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The Word Movers Distance (WMD) measures the semantic dissimilarity between two text documents by computing the cost of optimally moving all words of a source/query document to the most similar words of a target document. Computing WMD between two documents is costly because it requires solving an $O(V^3log(V))$ optimization problem where $V$ is the number of unique words in the document. Fortunately, WMD can be framed as an Earth Mover's Distance (EMD) for which the algorithmic complexity can be reduced to $O(V^2)$ by adding an entropy penalty to the optimization problem and solving it using the Sinkhorn-Knopp algorithm. Additionally, the computation can be made highly parallel by adopting a batching approach, i.e., computing the WMD of a single query document against multiple target documents at once. Sinkhorn WMD is a key kernel used in many ML/NLP applications. and usually gets implemented in Python. However, a straightforward Python implementation may leave significant performance on the table even though it may internally call optimized C++ BLAS routines. We present \emph{PASWD}: a new sparse {P}arallel {A}lgorithm for {S}inkhorn-Knopp {W}ord-movers {D}istance to compute the semantic distance of one document to many other documents by adopting the $O(V^2)$ EMD algorithm. We algorithmically transform $O(V^2)$ dense compute-heavy EMD version into an equivalent sparse one using new fused SDDMM-SpMM (sparse selection of dense-dense matrix-, sparse-dense matrix-multiplication) kernels. We implemented and optimized this algorithm for two very different architectures -- the new Intel Programmable Integrated Unified Memory Architecture (PIUMA) and Intel Xeon CPUs. We show that we were able to reach close to peak performance on both platforms.

Emerging distributed cloud architectures, e.g., fog and mobile edge computing, are playing an increasingly important role in the efficient delivery of real-time stream-processing applications such as augmented reality, multiplayer gaming, and industrial automation. While such applications require processed streams to be shared and simultaneously consumed by multiple users/devices, existing technologies lack efficient mechanisms to deal with their inherent multicast nature, leading to unnecessary traffic redundancy and network congestion. In this paper, we establish a unified framework for distributed cloud network control with generalized (mixed-cast) traffic flows that allows optimizing the distributed execution of the required packet processing, forwarding, and replication operations. We first characterize the enlarged multicast network stability region under the new control framework (with respect to its unicast counterpart). We then design a novel queuing system that allows scheduling data packets according to their current destination sets, and leverage Lyapunov drift-plus-penalty theory to develop the first fully decentralized, throughput- and cost-optimal algorithm for multicast cloud network flow control. Numerical experiments validate analytical results and demonstrate the performance gain of the proposed design over existing cloud network control techniques.

Universal fault-tolerant quantum computers will require the use of efficient protocols to implement encoded operations necessary in the execution of algorithms. In this work, we show how satisfiability modulo theories (SMT) solvers can be used to automate the construction of Clifford circuits with certain fault-tolerance properties and apply our techniques to a fault-tolerant magic state preparation protocol. Part of the protocol requires converting magic states encoded in the color code to magic states encoded in the surface code. Since the teleportation step involves decoding a color code merged with a surface code, we develop a new decoding algorithm applicable to such codes.

Spectral efficiency improvement is a key focus in most wireless communication systems and achieved by various means such as using large antenna arrays and/or advanced modulation schemes and signal formats. This work proposes to further improve spectral efficiency through combining non-orthogonal spectrally efficient frequency division multiplexing (SEFDM) systems with index modulation (IM), which can efficiently make use of the indices of activated subcarriers as communication information. Recent research has verified that IM may be used with SEFDM to alleviate inter-carrier interference (ICI) and improve error performance. This work proposes new SEFDM signal formats based on novel activation pattern designs, which limit the locations of activated subcarriers and enable a variable number of activated subcarriers in each SEFDM subblock. SEFDM-IM system designs are developed by jointly considering activation patterns, modulation schemes and signal waveform formats, with a set of solutions evaluated under different spectral efficiency scenarios. Detailed modelling of coded systems and simulation studies reveal that the proposed designs not only lead to better bit error rate (BER) but also lower peak-to-average power ratio (PAPR) and reduced computational complexity relative to other reported index-modulated systems.

