, we propose a new probing method that is based on image captioning to first empirically study the cross-modal semantics alignment of VLP models. Our probing method is built upon the fact that given an image-caption pair, the VLP models will give a score, indicating how well two modalities are aligned; maximizing such scores will generate sentences that VLP models believe are of good alignment. Analyzing these sentences thus will reveal in what way different modalities are aligned and how well these alignments are in VLP models. We apply our probing method to five popular VLP models, including UNITER, ROSITA, ViLBERT, CLIP, and LXMERT, and provide a comprehensive analysis of the generated captions guided by these models. Our results show that VLP models (1) focus more on just aligning objects with visual words, while neglecting global semantics; (2) prefer fixed sentence patterns, thus ignoring more important textual information including fluency and grammar; and (3) deem the captions with more visual words are better aligned with images. These findings indicate that VLP models still have weaknesses in cross-modal semantics alignment and we hope this work will draw researchers' attention to such problems when designing a new VLP model., Comment: Findings of EMNLP2022

Data imputation is an effective way to handle missing data, which is common in practical applications. In this study, we propose and test a novel data imputation process that achieve two important goals: (1) preserve the row-wise similarities among observations and column-wise contextual relationships among features in the feature matrix, and (2) tailor the imputation process to specific downstream label prediction task. The proposed imputation process uses Transformer network and graph structure learning to iteratively refine the contextual relationships among features and similarities among observations. Moreover, it uses a meta-learning framework to select features that are influential to the downstream prediction task of interest. We conduct experiments on real-world large data sets, and show that the proposed imputation process consistently improves imputation and label prediction performance over a variety of benchmark methods.

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., 12 pages, 11 figures, 7 tables

Deep neural network (DNN) usually learns the target function from low to high frequency, which is called frequency principle or spectral bias. This frequency principle sheds light on a high-frequency curse of DNNs -- difficult to learn high-frequency information. Inspired by the frequency principle, a series of works are devoted to develop algorithms for overcoming the high-frequency curse. A natural question arises: what is the upper limit of the decaying rate w.r.t. frequency when one trains a DNN? In this work, our theory, confirmed by numerical experiments, suggests that there is a critical decaying rate w.r.t. frequency in DNN training. Below the upper limit of the decaying rate, the DNN interpolates the training data by a function with a certain regularity. However, above the upper limit, the DNN interpolates the training data by a trivial function, i.e., a function is only non-zero at training data points. Our results indicate a better way to overcome the high-frequency curse is to design a proper pre-condition approach to shift high-frequency information to low-frequency one, which coincides with several previous developed algorithms for fast learning high-frequency information. More importantly, this work rigorously proves that the high-frequency curse is an intrinsic difficulty of DNNs., Comment: arXiv admin note: substantial text overlap with arXiv:2012.03238

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.

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.

The interpretability of Convolutional Neural Networks (CNNs) is an important topic in the field of computer vision. In recent years, works in this field generally adopt a mature model to reveal the internal mechanism of CNNs, helping to understand CNNs thoroughly. In this paper, we argue the working mechanism of CNNs can be revealed through a totally different interpretation, by comparing the communication systems and CNNs. This paper successfully obtained the corresponding relationship between the modules of the two, and verified the rationality of the corresponding relationship with experiments. Finally, through the analysis of some cutting-edge research on neural networks, we find the inherent relation between these two tasks can be of help in explaining these researches reasonably, as well as helping us discover the correct research direction of neural networks., Deep learning, adversarial example, interpretability

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., Comment: 18 pages, 5 figures

In recent years, deep learning has shown impressive performance on many tasks. However, recent researches showed that deep learning systems are vulnerable to small, specially crafted perturbations that are imperceptible to humans. Images with such perturbations are the so called adversarial examples, which have proven to be an indisputable threat to the DNN based applications. The lack of better understanding of the DNNs has prevented the development of efficient defenses against adversarial examples. In this paper, we propose a two-stream architecture to protect CNN from attacking by adversarial examples. Our model draws on the idea of "two-stream" which commonly used in the security field, and successfully defends different kinds of attack methods by the differences of "high-resolution" and "low-resolution" networks in feature extraction. We provide a reasonable interpretation on why our two-stream architecture is difficult to defeat, and show experimentally that our method is hard to defeat with state-of-the-art attacks. We demonstrate that our two-stream architecture is robust to adversarial examples built by currently known attacking algorithms., 10 pages, 5 figures

Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph convolution framework 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. PAN generalizes the graph Laplacian to a new transition matrix we call \emph{maximal entropy transition} (MET) matrix derived from a path integral formalism. Most previous graph convolutional network architectures can be adapted to our framework, and many variations and derivatives based on the path integral idea can be developed. Experimental results show that the path integral based graph neural networks have great learnability and fast convergence rate, and achieve state-of-the-art performance on benchmark tasks.

