We consider the downlink of a cooperative cellular communications system, where several base-stations around each mobile cooperate and perform zero-forcing to reduce the received interference at the mobile. We derive closed-form expressions for the asymptotic performance of the network as the number of antennas per base station grows large. These expressions capture the trade off between various system parameters, and characterize the joint effect of noise and interference (where either noise or interference is asymptotically dominant and where both are asymptotically relevant). The asymptotic results are verified using Monte Carlo simulations, which indicate that they are useful even when the number of antennas per base station is only moderately large. Additionally, we show that when the number of antennas per base station grows large, power allocation can be optimized locally at each base station. We hence present a power allocation algorithm that achieves near optimal performance while significantly reducing the coordination overhead between base stations. The presented analysis is significantly more challenging than the uplink analysis, due to the dependence between beamforming vectors of nearby base stations. This statistical dependence is handled by introducing novel bounds on marked shot-noise point processes with dependent marks, which are also useful in other contexts.
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In contrast to regular (simple) networks, hyper networks possess the ability to depict more complex relationships among nodes and store extensive information. Such networks are commonly found in real-world applications, such as in social interactions. Learning embedded representations for nodes involves a process that translates network structures into more simplified spaces, thereby enabling the application of machine learning approaches designed for vector data to be extended to network data. Nevertheless, there remains a need to delve into methods for learning embedded representations that prioritize structural aspects. This research introduces HyperS2V, a node embedding approach that centers on the structural similarity within hyper networks. Initially, we establish the concept of hyper-degrees to capture the structural properties of nodes within hyper networks. Subsequently, a novel function is formulated to measure the structural similarity between different hyper-degree values. Lastly, we generate structural embeddings utilizing a multi-scale random walk framework. Moreover, a series of experiments, both intrinsic and extrinsic, are performed on both toy and real networks. The results underscore the superior performance of HyperS2V in terms of both interpretability and applicability to downstream tasks.
Deep neural networks have emerged as the workhorse for a large section of robotics and control applications, especially as models for dynamical systems. Such data-driven models are in turn used for designing and verifying autonomous systems. They are particularly useful in modeling medical systems where data can be leveraged to individualize treatment. In safety-critical applications, it is important that the data-driven model is conformant to established knowledge from the natural sciences. Such knowledge is often available or can often be distilled into a (possibly black-box) model. For instance, an F1 racing car should conform to Newton's laws (which are encoded within a unicycle model). In this light, we consider the following problem - given a model $M$ and a state transition dataset, we wish to best approximate the system model while being a bounded distance away from $M$. We propose a method to guarantee this conformance. Our first step is to distill the dataset into a few representative samples called memories, using the idea of a growing neural gas. Next, using these memories we partition the state space into disjoint subsets and compute bounds that should be respected by the neural network in each subset. This serves as a symbolic wrapper for guaranteed conformance. We argue theoretically that this only leads to a bounded increase in approximation error; which can be controlled by increasing the number of memories. We experimentally show that on three case studies (Car Model, Drones, and Artificial Pancreas), our constrained neurosymbolic models conform to specified models (each encoding various constraints) with order-of-magnitude improvements compared to the augmented Lagrangian and vanilla training methods. Our code can be found at: //github.com/kaustubhsridhar/Constrained_Models
With the increasing interconnection of smart devices, users often desire to adopt the same app on quite different devices for identical tasks, such as watching the same movies on both their smartphones and TVs. However, the significant differences in screen size, aspect ratio, and interaction styles make it challenging to adapt Graphical User Interfaces (GUIs) across these devices. Although there are millions of apps available on Google Play, only a few thousand are designed to support smart TV displays. Existing techniques to map a mobile app GUI to a TV either adopt a responsive design, which struggles to bridge the substantial gap between phone and TV or use mirror apps for improved video display, which requires hardware support and extra engineering efforts. Instead of developing another app for supporting TVs, we propose a semi-automated approach to generate corresponding adaptive TV GUIs, given the phone GUIs as the input. Based on our empirical study of GUI pairs for TVs and phones in existing apps, we synthesize a list of rules for grouping and classifying phone GUIs, converting them to TV GUIs, and generating dynamic TV layouts and source code for the TV display. Our tool is not only beneficial to developers but also to GUI designers, who can further customize the generated GUIs for their TV app development. An evaluation and user study demonstrate the accuracy of our generated GUIs and the usefulness of our tool.
We study reliable communication over point-to-point adversarial channels in which the adversary can observe the transmitted codeword via some function that takes the $n$-bit codeword as input and computes an $rn$-bit output for some given $r \in [0,1]$. We consider the scenario where the $rn$-bit observation is computationally bounded -- the adversary is free to choose an arbitrary observation function as long as the function can be computed using a polynomial amount of computational resources. This observation-based restriction differs from conventional channel-based computational limitations, where in the later case, the resource limitation applies to the computation of the (adversarial) channel error. For all $r \in [0,1-H(p)]$ where $H(\cdot)$ is the binary entropy function and $p$ is the adversary's error budget, we characterize the capacity of the above channel. For this range of $r$, we find that the capacity is identical to the completely obvious setting ($r=0$). This result can be viewed as a generalization of known results on myopic adversaries and channels with active eavesdroppers for which the observation process depends on a fixed distribution and fixed-linear structure, respectively, that cannot be chosen arbitrarily by the adversary.
This study addresses the security challenges associated with the current internet transformations, specifically focusing on emerging technologies such as blockchain and decentralized storage. It also investigates the role of Web3 applications in shaping the future of the internet. The primary objective is to propose a novel design for 'smart certificates,' which are digital certificates that can be programmatically enforced. Utilizing such certificates, an enterprise can better protect itself from cyberattacks and ensure the security of its data and systems. Web3 recent security solutions by companies and projects like Certik, Forta, Slither, and Securify are the equivalent of code scanning tool that were originally developed for Web1 and Web2 applications, and definitely not like certificates to help enterprises feel safe against cyberthreats. We aim to improve the resilience of enterprises' digital infrastructure by building on top of Web3 application and put methodologies in place for vulnerability analysis and attack correlation, focusing on architecture of different layers, Wallet/Client, Application and Smart Contract, where specific components are provided to identify and predict threats and risks. Furthermore, Certificate Transparency is used for enhancing the security, trustworthiness and decentralized management of the certificates, and detecting misuses, compromises, and malfeasances.
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.
Deep neural networks have achieved remarkable success in computer vision tasks. Existing neural networks mainly operate in the spatial domain with fixed input sizes. For practical applications, images are usually large and have to be downsampled to the predetermined input size of neural networks. Even though the downsampling operations reduce computation and the required communication bandwidth, it removes both redundant and salient information obliviously, which results in accuracy degradation. Inspired by digital signal processing theories, we analyze the spectral bias from the frequency perspective and propose a learning-based frequency selection method to identify the trivial frequency components which can be removed without accuracy loss. The proposed method of learning in the frequency domain leverages identical structures of the well-known neural networks, such as ResNet-50, MobileNetV2, and Mask R-CNN, while accepting the frequency-domain information as the input. Experiment results show that learning in the frequency domain with static channel selection can achieve higher accuracy than the conventional spatial downsampling approach and meanwhile further reduce the input data size. Specifically for ImageNet classification with the same input size, the proposed method achieves 1.41% and 0.66% top-1 accuracy improvements on ResNet-50 and MobileNetV2, respectively. Even with half input size, the proposed method still improves the top-1 accuracy on ResNet-50 by 1%. In addition, we observe a 0.8% average precision improvement on Mask R-CNN for instance segmentation on the COCO dataset.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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