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

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

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Image-to-image translation is a class of vision and graphics problems where the goal is to learn the mapping between an input image and an output image using a training set of aligned image pairs. However, for many tasks, paired training data will not be available. We present an approach for learning to translate an image from a source domain X to a target domain Y in the absence of paired examples. Our goal is to learn a mapping G : X → Y such that the distribution of images from G(X) is indistinguishable from the distribution Y using an adversarial loss. Because this mapping is highly under-constrained, we couple it with an inverse mapping F : Y → X and introduce a cycle consistency loss to push F(G(X)) ≈ X (and vice versa). Qualitative results are presented on several tasks where paired training data does not exist, including collection style transfer, object transfiguration, season transfer, photo enhancement, etc. Quantitative comparisons against several prior methods demonstrate the superiority of our approach.

Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks

We study combinatorial and algorithmic problems involving arrangements of n lines in 3-dimensional space, and then present applications of our results to a variety of problems on polyhedral terrains. Our main results include: A tight T(n2) bound on the complexity of the space of all lines passing above all the n given lines (their “upper envelope”) and satisfying a certain orientation consistency constraint.A preprocessing procedure using near-quadratic time and storage that builds a structure supporting O(log n) time queries for testing if a line lies above all the given lines.An O(n4/3+e) randomized expected time algorithm, for any fixed e > 0, that tests the “towering property”: do n given red lines lie all above n given blue lines?A preprocessing procedure for a polyhedral terrain S with n edges, that uses near-quadratic time and storage and builds a structure supporting O(log2n) time rayshooting queries for computing the first intersection of an arbitrary query ray with S.Finding the smallest vertical distance between two disjoint polyhedral terrains with a total of n edges, in time O(n4/3+e), for any e > 0.Computing the upper envelope (pointwise maximum) of two polyhedral terrains with a total of n edges, in time O(n1.5+e + klog2n), for any e > 0, where k is the size of the output envelope.The tools used to obtain these results include Plucker coordinates for lines in space, random sampling in geometric problems, and a new variant of segment trees.

Lines in space-combinators, algorithms and applications

A compositional understanding of the world in terms of objects and their geometry in 3D space is considered a cornerstone of human cognition. Facilitating the learning of such a representation in neural networks holds promise for substantially improving labeled data efficiency. As a key step in this direction, we make progress on the problem of learning 3D-consistent decompositions of complex scenes into individual objects in an unsupervised fashion. We introduce Object Scene Representation Transformer (OSRT), a 3D-centric model in which individual object representations naturally emerge through novel view synthesis. OSRT scales to significantly more complex scenes with larger diversity of objects and backgrounds than existing methods. At the same time, it is multiple orders of magnitude faster at compositional rendering thanks to its light field parametrization and the novel Slot Mixer decoder. We believe this work will not only accelerate future architecture exploration and scaling efforts, but it will also serve as a useful tool for both object-centric as well as neural scene representation learning communities.

Object Scene Representation Transformer

Invariance and equivariance to the rotation group have been widely discussed in the 3D deep learning community for pointclouds. Yet most proposed methods either use complex mathematical tools that may limit their accessibility, or are tied to specific input data types and network architectures. In this paper, we introduce a general framework built on top of what we call Vector Neuron representations for creating SO(3)-equivariant neural networks for pointcloud processing. Extending neurons from 1D scalars to 3D vectors, our vector neurons enable a simple mapping of SO(3) actions to latent spaces thereby providing a framework for building equivariance in common neural operations -- including linear layers, non-linearities, pooling, and normalizations. Due to their simplicity, vector neurons are versatile and, as we demonstrate, can be incorporated into diverse network architecture backbones, allowing them to process geometry inputs in arbitrary poses. Despite its simplicity, our method performs comparably well in accuracy and generalization with other more complex and specialized state-of-the-art methods on classification and segmentation tasks. We also show for the first time a rotation equivariant reconstruction network.

Vector Neurons: A General Framework for SO(3)-Equivariant Networks

Soft maps taking points on one surface to probability distributions on another are attractive for representing surface mappings in the presence of symmetry, ambiguity, and combinatorial complexity. Few techniques, however, are available to measure their continuity and other properties. To this end, we introduce a novel Dirichlet energy for soft maps generalizing the classical map Dirichlet energy, which measures distortion by computing how soft maps transport probabilistic mass from one distribution to another. We formulate the computation of the Dirichlet energy in terms of a differential equation and provide a finite elements discretization that enables all of the quantities introduced to be computed. We demonstrate the effectiveness of our framework for understanding soft maps arising from various sources. Furthermore, we suggest how these energies can be applied to generate continuous soft or point-to-point maps.

/pdf/dirichlet-energy-for-analysis-and-synthesis-of-soft-maps-v58aadh5bm.pdf

Dirichlet energy for analysis and synthesis of soft maps

We describe the first known algorithm for efficiently maintaining a Binary Space Partition (BSP) for n continuously moving segments in the plane, whose interiors remain disjoint throughout the motion. Under reasonable assumptions on the motion, we show that the total number of times this BSP changes is O (n 2 ) , and that we can update the BSP in O ( log n) expected time per change. Throughout the motion, the expected size of the BSP is O (n log n) . We also consider the problem of constructing a BSP for n static triangles with pairwise-disjoint interiors in R 3 . We present a randomized algorithm that constructs a BSP of size O (n 2 ) in O (n 2 log 2 n) expected time. We also describe a deterministic algorithm that constructs a BSP of size O ((n+k) log 2 n) and height O ( log n) in O ((n+k) log 3 n) time, where k is the number of intersection points between the edges of the projections of the triangles onto the xy -plane. This is the first known algorithm that constructs a BSP of O ( log n) height for disjoint triangles in R 3 .

Leonidas J. Guibas

Papers

Lines in space-combinators, algorithms and applications

Object Scene Representation Transformer

Vector Neurons: A General Framework for SO(3)-Equivariant Networks

Dirichlet energy for analysis and synthesis of soft maps

Cylindrical static and kinetic binary space partitions