Spatio-temporal information is very important to capture the discriminative cues between genuine and fake faces from video sequences. To explore such a temporal feature, the fine-grained motions (e.g., eye blinking, mouth movements and head swing) across video frames are very critical. In this paper, we propose a joint CNN-LSTM network for face anti-spoofing, focusing on the motion cues across video frames. We first extract the high discriminative features of video frames using the conventional Convolutional Neural Network (CNN). Then we leverage Long Short-Term Memory (LSTM) with the extracted features as inputs to capture the temporal dynamics in videos. To ensure the fine-grained motions more easily to be perceived in the training process, the eulerian motion magnification is used as the preprocessing to enhance the facial expressions exhibited by individuals, and the attention mechanism is embedded in LSTM to ensure the model learn to focus selectively on the dynamic frames across the video clips. Experiments on Replay Attack and MSU-MFSD databases show that the proposed method yields state-of-the-art performance with better generalization ability compared with several other popular algorithms., Comment: 20 pages; 3 figures; 3 tables

How initialization and loss function affect the learning of a deep neural network (DNN), specifically its generalization error, is an important problem in practice. In this work, by exploiting the linearity of DNN training dynamics in the NTK regime \citep{jacot2018neural,lee2019wide}, we provide an explicit and quantitative answer to this problem. Focusing on regression problem, we prove that, in the NTK regime, for any loss in a general class of functions, the DNN finds the same \emph{global} minima---the one that is nearest to the initial value in the parameter space, or equivalently, the one that is closest to the initial DNN output in the corresponding reproducing kernel Hilbert space. Using these optimization problems, we quantify the impact of initial output and prove that a random non-zero one increases the generalization error. We further propose an antisymmetrical initialization (ASI) trick that eliminates this type of error and accelerates the training. To understand whether the above results hold in general, we also perform experiments for DNNs in the non-NTK regime, which demonstrate the effectiveness of our theoretical results and the ASI trick in a qualitative sense. Overall, our work serves as a baseline for the further investigation of the impact of initialization and loss function on the generalization of DNNs, which can potentially guide and improve the training of DNNs in practice., Comment: Accepted by MSML Revised the proof of Lemma 2

Graph Neural Networks (GNNs) have become a topic of intense research recently due to their powerful capability in high-dimensional classification and regression tasks for graph-structured data. However, as GNNs typically define the graph convolution by the orthonormal basis for the graph Laplacian, they suffer from high computational cost when the graph size is large. This paper introduces Haar basis which is a sparse and localized orthonormal system for a coarse-grained chain on graph. The graph convolution under Haar basis, called Haar convolution, can be defined accordingly for GNNs. The sparsity and locality of the Haar basis allow Fast Haar Transforms (FHTs) on graph, by which a fast evaluation of Haar convolution between graph data and filters can be achieved. We conduct experiments on GNNs equipped with Haar convolution, which demonstrates state-of-the-art results on graph-based regression and node classification tasks., Comment: 24 pages, 5 figures, 3 tables

It remains a puzzle that why deep neural networks (DNNs), with more parameters than samples, often generalize well. An attempt of understanding this puzzle is to discover implicit biases underlying the training process of DNNs, such as the Frequency Principle (F-Principle), i.e., DNNs often fit target functions from low to high frequencies. Inspired by the F-Principle, we propose an effective model of linear F-Principle (LFP) dynamics which accurately predicts the learning results of two-layer ReLU neural networks (NNs) of large widths. This LFP dynamics is rationalized by a linearized mean field residual dynamics of NNs. Importantly, the long-time limit solution of this LFP dynamics is equivalent to the solution of a constrained optimization problem explicitly minimizing an FP-norm, in which higher frequencies of feasible solutions are more heavily penalized. Using this optimization formulation, an a priori estimate of the generalization error bound is provided, revealing that a higher FP-norm of the target function increases the generalization error. Overall, by explicitizing the implicit bias of the F-Principle as an explicit penalty for two-layer NNs, our work makes a step towards a quantitative understanding of the learning and generalization of general DNNs.

Face anti-spoofing (a.k.a presentation attack detection) has drawn growing attention due to the high-security demand in face authentication systems. Existing CNN-based approaches usually well recognize the spoofing faces when training and testing spoofing samples display similar patterns, but their performance would drop drastically on testing spoofing faces of unseen scenes. In this paper, we try to boost the generalizability and applicability of these methods by designing a CNN model with two major novelties. First, we propose a simple yet effective Total Pairwise Confusion (TPC) loss for CNN training, which enhances the generalizability of the learned Presentation Attack (PA) representations. Secondly, we incorporate a Fast Domain Adaptation (FDA) component into the CNN model to alleviate negative effects brought by domain changes. Besides, our proposed model, which is named Generalizable Face Authentication CNN (GFA-CNN), works in a multi-task manner, performing face anti-spoofing and face recognition simultaneously. Experimental results show that GFA-CNN outperforms previous face anti-spoofing approaches and also well preserves the identity information of input face images., Comment: 8 pages; 8 figures; 4 tables

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., Need to resolve ownership of intellectual property

