  This paper presents a novel adaptively connected neural network (ACNet) to
improve the traditional convolutional neural networks (CNNs) {in} two aspects.
First, ACNet employs a flexible way to switch global and local inference in
processing the internal feature representations by adaptively determining the
connection status among the feature nodes (e.g., pixels of the feature maps)
\footnote{In a computer vision domain, a node refers to a pixel of a feature
map{, while} in {the} graph domain, a node denotes a graph node.}. We can show
that existing CNNs, the classical multilayer perceptron (MLP), and the recently
proposed non-local network (NLN) \cite{nonlocalnn17} are all special cases of
ACNet. Second, ACNet is also capable of handling non-Euclidean data. Extensive
experimental analyses on {a variety of benchmarks (i.e.,} ImageNet-1k
classification, COCO 2017 detection and segmentation, CUHK03 person
re-identification, CIFAR analysis, and Cora document categorization)
demonstrate that {ACNet} cannot only achieve state-of-the-art performance but
also overcome the limitation of the conventional MLP and CNN
\footnote{Corresponding author: Liang Lin (linliang@ieee.org)}. The code is
available at
\url{https://github.com/wanggrun/Adaptively-Connected-Neural-Networks}.
