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The method of types presented by Csiszar and Korner is a central tool used to develop and analyze the basic properties and constraints on sequences of data over finite alphabets. A central problem considered using these tools is that of data compression, and specifically lossy data compression. In this work we consider this very problem, however, instead of sequences of data we consider directed graphs. We show that given a more natural distortion measure, fitting the data structure of a directed graph, the method of types cannot be applied. The suggested distortion measure aims to preserves the local structure of a directed graph. We build on the recent work of Barvinok and extend the method of types to the two dimensional setting of directed graphs. We see that the extension is quite natural in many ways. Given this extension we provide a lower and upper bound on the rate-distortion problem of lossy compression given the suggested distortion measure.

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iOS 8 提供的應用間和應用跟系統的功能交互特性。
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Learned image compression methods generally optimize a rate-distortion loss, trading off improvements in visual distortion for added bitrate. Increasingly, however, compressed imagery is used as an input to deep learning networks for various tasks such as classification, object detection, and superresolution. We propose a recognition-aware learned compression method, which optimizes a rate-distortion loss alongside a task-specific loss, jointly learning compression and recognition networks. We augment a hierarchical autoencoder-based compression network with an EfficientNet recognition model and use two hyperparameters to trade off between distortion, bitrate, and recognition performance. We characterize the classification accuracy of our proposed method as a function of bitrate and find that for low bitrates our method achieves as much as 26% higher recognition accuracy at equivalent bitrates compared to traditional methods such as Better Portable Graphics (BPG).

We study the problem of computing the vitality with respect to max flow of edges and vertices in undirected planar graphs, where the vitality of an edge/vertex in a graph with respect to max flow between two fixed vertices $s,t$ is defined as the max flow decrease when the edge/vertex is removed from the graph. We show that the vitality of any $k$ selected edges can be computed in $O(kn + n\log\log n)$ worst-case time, and that a $\delta$ additive approximation of the vitality of all edges with capacity at most $c$ can be computed in $O(\frac{c}{\delta}n +n \log \log n)$ worst-case time, where $n$ is the size of the graph. Similar results are given for the vitality of vertices. All our algorithms work in $O(n)$ space.

Today's scientific high performance computing (HPC) applications or advanced instruments are producing vast volumes of data across a wide range of domains, which introduces a serious burden on data transfer and storage. Error-bounded lossy compression has been developed and widely used in scientific community, because not only can it significantly reduce the data volumes but it can also strictly control the data distortion based on the use-specified error bound. Existing lossy compressors, however, cannot offer ultra-fast compression speed, which is highly demanded by quite a few applications or use-cases (such as in-memory compression and online instrument data compression). In this paper, we propose a novel ultra-fast error-bounded lossy compressor, which can obtain fairly high compression performance on both CPU and GPU, also with reasonably high compression ratios. The key contributions are three-fold: (1) We propose a novel, generic ultra-fast error-bounded lossy compression framework -- called UFZ, by confining our design to be composed of only super-lightweight operations such as bitwise and addition/subtraction operation, still keeping a certain high compression ratio. (2) We implement UFZ on both CPU and GPU and optimize the performance according to their architectures carefully. (3) We perform a comprehensive evaluation with 6 real-world production-level scientific datasets on both CPU and GPU. Experiments show that UFZ is 2~16X as fast as the second-fastest existing error-bounded lossy compressor (either SZ or ZFP) on CPU and GPU, with respect to both compression and decompression.

We develop a sparse optimization problem for the determination of the total set of features that discriminate two or more classes. This is a sparse implementation of the centroid-encoder for nonlinear data reduction and visualization called Sparse Centroid-Encoder (SCE). We also provide a feature selection framework that first ranks each feature by its occurrence, and the optimal number of features is chosen using a validation set. The algorithm is applied to a wide variety of data sets including, single-cell biological data, high dimensional infectious disease data, hyperspectral data, image data, and speech data. We compared our method to various state-of-the-art feature selection techniques, including two neural network-based models (DFS, and LassoNet), Sparse SVM, and Random Forest. We empirically showed that SCE features produced better classification accuracy on the unseen test data, often with fewer features.

