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

This paper describes an L1 regularized variational framework for developing a spatially localized basis, compressed plane waves, that spans the eigenspace of a differential operator, for instance, the Laplace operator. Our approach generalizes the concept of plane waves to an orthogonal real-space basis with multiresolution capabilities.

/pdf/compressed-plane-waves-yield-a-compactly-supported-4c0c9l7zsy.pdf

Compressed plane waves yield a compactly supported multiresolution basis for the Laplace operator

with A a diagonal matrix. Appropriate boundary and initial conditions are given. The amplification matrix Q(t) need not be diagonal. However, he required that IQ() I < 1. We use certain results in matrix theory and Wiener-Hopf factorization to replace this restrictive assumption by certain reasonable assumptions on accuracy of W(t) and smoothness of an associated positive-definite symmetric matrix. This technique will be important in half-space problems in many space variables since for such problems the amplification matrix will certainly not be diagonal. M

/pdf/stability-of-difference-approximations-of-dissipative-type-2xncnfwqza.pdf

Stability of difference approximations of dissipative type for mixed initial-boundary value problems. I

We will describe an alternating direction (aka split Bregman) method for solving problems of the form min u ∥Au − f∥2 + η∥u∥ 1 such that u ≥ 0, where A is an m×n matrix, and η is a nonnegative parameter. The algorithm works especially well for solving large numbers of small to medium overdetermined problems (i.e. m > n) with a fixed A. We will demonstrate applications in the analysis of hyperspectral images.

A split Bregman method for non-negative sparsity penalized least squares with applications to hyperspectral demixing

In this paper, we model grain boundary evolution based on a multiple level set method. Grain boundary migration under a curvature-induced driving force is considered and the level set method is employed to deal with the resulting topological changes of grain structures. The complexity of using a level set method for modeling grain structure evolution is due to its N-phase nature and the associated geometry compatibility constraint. We employ a multiple level set method with a predictor-multicorrectors approach to reduce the gaps in the triple junctions down to the grid resolution level. A ghost cell approach for imposing periodic boundary conditions is introduced without solving a constrained problem with a Lagrange multiplier method or a penalty method. Numerical results for both uniform and random grain structures evolution are presented and the results are compared with the solutions based on a front tracking approach (Chen and Kotta et al. 2004b).

http://www.techno-press.org/download.php?journal=imm&volume=1&num=2&ordernum=2

A multiple level set method for modeling grain boundary evolution of polycrystalline materials

Keywords: LTS2 ; LTS5 Reference EPFL-CONF-87269 Record created on 2006-06-14, modified on 2017-05-10

Stanley Osher

Papers

Compressed plane waves yield a compactly supported multiresolution basis for the Laplace operator

Stability of difference approximations of dissipative type for mixed initial-boundary value problems. I

A split Bregman method for non-negative sparsity penalized least squares with applications to hyperspectral demixing

A multiple level set method for modeling grain boundary evolution of polycrystalline materials

Global Minimizers of The Active Contour/Snake Model