There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

Modern mobile devices have access to a wealth of data suitable for learning models, which in turn can greatly improve the user experience on the device. For example, language models can improve speech recognition and text entry, and image models can automatically select good photos. However, this rich data is often privacy sensitive, large in quantity, or both, which may preclude logging to the data center and training there using conventional approaches. We advocate an alternative that leaves the training data distributed on the mobile devices, and learns a shared model by aggregating locally-computed updates. We term this decentralized approach Federated Learning. 
We present a practical method for the federated learning of deep networks based on iterative model averaging, and conduct an extensive empirical evaluation, considering five different model architectures and four datasets. These experiments demonstrate the approach is robust to the unbalanced and non-IID data distributions that are a defining characteristic of this setting. Communication costs are the principal constraint, and we show a reduction in required communication rounds by 10-100x as compared to synchronized stochastic gradient descent.

Communication-Efficient Learning of Deep Networks from Decentralized Data

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Convex Analysisの二,三の進展について

Machine learning techniques based on neural networks are achieving remarkable results in a wide variety of domains. Often, the training of models requires large, representative datasets, which may be crowdsourced and contain sensitive information. The models should not expose private information in these datasets. Addressing this goal, we develop new algorithmic techniques for learning and a refined analysis of privacy costs within the framework of differential privacy. Our implementation and experiments demonstrate that we can train deep neural networks with non-convex objectives, under a modest privacy budget, and at a manageable cost in software complexity, training efficiency, and model quality.

Deep Learning with Differential Privacy

Influence maximization is the problem of finding a small set of most influential nodes in a social network so that their aggregated influence in the network is maximized. In this paper, we study influence maximization in the linear threshold model, one of the important models formalizing the behavior of influence propagation in social networks. We first show that computing exact influence in general networks in the linear threshold model is #P-hard, which closes an open problem left in the seminal work on influence maximization by Kempe, Kleinberg, and Tardos, 2003. As a contrast, we show that computing influence in directed a cyclic graphs (DAGs) can be done in time linear to the size of the graphs. Based on the fast computation in DAGs, we propose the first scalable influence maximization algorithm tailored for the linear threshold model. We conduct extensive simulations to show that our algorithm is scalable to networks with millions of nodes and edges, is orders of magnitude faster than the greedy approximation algorithm proposed by Kempe et al. and its optimized versions, and performs consistently among the best algorithms while other heuristic algorithms not design specifically for the linear threshold model have unstable performances on different real-world networks.

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Scalable Influence Maximization in Social Networks under the Linear Threshold Model

We demonstrate that it is possible to train large recurrent language models with user-level differential privacy guarantees with only a negligible cost in predictive accuracy. Our work builds on recent advances in the training of deep networks on user-partitioned data and privacy accounting for stochastic gradient descent. In particular, we add user-level privacy protection to the federated averaging algorithm, which makes "large step" updates from user-level data. Our work demonstrates that given a dataset with a sufficiently large number of users (a requirement easily met by even small internet-scale datasets), achieving differential privacy comes at the cost of increased computation, rather than in decreased utility as in most prior work. We find that our private LSTM language models are quantitatively and qualitatively similar to un-noised models when trained on a large dataset.

Learning Differentially Private Recurrent Language Models

We propose a new routing graph, the Restricted Delaunay Graph (RDG), for ad hoc networks. Combined with a node clustering algorithm RDG can be used as an underlying graph for geographic routing protocols. This graph has the following attractive properties: (1) it is a planar graph; (2) between any two nodes there exists a path in the RDG whose length, whether measured in terms of topological or Euclidean distance, is only a constant times the optimum length possible; and (3) the graph can be maintained efficiently in a distributed manner when the nodes move around. Furthermore, each node only needs constant time to make routing decisions. We also show by simulation that the RDG outperforms the previously proposed routing graphs under the Greedy Perimeter Stateless Routing (GPSR) protocol. In addition, we investigate theoretical bounds on the quality of paths discovered using GPSR

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Li Zhang

Papers

Deep Learning with Differential Privacy

Deep Learning with Differential Privacy

Scalable Influence Maximization in Social Networks under the Linear Threshold Model

Learning Differentially Private Recurrent Language Models

Geometric spanner for routing in mobile networks