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multi-grid [2017/09/05 19:29] (current)
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 +**Related To**
 +Filter Groups
 +** References **
 +https://​arxiv.org/​pdf/​1611.07661v1.pdf ​ Neural Multigrid
 +Rather than manipulating representations
 +living on a single spatial grid, our network layers
 +operate across scale space, on a pyramid of tensors. 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.   ​https://​github.com/​buttomnutstoast/​Multigrid-Neural-Architectures
 +https://​arxiv.org/​pdf/​1512.02767v2.pdf ​ Affinity CNN: Learning Pixel-Centric Pairwise Relations for Figure/​Ground Embedding
 +http://​redwood.berkeley.edu/​vs265/​olshausen-etal93.pdf A Neurobiological Model of Visual Attention and Invariant Pattern
 +Recognition Based on Dynamic Routing of Information ​
 +https://​arxiv.org/​pdf/​1611.09326v1.pdf The One Hundred Layers Tiramisu: Fully Convolutional DenseNets for Semantic Segmentation
 +In this paper, we extend DenseNets to deal with the problem
 +of semantic segmentation. We achieve state-of-the-art
 +results on urban scene benchmark datasets such as CamVid
 +and Gatech, without any further post-processing module
 +nor pretraining. Moreover, due to smart construction of the
 +model, our approach has much less parameters than currently
 +published best entries for these datasets.
 +https://​arxiv.org/​pdf/​1708.07038v1.pdf Non-linear Convolution Filters for CNN-based Learning
 +Typical convolutional
 +layers are linear systems, hence their expressiveness
 +is limited. To overcome this, various non-linearities
 +have been used as activation functions inside CNNs, while
 +also many pooling strategies have been applied. We address
 +the issue of developing a convolution method in the
 +context of a computational model of the visual cortex, exploring
 +quadratic forms through the Volterra kernels. Such
 +forms, constituting a more rich function space, are used as
 +approximations of the response profile of visual cells.
 +The Volterra series model is a sequence of approximations
 +for continuous functions, developed to represent the
 +input-output relationship of non-linear dynamical systems,
 +using a polynomial functional expansion. Their equations
 +can be composed by terms of infinite orders, but practical
 +implementations based on them use truncated versions, retaining
 +the terms up to some order r.
 +https://​arxiv.org/​pdf/​1707.08308v1.pdf Tensor Regression Networks
 +To date, most convolutional neural network architectures output predictions by
 +flattening 3rd-order activation tensors, and applying fully-connected output layers.
 +This approach has two drawbacks: (i) we lose rich, multi-modal structure during
 +the flattening process and (ii) fully-connected layers require many parameters. We
 +present the first attempt to circumvent these issues by expressing the output of a
 +neural network directly as the the result of a multi-linear mapping from an activation
 +tensor to the output. By imposing low-rank constraints on the regression tensor, we
 +can efficiently solve problems for which existing solutions are badly parametrized.
 +Our proposed tensor regression layer replaces flattening operations and fullyconnected
 +layers by leveraging multi-modal structure in the data and expressing the
 +regression weights via a low rank tensor decomposition. Additionally,​ we combine
 +tensor regression with tensor contraction to further increase efficiency. Augmenting
 +the VGG and ResNet architectures,​ we demonstrate large reductions in the number
 +of parameters with negligible impact on performance on the ImageNet dataset.