Reinforcement learning agents need exploratory behaviors to escape from local optima. These behaviors may include both immediate dithering perturbation and temporally consistent exploration. To achieve these, a stochastic policy model that is inherently consistent through a period of time is in desire, especially for tasks with either sparse rewards or long term information. In this work, we introduce a novel on-policy temporally consistent exploration strategy - Neural Adaptive Dropout Policy Exploration (NADPEx) - for deep reinforcement learning agents. Modeled as a global random variable for conditional distribution, dropout is incorporated to reinforcement learning policies, equipping them with inherent temporal consistency, even when the reward signals are sparse. Two factors, gradients' alignment with the objective and KL constraint in policy space, are discussed to guarantee NADPEx policy's stable improvement. Our experiments demonstrate that NADPEx solves tasks with sparse reward while naive exploration and parameter noise fail. It yields as well or even faster convergence in the standard mujoco benchmark for continuous control., Comment: To appear in ICLR 2019

Recently, the physical layer security (PLS) of the communication systems has been shown to be enhanced by using legal receiver's feedback. The present secret key based feedback scheme mainly focuses on producing key from the feedback and using this key to protect part of the transmitted message. However, this feedback scheme has been proved only optimal for several degraded cases. The broadcast channel with mutual secrecy requirement (BC-MSR) is important as it constitutes the essence of physical layer security (PLS) in the down-link of the wireless communication systems. In this paper, we investigate the feedback effects on the BC-MSR, and propose two inner bounds and one outer bound on the secrecy capacity region of the BC-MSR with noiseless feedback. One inner bound is constructed according to the already existing secret key based feedback coding scheme for the wiretap channel, and the other is constructed by a hybrid coding scheme using feedback to generate not only keys protecting the transmitted messages but also cooperative messages helping the receivers to improve their decoding performance. The performance of the proposed feedback schemes and the gap between the inner and outer bounds are further explained via two examples., Comment: Submitted to IEEE TIFS

For crowded scenes, the accuracy of object-based computer vision methods declines when the images are low-resolution and objects have severe occlusions. Taking counting methods for example, almost all the recent state-of-the-art counting methods bypass explicit detection and adopt regression-based methods to directly count the objects of interest. Among regression-based methods, density map estimation, where the number of objects inside a subregion is the integral of the density map over that subregion, is especially promising because it preserves spatial information, which makes it useful for both counting and localization (detection and tracking). With the power of deep convolutional neural networks (CNNs) the counting performance has improved steadily. The goal of this paper is to evaluate density maps generated by density estimation methods on a variety of crowd analysis tasks, including counting, detection, and tracking. Most existing CNN methods produce density maps with resolution that is smaller than the original images, due to the downsample strides in the convolution/pooling operations. To produce an original-resolution density map, we also evaluate a classical CNN that uses a sliding window regressor to predict the density for every pixel in the image. We also consider a fully convolutional (FCNN) adaptation, with skip connections from lower convolutional layers to compensate for loss in spatial information during upsampling. In our experiments, we found that the lower-resolution density maps sometimes have better counting performance. In contrast, the original-resolution density maps improved localization tasks, such as detection and tracking, compared to bilinear upsampling the lower-resolution density maps. Finally, we also propose several metrics for measuring the quality of a density map, and relate them to experiment results on counting and localization., accepted to IEEE Transactions on Circuits and Systems for Video Technology (TCSVT)

Recently, it has been shown that the time-varying multiple-access channel (MAC) with perfect channel state information (CSI) at the receiver and delayed feedback CSI at the transmitters can be modeled as the finite state MAC (FS-MAC) with delayed state feedback, where the time variation of the channel is characterized by the statistics of the underlying state process. To study the fundamental limit of the secure transmission over multi-user wireless communication systems, we re-visit the FS-MAC with delayed state feedback by considering an external eavesdropper, which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed feedback. The main contribution of this paper is to show that taking full advantage of the delayed channel output feedback helps to increase the secrecy rate region of the FS-MAC-WT with delayed state feedback, and the results of this paper are further illustrated by a degraded Gaussian fading example., Comment: Accepted by IEEE JSAC, special issue on physical layer security for 5G wireless networks

Broadcasting/multicasting is an efficient mechanism for multimedia communications due to its high spectrum efficiency, which achieves point-to-multipoint transmission on the same radio resources. To satisfy the increasing demands for multimedia broadcast multicast service (MBMS), we present a power domain non-orthogonal MBMS transmission scheme in a K-tier heterogeneous network (HetNet). Firstly, the system model, usage scenarios, and fundamentals of the presented scheme are discussed. Next, a tractable framework is developed to analyse the performance of non-orthogonal MBMS transmission, by using stochastic geometry. Based on this framework, the analytical expressions for the signal-to-interference-plus-noise ratio (SINR) coverage probability, average number of served users, and sum rate are derived. Furthermore, synchronous non-orthogonal MBMS transmission to further improving the system performance is also studied. The results demonstrate that non-orthogonal MBMS transmission can achieve better performance than the conventional one, in which non-orthogonal multirate one can fully utilize channel conditions to achieve a significant rate gain, while non-orthogonal multi-service one can efficiently use power resources to guarantee the quality of service (QoS) of high priority users, and also provide services for low priority users simultaneously., Comment: 30 pages, 8 figures