We propose a multigrid extension of convolutional neural networks (CNNs).
Rather than manipulating representations living on a single spatial grid, our
network layers operate across scale space, on a pyramid of grids. They consume
multigrid inputs and produce multigrid outputs; convolutional filters
themselves have both within-scale and cross-scale extent. This aspect is
distinct from simple multiscale designs, which only process the input at
different scales. Viewed in terms of information flow, a multigrid network
passes messages across a spatial pyramid. As a consequence, receptive field
size grows exponentially with depth, facilitating rapid integration of context.
Most critically, multigrid structure enables networks to learn internal
attention and dynamic routing mechanisms, and use them to accomplish tasks on
which modern CNNs fail.
Experiments demonstrate wide-ranging performance advantages of multigrid. On
CIFAR and ImageNet classification tasks, flipping from a single grid to
multigrid within the standard CNN paradigm improves accuracy, while being
compute and parameter efficient. Multigrid is independent of other
architectural choices; we show synergy in combination with residual
connections. Multigrid yields dramatic improvement on a synthetic semantic
segmentation dataset. Most strikingly, relatively shallow multigrid networks
can learn to directly perform spatial transformation tasks, where, in contrast,
current CNNs fail. Together, our results suggest that continuous evolution of
features on a multigrid pyramid is a more powerful alternative to existing CNN
designs on a flat grid.

本研究提出了一种基于多重网格结构的卷积神经网络，能够在不同尺度空间上操作输入和输出，实现任务的动态路由和内部注意力机制，以及通过逐级概括将上下文信息融合到网络中。在分类和语义分割等多项任务中得到了相对较好的表现表明，相对于传统的基于单一网格的卷积神经网络结构，基于多重网格的设计方案更加高效且灵活。

多重网格神经架构

Multigrid Neural Architectures

The workflow of extracting features from images using convolutional neural
networks (CNN) and generating captions with recurrent neural networks (RNN) has
become a de-facto standard for image captioning task. However, since CNN
features are originally designed for classification task, it is mostly
concerned with the main conspicuous element of the image, and often fails to
correctly convey information on local, secondary elements. We propose to
incorporate coding with vector of locally aggregated descriptors (VLAD) on
spatial pyramid for CNN features of sub-regions in order to generate image
representations that better reflect the local information of the images. Our
results show that our method of compact VLAD coding can match CNN features with
as little as 3% of dimensionality and, when combined with spatial pyramid, it
results in image captions that more accurately take local elements into
account.

本文提出了一种使用局部聚合描述符（VLAD）将空间金字塔 CNN 特征编码的方法，以更准确地反映图像的局部信息。结果表明，使用 VLAD 编码可以仅使用 3％的维度匹配 CNN 特征，并与空间金字塔结合使用可以更准确地将局部元素考虑在内。

基于 CNN 的空间金字塔 VLAD 编码的稠密图像表示与本地鲁棒性字幕生成

Dense Image Representation with Spatial Pyramid VLAD Coding of CNN for  Locally Robust Captioning

With the rapid development of location-based social networks (LBSNs), spatial
item recommendation has become an important means to help people discover
attractive and interesting venues and events, especially when users travel out
of town. However, this recommendation is very challenging compared to the
traditional recommender systems. A user can visit only a limited number of
spatial items, leading to a very sparse user-item matrix. Most of the items
visited by a user are located within a short distance from where he/she lives,
which makes it hard to recommend items when the user travels to a far away
place. Moreover, user interests and behavior patterns may vary dramatically
across different geographical regions. In light of this, we propose Geo-SAGE, a
geographical sparse additive generative model for spatial item recommendation
in this paper. Geo-SAGE considers both user personal interests and the
preference of the crowd in the target region, by exploiting both the
co-occurrence pattern of spatial items and the content of spatial items. To
further alleviate the data sparsity issue, Geo-SAGE exploits the geographical
correlation by smoothing the crowd's preferences over a well-designed spatial
index structure called spatial pyramid. We conduct extensive experiments to
evaluate the performance of our Geo-SAGE model on two real large-scale
datasets. The experimental results clearly demonstrate our Geo-SAGE model
outperforms the state-of-the-art in the two tasks of both out-of-town and
home-town recommendations.

该论文提出了一种基于地理位置的稀疏加性生成模型 Geo-SAGE，用于解决基于位置的社交网络中的稀疏用户 - 空间项目矩阵和地理位置相关性问题，并在实验中证明其在家乡和外出旅行两个任务中的表现优于其他最新模型。