Neural compression algorithms are typically based on autoencoders that require specialized encoder and decoder architectures for different data modalities. In this paper, we propose COIN++, a neural compression framework that seamlessly handles a wide range of data modalities. Our approach is based on converting data to implicit neural representations, i.e. neural functions that map coordinates (such as pixel locations) to features (such as RGB values). Then, instead of storing the weights of the implicit neural representation directly, we store modulations applied to a meta-learned base network as a compressed code for the data. We further quantize and entropy code these modulations, leading to large compression gains while reducing encoding time by two orders of magnitude compared to baselines. We empirically demonstrate the effectiveness of our method by compressing various data modalities, from images to medical and climate data.

Optimal $k$-thresholding algorithms are a class of sparse signal recovery algorithms that overcome the shortcomings of traditional hard thresholding algorithms caused by the oscillation of the residual function. In this paper, a novel convergence analysis for optimal $k$-thresholding algorithms is established, which reveals the data-time tradeoffs of these algorithms. Both the analysis and numerical results demonstrate that when the number of measurements is small, the algorithms cannot converge; when the number of measurements is suitably large, the number of iterations required for successful recovery has a negative correlation with the number of measurements, and the algorithms can achieve linear convergence. Furthermore, the main theorems indicate that the number of measurements required for successful recovery is on the order of $k \log({n}/{k})$, where $n$ is the dimension of the target signal.

In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field, and we show that the method generalizes CNNs on an n-dimensional grid, and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection, rotation and distortion on the underlying directional field. We evaluate our method on different standard benchmarks and see a relative error reduction of 8\% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset. An important outcome of this work is that it enables to translate any physical or biological problems with intrinsic directional axes into a graph network formalism with an embedded directional field.

The spatial convolution layer which is widely used in the Graph Neural Networks (GNNs) aggregates the feature vector of each node with the feature vectors of its neighboring nodes. The GNN is not aware of the locations of the nodes in the global structure of the graph and when the local structures corresponding to different nodes are similar to each other, the convolution layer maps all those nodes to similar or same feature vectors in the continuous feature space. Therefore, the GNN cannot distinguish two graphs if their difference is not in their local structures. In addition, when the nodes are not labeled/attributed the convolution layers can fail to distinguish even different local structures. In this paper, we propose an effective solution to address this problem of the GNNs. The proposed approach leverages a spatial representation of the graph which makes the neural network aware of the differences between the nodes and also their locations in the graph. The spatial representation which is equivalent to a point-cloud representation of the graph is obtained by a graph embedding method. Using the proposed approach, the local feature extractor of the GNN distinguishes similar local structures in different locations of the graph and the GNN infers the topological structure of the graph from the spatial distribution of the locally extracted feature vectors. Moreover, the spatial representation is utilized to simplify the graph down-sampling problem. A new graph pooling method is proposed and it is shown that the proposed pooling method achieves competitive or better results in comparison with the state-of-the-art methods.

Referring expression comprehension aims to locate the object instance described by a natural language referring expression in an image. This task is compositional and inherently requires visual reasoning on top of the relationships among the objects in the image. Meanwhile, the visual reasoning process is guided by the linguistic structure of the referring expression. However, existing approaches treat the objects in isolation or only explore the first-order relationships between objects without being aligned with the potential complexity of the expression. Thus it is hard for them to adapt to the grounding of complex referring expressions. In this paper, we explore the problem of referring expression comprehension from the perspective of language-driven visual reasoning, and propose a dynamic graph attention network to perform multi-step reasoning by modeling both the relationships among the objects in the image and the linguistic structure of the expression. In particular, we construct a graph for the image with the nodes and edges corresponding to the objects and their relationships respectively, propose a differential analyzer to predict a language-guided visual reasoning process, and perform stepwise reasoning on top of the graph to update the compound object representation at every node. Experimental results demonstrate that the proposed method can not only significantly surpass all existing state-of-the-art algorithms across three common benchmark datasets, but also generate interpretable visual evidences for stepwisely locating the objects referred to in complex language descriptions.

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.

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