We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

/pdf/going-deeper-with-convolutions-1yobw2o2ds.pdf

Going deeper with convolutions

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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

/pdf/distributed-optimization-and-statistical-learning-via-the-8s9gtddw0d.pdf

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to a collection of low dimensional manifolds. To emphasize this, the dimension of the manifold is directly used as a regularizer in a variational functional, which is solved efficiently by alternating direction of minimization and weighted nonlocal Laplacian. Unlike general 3D images, the same similarity matrix can be shared across all spectral bands for a hyperspectral image, therefore the resulting algorithm is much more scalable than that for general 3D data [1]. Numerical experiments on the reconstruction of hyperspectral images from sparse and noisy sampling demonstrate the superiority of our proposed algorithm in terms of both speed and accuracy.

Scalable Low Dimensional Manifold Model In The Reconstruction Of Noisy And Incomplete Hyperspectral Images

Belief and opinion evolution in social networks (SNs) can aid in understanding how people influence others’ decisions through social relationships as well as provide a solid foundation for many valuable social applications. As large numbers of users are involved in SNs, the complexity of traditional optimization techniques is high as they deal with the interactions between users separately. Moreover, the state variable (opinion) is high-dimensional because a person usually has opinions about many different social issues. To overcome those challenges, we formulate the opinion evolution in SNs as a high-dimensional stochastic mean field game (MFG). Numerical methods for high-dimensional MFGs are practically non-existent because of the need for grid-based spatial discretization. Thus, we propose a machine-learning based method, where we use an alternating population and agent control neural network (APAC-net), to tractably solve high-dimensional stochastic MFGs. Through APAC-net, solving MFGs can be regarded as a special case of training a generative adversarial network (GAN). To the best of our knowledge, the APAC-Net is the first model that can solve high-dimensional stochastic MFGs. The simulation results affirm the efficiency of the APAC-net.

Belief and Opinion Evolution in Social Networks: A High-Dimensional Mean Field Game Approach

Numerical solution of high frequency expansion for hyperbolic equations

We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm with $\ell_1$ regularization. The minimization problem can be efficiently solved by a split Bergman iteration type algorithm. We further prove that from any initial condition, the algorithm converges to a minimizer of the variational principle.

Density matrix minimization with $\ell_1$ regularization

We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to a collection of low dimensional manifolds. To emphasize this, the dimension of the manifold is directly used as a regularizer in a variational functional, which is solved efficiently by alternating direction of minimization and weighted nonlocal Laplacian. Unlike general 3D images, the same similarity matrix can be shared across all spectral bands for a hyperspectral image, therefore the resulting algorithm is much more scalable than that for general 3D data. Numerical experiments on the reconstruction of hyperspectral images from sparse and noisy sampling demonstrate the superiority of our proposed algorithm in terms of both speed and accuracy.

Stanley Osher

Papers

Scalable Low Dimensional Manifold Model In The Reconstruction Of Noisy And Incomplete Hyperspectral Images

Belief and Opinion Evolution in Social Networks: A High-Dimensional Mean Field Game Approach

Numerical solution of high frequency expansion for hyperbolic equations

Density matrix minimization with $\ell_1$ regularization

Scalable low dimensional manifold model in the reconstruction of noisy and incomplete hyperspectral images