We propose an extension of Convolutional Neural Networks (CNNs) to graph-structured data, including strided convolutions and data augmentation on graphs. Our method matches the accuracy of state-of-the-art CNNs when applied on images, without any prior about their 2D regular structure. On fMRI data, we obtain a significant gain in accuracy compared with existing graph-based alternatives.
In the second category, convolution is defined directly in the vertex domain. These works were originally motivated by chemistry datasets @cite_7 @cite_25 . Convolution is defined as a function of the kernel weights and neighboring vertices (the receptive field), usually based on dot products. As such, it retains the property of being localized and of sharing weights. But there remains the need to specify how the shared weights are allocated in this receptive field @cite_1 . This allocation can depend on an arbitrary order @cite_26 , on the number of hops @cite_22 @cite_18 , on both vertices and their neighbors @cite_16 @cite_12 , on another learned kernel @cite_13 , on an attention mechanism @cite_24 , on pattern identification @cite_15 , or on translation identification @cite_3 . All these methods also differ in the function that maps the receptive fields and the weight kernel to the neuron's outputs. But in the end, these definitions overlap. That is why some authors have proposed unified frameworks @cite_5 .
@cite_18 @cite_26 @cite_22 @cite_7 @cite_1 @cite_3 @cite_24 @cite_5 @cite_15 @cite_16 @cite_13 @cite_25 @cite_12
2145889472 2766931946 2949457404 2891894830
THE receptive fields of simple cells in mammalian primary visual cortex can be characterized as being spatially localized, oriented1–4 and bandpass (selective to structure at different spatial scales), comparable to the basis functions of wavelet transforms5,6. One approach to understanding such response properties of visual neurons has been to consider their relationship to the statistical structure of natural images in terms of efficient coding7–12. Along these lines, a number of studies have attempted to train unsupervised learning algorithms on natural images in the hope of developing receptive fields with similar properties13–18, but none has succeeded in producing a full set that spans the image space and contains all three of the above properties. Here we investigate the proposal8,12 that a coding strategy that maximizes sparseness is sufficient to account for these properties. We show that a learning algorithm that attempts to find sparse linear codes for natural scenes will develop a complete family of localized, oriented, bandpass receptive fields, similar to those found in the primary visual cortex. The resulting sparse image code provides a more efficient representation for later stages of processing because it possesses a higher degree of statistical independence among its outputs. We propose a generalization of convolutional neural networks (CNNs) to irregular domains, through the use of an inferred graph structure. In more details, we introduce a three-step methodology to create convolutional layers that are adapted to the signals to process: 1) From a training set of signals, infer a graph representing the topology on which they evolve; 2) Identify translation operators in the vertex domain; 3) Emulate a convolution operator by translating a localized kernel on the graph. Using these layers, a convolutional neural network is built, and is trained on the initial signals to perform a classification task. Contributions are twofold. First, we adapt a definition of translations on graphs to make them more robust to irregularities, and to take into account locality of the kernel. Second, we introduce a procedure to build CNNs from data. We apply our methodology on a scrambled version of the CIFAR-10 and Haxby datasets. Without using any knowledge on the signals, we significantly outperform existing methods. Moreover, our approach extends classical CNNs on images in the sense that such networks are a particular case of our approach when the inferred graph is a grid. We show that a generative random field model, which we call generative ConvNet, can be derived from the commonly used discriminative ConvNet, by assuming a ConvNet for multi-category classification and assuming one of the categories is a base category generated by a reference distribution. If we further assume that the non-linearity in the ConvNet is Rectified Linear Unit (ReLU) and the reference distribution is Gaussian white noise, then we obtain a generative ConvNet model that is unique among energy-based models: The model is piecewise Gaussian, and the means of the Gaussian pieces are defined by an auto-encoder, where the filters in the bottom-up encoding become the basis functions in the top-down decoding, and the binary activation variables detected by the filters in the bottom-up convolution process become the coefficients of the basis functions in the top-down deconvolution process. The Langevin dynamics for sampling the generative ConvNet is driven by the reconstruction error of this auto-encoder. The contrastive divergence learning of the generative ConvNet reconstructs the training images by the auto-encoder. The maximum likelihood learning algorithm can synthesize realistic natural image patterns. The field of object detection has made great progress in recent years. Most of these improvements are derived from using a more sophisticated convolutional neural network. However, in the case of humans, the attention mechanism, global structure information, and local details of objects all play an important role for detecting an object. In this paper, we propose a novel fully convolutional network, named as Attention CoupleNet, to incorporate the attention-related information and global and local information of objects to improve the detection performance. Specifically, we first design a cascade attention structure to perceive the global scene of the image and generate class-agnostic attention maps. Then the attention maps are encoded into the network to acquire object-aware features. Next, we propose a unique fully convolutional coupling structure to couple global structure and local parts of the object to further formulate a discriminative feature representation. To fully explore the global and local properties, we also design different coupling strategies and normalization ways to make full use of the complementary advantages between the global and local information. Extensive experiments demonstrate the effectiveness of our approach. We achieve state-of-the-art results on all three challenging data sets, i.e., a mAP of 85.7 on VOC07, 84.3 on VOC12, and 35.4 on COCO. Codes are publicly available at https: github.com tshizys CoupleNet .