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In this paper, we consider a distributed lossy compression network with $L$ encoders and a decoder. Each encoder observes a source and compresses it, which is sent to the decoder. Moreover, each observed source can be written as the sum of a target signal and a noise which are independently generated from two symmetric multivariate Gaussian distributions. The decoder jointly constructs the target signals given a threshold on the mean squared error distortion. We are interested in the minimum compression rate of this network versus the distortion threshold which is known as the \emph{rate-distortion function}. We derive a lower bound on the rate-distortion function by solving a convex program, explicitly. The proposed lower bound matches the well-known Berger-Tung's upper bound for some values of the distortion threshold. The asymptotic expressions of the upper and lower bounds are derived in the large $L$ limit. Under specific constraints, the bounds match in the asymptotic regime yielding the characterization of the rate-distortion function.

Modern machine learning tools such as deep neural networks (DNNs) are playing a revolutionary role in many fields such as natural language processing, computer vision, and the internet of things. Once they are trained, deep learning models can be deployed on edge computers to perform classification and prediction on real-time data for these applications. Particularly for large models, the limited computational and memory resources on a single edge device can become the throughput bottleneck for an inference pipeline. To increase throughput and decrease per-device compute load, we present DEFER (Distributed Edge inFERence), a framework for distributed edge inference, which partitions deep neural networks into layers that can be spread across multiple compute nodes. The architecture consists of a single "dispatcher" node to distribute DNN partitions and inference data to respective compute nodes. The compute nodes are connected in a series pattern where each node's computed result is relayed to the subsequent node. The result is then returned to the Dispatcher. We quantify the throughput, energy consumption, network payload, and overhead for our framework under realistic network conditions using the CORE network emulator. We find that for the ResNet50 model, the inference throughput of DEFER with 8 compute nodes is 53% higher and per node energy consumption is 63% lower than single device inference. We further reduce network communication demands and energy consumption using the ZFP serialization and LZ4 compression algorithms. We have implemented DEFER in Python using the TensorFlow and Keras ML libraries, and have released DEFER as an open-source framework to benefit the research community.

Coded distributed computing (CDC) can trade extra computing power to reduce the communication load for the MapReduce-type systems. The optimal computation-communication tradeoff has been well studied for homogeneous systems, and some results have also been obtained under the heterogeneous condition in recent studies. However, the previous works allow the file placement and Reduce function assignment free to design for the scheme. In this paper, we consider the general heterogeneous MapReduce system, where the file placement and Reduce function assignment are arbitrary but prefixed among all nodes (i.e., can not be designed by the scheme), and the storage and the computational capabilities for different nodes are not necessarily equal. We propose two {universal} CDC schemes and establish upper bounds of the optimal communication load. The first achievable scheme, namely One-Shot Coded Transmission (OSCT), encodes the intermediate values (IVs) into message blocks with different sizes to exploit the multicasting gain, and each message block can be decoded independently by the intended nodes. The second scheme, namely Few-Shot Coded Transmission (FSCT), splits IVs into smaller pieces and each node jointly decodes multiple message blocks to obtain its desired IVs. We prove that our OSCT and FSCT are optimal in many cases, and give sufficient conditions for the optimality of OSCT and FSCT, respectively.

Deep neural networks (DNNs) exploit many layers and a large number of parameters to achieve excellent performance. The training process of DNN models generally handles large-scale input data with many sparse features, which incurs high Input/Output (IO) cost, while some layers are compute-intensive. The training process generally exploits distributed computing resources to reduce training time. In addition, heterogeneous computing resources, e.g., CPUs, GPUs of multiple types, are available for the distributed training process. Thus, the scheduling of multiple layers to diverse computing resources is critical for the training process. To efficiently train a DNN model using the heterogeneous computing resources, we propose a distributed framework, i.e., Paddle-Heterogeneous Parameter Server (Paddle-HeterPS), composed of a distributed architecture and a Reinforcement Learning (RL)-based scheduling method. The advantages of Paddle-HeterPS are three-fold compared with existing frameworks. First, Paddle-HeterPS enables efficient training process of diverse workloads with heterogeneous computing resources. Second, Paddle-HeterPS exploits an RL-based method to efficiently schedule the workload of each layer to appropriate computing resources to minimize the cost while satisfying throughput constraints. Third, Paddle-HeterPS manages data storage and data communication among distributed computing resources. We carry out extensive experiments to show that Paddle-HeterPS significantly outperforms state-of-the-art approaches in terms of throughput (14.5 times higher) and monetary cost (312.3% smaller). The codes of the framework are publicly available at: //github.com/PaddlePaddle/Paddle.

In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.

In this study, we analyze the efficiency of a protocol with discrete modulation of continuous variable non-Gaussian states, the coherent states having one photon added and then one photon subtracted (PASCS). We calculate the secure key generation rate against collective attacks using the fact that Eve's information can be bounded based on the protocol with Gaussian modulation, which in turn is unconditionally secure. Our results for a four-state protocol show that the PASCS always outperforms the equivalent coherent states protocol under the same environmental conditions. Interestingly, we find that for the protocol using discrete-modulated PASCS, the noisier the line, the better will be its performance compared to the protocol using coherent states. Thus, our proposal proves to be advantageous for performing quantum key distribution in non-ideal situations.

The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.

Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and often assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to bound the end-to-end privacy loss. The theoretical analysis shows that DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee.

In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the error is in $O(1/\sqrt{t})$, the structure of the communication network only impacts a second-order term in $O(1/t)$, where $t$ is time. In other words, the error due to limits in communication resources decreases at a fast rate even in the case of non-strongly-convex objective functions. Under the global regularity assumption, we provide a simple yet efficient algorithm called distributed randomized smoothing (DRS) based on a local smoothing of the objective function, and show that DRS is within a $d^{1/4}$ multiplicative factor of the optimal convergence rate, where $d$ is the underlying dimension.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.