Differences

This shows you the differences between two versions of the page.

Link to this comparison view

generalized_convolution [2016/12/10 11:32] (current)
Line 1: Line 1:
 +
 +** Name **
 +
 +**Intent**
 +
 +
 +**Motivation**
 +
 +Convolution is usually applicable to spatial/​temporal input data wherein the dimensions of the input share a common type.  The common type across dimensions is necessary for the convolution operation to make sense.
 +
 +**Structure**
 +
 +<​Diagram>​
 +
 +**Discussion**
 +
 +
 +
 +**Known Uses**
 +
 +**Related Patterns**
 +
 +<​Diagram>​
 +
 +**References**
 +
 +http://​arxiv.org/​abs/​1312.6203 Spectral Networks and Locally Connected Networks on Graphs
 +
 +In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions,​ one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian.
 +
 +http://​arxiv.org/​abs/​1506.05163 Deep Convolutional Networks on Graph-Structured Data
 +
 +We develop an extension of Spectral Networks which incorporates a Graph Estimation procedure, that we test on large-scale classification problems, matching or improving over Dropout Networks with far less parameters to estimate.
 +
 +http://​arxiv.org/​abs/​1606.01166v1 ​ Generalizing the Convolution Operator to Extend CNNs to Irregular Domains
 +
 +We propose a novel approach to generalize CNNs to irregular domains using weight sharing and graph-based operators. Using experiments,​ we show that these models resemble CNNs on regular domains and offer better performance than multilayer perceptrons on distorded ones.
 +
 +http://​arxiv.org/​abs/​1602.07576v3 Group Equivariant Convolutional Networks
 +
 +We introduce Group equivariant Convolutional
 +Neural Networks (G-CNNs), a natural generalization
 +of convolutional neural networks that reduces
 +sample complexity by exploiting symmetries.
 +G-CNNs use G-convolutions,​ a new type of
 +layer that enjoys a substantially higher degree of
 +weight sharing than regular convolution layers.
 +
 +https://​arxiv.org/​abs/​1511.07122v3 ​ Multi-Scale Context Aggregation by Dilated Convolutions
 +
 +http://​arxiv.org/​abs/​1607.05695v1 ​ FusionNet: 3D Object Classification Using Multiple Data Representations
 +
 +We use Volumetric CNNs to bridge the gap between the efficiency of the above two representations. We combine both representations and exploit them to learn new features, which yield a significantly better classifier than using either of the representations in isolation. To do this, we introduce new Volumetric CNN (V-CNN) architectures.
 +
 +https://​arxiv.org/​pdf/​1610.02357v1.pdf ​ Deep Learning with Separable Convolutions
 +
 +In this light, a separable convolution can be
 +understood as an Inception module with a maximally large number of towers. This
 +observation leads us to propose a novel deep convolutional neural network architecture
 +inspired by Inception, where Inception modules have been replaced with separable
 +convolutions. We show that this architecture,​ dubbed Xception, slightly outperforms
 +Inception V3 on the ImageNet dataset.
 +
 +https://​arxiv.org/​abs/​1606.01166 ​ Generalizing the Convolution Operator to Extend CNNs to Irregular Domains
 +
 +We propose a novel approach to generalize CNNs to irregular domains using weight sharing and graph-based operators. Using experiments,​ we show that these models resemble CNNs on regular domains and offer better performance than multilayer perceptrons on distorded ones.
 +
 +
 +https://​arxiv.org/​abs/​1611.08097v1 Geometric deep learning: going beyond Euclidean data
 +
 +The purpose of this paper is to overview the problems arising in relation to geometric deep learning and present solutions existing today for this class of problems, as well as key difficulties and future research directions.
 +
 +https://​arxiv.org/​pdf/​1602.02867.pdf Value Iteration Networks
 +
 +We introduce the value iteration network (VIN): a fully differentiable neural network
 +with a ‘planning module’ embedded within. VINs can learn to plan, and are
 +suitable for predicting outcomes that involve planning-based reasoning, such as
 +policies for reinforcement learning. Key to our approach is a novel differentiable
 +approximation of the value-iteration algorithm, which can be represented as a convolutional
 +neural network, and trained end-to-end using standard backpropagation.
 +We evaluate VIN based policies on discrete and continuous path-planning domains,
 +and on a natural-language based search task. We show that by learning an explicit
 +planning computation,​ VIN policies generalize better to new, unseen domains.
 +
 +The key to our approach is an observation that
 +the classic value-iteration (VI) planning algorithm
 +[2, 3] may be represented by a specific
 +type of CNN. By embedding such a VI network
 +module inside a standard feed-forward classifi-
 +cation network, we obtain a NN model that can
 +learn a planning computation. The VI block is differentiable,​ and the whole network can be trained
 +using standard backpropagation.
 +
 +{{:​wiki:​vi.png?​nolink|}}
 +
 +https://​arxiv.org/​abs/​1612.00606 ​ SyncSpecCNN:​ Synchronized Spectral CNN for 3D Shape Segmentation
 +
 +In this paper, we study the problem of semantic annotation on 3D models that are represented as shape graphs. A functional view is taken to represent localized information on graphs, so that annotations such as part segment or keypoint are nothing but 0-1 indicator vertex functions. Compared with images that are 2D grids, shape graphs are irregular and non-isomorphic data structures. To enable the prediction of vertex functions on them by convolutional neural networks, we resort to spectral CNN method that enables weight sharing by parameterizing kernels in the spectral domain spanned by graph laplacian eigenbases. Under this setting, our network, named SyncSpecCNN,​ strive to overcome two key challenges: how to share coefficients and conduct multi-scale analysis in different parts of the graph for a single shape, and how to share information across related but different shapes that may be represented by very different graphs. Towards these goals, we introduce a spectral parameterization of dilated convolutional kernels and a spectral transformer network. Experimentally we tested our SyncSpecCNN on various tasks, including 3D shape part segmentation and 3D keypoint prediction. State-of-the-art performance has been achieved on all benchmark datasets.
 +