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.

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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.

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

A Primal-Dual Framework for Transformers and Neural Networks

Level Set Methods, with an Application to Modeling the Growth of Thin Films

We present and review an algorithmic and theoretical framework for improving neural network architecture design via momentum. As case studies, we consider how momentum can improve the architecture design for recurrent neural networks (RNNs), neural ordinary differential equations (ODEs), and transformers. We show that integrating momentum into neural network architectures has several remarkable theoretical and empirical benefits, including (1) integrating momentum into RNNs and neural ODEs can overcome the vanishing gradient issues in training RNNs and neural ODEs, resulting in effective learning long-term dependencies; (2) momentum in neural ODEs can reduce the stiffness of the ODE dynamics, which significantly enhances the computational efficiency in training and testing; (3) momentum can improve the efficiency and accuracy of transformers. 

/pdf/how-does-momentum-benefit-deep-neural-networks-architecture-28enonjh.pdf

How does momentum benefit deep neural networks architecture design? A few case studies

Liquid-gas interactions, e.g., the vaporization and subsequent combustion of liquid fuel droplets or the shock-induced mixing of liquids, are rather difficult problems in computational fluid dynamics. These problems address the interaction of liquid droplets with a compressible gas medium. There are three classical approaches to such problems: Both phases can be treated as compressible fluids (as we did in Chapter 15), both phases can be treated as incompressible fluids (as we did in Chapter 21), or the gas can be treated as a compressible fluid while the liquid is treated as an incompressible fluid. A completely incompressible treatment can be ruled out any time one is interested in shock waves or other compressible phenomena. A completely compressible treatment is not desirable, since a relatively high sound speed in the liquid phase can impose a restrictive (and inefficient) CFL condition. Moreover, a completely compressible approach is limited to liquids for which there are acceptable models for their compressible evolution. To overcome these difficulties, Caiden et al. [23] modeled the gas as a compressible fluid and the liquid as an incompressible fluid. They coupled a high-resolution shock-capturing scheme for the compressible gas flow to a standard incompressible flow solver for the liquid phase.

Liquid-Gas Interactions

We propose a detail-preserving image deconvolution method which outperforms state-of-the-art methods, and can further improve image quality in the super-resolution optical fluctuation imaging and other diffraction-limited/superresolution imaging modalities. Article not available.

Stanley Osher

Papers

A Primal-Dual Framework for Transformers and Neural Networks

Level Set Methods, with an Application to Modeling the Growth of Thin Films

How does momentum benefit deep neural networks architecture design? A few case studies

Liquid-Gas Interactions

Detail-preserving Fluorescence Microscopy Image Deconvolution