Recurrent models have been dominating the field of neural machine translation (NMT) for the past few years. Transformers \citep{vaswani2017attention}, have radically changed it by proposing a novel architecture that relies on a feed-forward backbone and self-attention mechanism. Although Transformers are powerful, they could fail to properly encode sequential/positional information due to their non-recurrent nature. To solve this problem, position embeddings are defined exclusively for each time step to enrich word information. However, such embeddings are fixed after training regardless of the task and the word ordering system of the source or target language. In this paper, we propose a novel architecture with new position embeddings depending on the input text to address this shortcoming by taking the order of target words into consideration. Instead of using predefined position embeddings, our solution \textit{generates} new embeddings to refine each word's position information. Since we do not dictate the position of source tokens and learn them in an end-to-end fashion, we refer to our method as \textit{dynamic} position encoding (DPE). We evaluated the impact of our model on multiple datasets to translate from English into German, French, and Italian and observed meaningful improvements in comparison to the original Transformer.

Autonomous marine vessels are expected to avoid inter-vessel collisions and comply with the international regulations for safe voyages. This paper presents a stepwise path planning method using stream functions. The dynamic flow of fluids is used as a guidance model, where the collision avoidance in static environments is achieved by applying the circular theorem in the sink flow. We extend this method to dynamic environments by adding vortex flows in the flow field. The stream function is recursively updated to enable on the fly waypoint decisions. The vessel avoids collisions and also complies with several rules of the Convention on the International Regulations for Preventing Collisions at Sea. The method is conceptually and computationally simple and convenient to tune, and yet versatile to handle complex and dense marine traffic with multiple dynamic obstacles. The ship dynamics are taken into account, by using B\'{e}zier curves to generate a sufficiently smooth path with feasible curvature. Numerical simulations are conducted to verify the proposed method.

Generalized pair weights of linear codes are generalizations of minimum symbol-pair weights, which were introduced by Liu and Pan \cite{LP} recently. Generalized pair weights can be used to characterize the ability of protecting information in the symbol-pair read wire-tap channels of type II. In this paper, we introduce the notion of generalized $b$-symbol weights of linear codes over finite fields, which is a generalization of generalized Hamming weights and generalized pair weights. We obtain some basic properties and bounds of generalized $b$-symbol weights which are called Singleton-like bounds for generalized $b$-symbol weights. As examples, we calculate generalized weight matrices for simplex codes and Hamming codes. We provide a necessary and sufficient condition for a linear code to be a $b$-symbol MDS code by using the generator matrix and the parity check matrix of this linear code. Finally, a necessary and sufficient condition of a linear isomorphism preserving $b$-symbol weights between two linear codes is obtained. As a corollary, we get the classical MacWilliams extension theorem when $b=1$.

In this work, we develop quantization and variable-length source codecs for the feedback links in linear-quadratic-Gaussian (LQG) control systems. We prove that for any fixed control performance, the approaches we propose nearly achieve lower bounds on communication cost that have been established in prior work. In particular, we refine the analysis of a classical achievability approach with an eye towards more practical details. Notably, in the prior literature the source codecs used to demonstrate the (near) achievability of these lower bounds are often implicitly assumed to be time-varying. For single-input single-output (SISO) plants, we prove that it suffices to consider time-invariant quantization and source coding. This result follows from analyzing the long-term stochastic behavior of the system's quantized measurements and reconstruction errors. To our knowledge, this time-invariant achievability result is the first in the literature.

Most existing works of polar codes focus on the analysis of block error probability. However, in many scenarios, bit error probability is also important for evaluating the performance of channel codes. In this paper, we establish a new framework to analyze the bit error probability of polar codes. Specifically, by revisiting the error event of bit-channel, we first introduce the conditional bit error probability as a metric to evaluate the reliability of bit-channel for both systematic and non-systematic polar codes. Guided by the concept of polar subcode, we then derive an upper bound on the conditional bit error probability of each bit-channel, and accordingly, an upper bound on the bit error probability of polar codes. Based on these, two types of construction metrics aiming at minimizing the bit error probability of polar codes are proposed, which are of linear computational complexity and explicit forms. Simulation results show that the polar codes constructed by the proposed methods can outperform those constructed by the conventional methods.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.