CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters

The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs. The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands of interest. Our model generates rich spectral filters that are localized in space, scales linearly with the size of the input data for sparsely-connected graphs, and can handle different constructions of Laplacian operators. Extensive experimental results show the superior performance of our approach, in comparison to other spectral domain convolutional architectures, on spectral image classification, community detection, vertex classification and matrix completion tasks

Sparsely Aggregated Convolutional Networks

We explore a key architectural aspect of deep convolutional neural networks: the pattern of internal skip connections used to aggregate outputs of earlier layers for consumption by deeper layers. Such aggregation is critical to facilitate training of very deep networks in an end-to-end manner. This is a primary reason for the widespread adoption of residual networks, which aggregate outputs via cumulative summation. While subsequent works investigate alternative aggregation operations (e.g. concatenation), we focus on an orthogonal question: which outputs to aggregate at a particular point in the network. We propose a new internal connection structure which aggregates only a sparse set of previous outputs at any given depth. Our experiments demonstrate this simple design change offers superior performance with fewer parameters and lower computational requirements. Moreover, we show that sparse aggregation allows networks to scale more robustly to 1000+ layers, thereby opening future avenues for training long-running visual processes.Comment: Accepted to ECCV 201

Efficient Deep Feature Learning and Extraction via StochasticNets

Deep neural networks are a powerful tool for feature learning and extraction given their ability to model high-level abstractions in highly complex data. One area worth exploring in feature learning and extraction using deep neural networks is efficient neural connectivity formation for faster feature learning and extraction. Motivated by findings of stochastic synaptic connectivity formation in the brain as well as the brain's uncanny ability to efficiently represent information, we propose the efficient learning and extraction of features via StochasticNets, where sparsely-connected deep neural networks can be formed via stochastic connectivity between neurons. To evaluate the feasibility of such a deep neural network architecture for feature learning and extraction, we train deep convolutional StochasticNets to learn abstract features using the CIFAR-10 dataset, and extract the learned features from images to perform classification on the SVHN and STL-10 datasets. Experimental results show that features learned using deep convolutional StochasticNets, with fewer neural connections than conventional deep convolutional neural networks, can allow for better or comparable classification accuracy than conventional deep neural networks: relative test error decrease of ~4.5% for classification on the STL-10 dataset and ~1% for classification on the SVHN dataset. Furthermore, it was shown that the deep features extracted using deep convolutional StochasticNets can provide comparable classification accuracy even when only 10% of the training data is used for feature learning. Finally, it was also shown that significant gains in feature extraction speed can be achieved in embedded applications using StochasticNets. As such, StochasticNets allow for faster feature learning and extraction performance while facilitate for better or comparable accuracy performances.Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1508.0546

Convolutional Neural Fabrics

Despite the success of CNNs, selecting the optimal architecture for a given task remains an open problem. Instead of aiming to select a single optimal architecture, we propose a "fabric" that embeds an exponentially large number of architectures. The fabric consists of a 3D trellis that connects response maps at different layers, scales, and channels with a sparse homogeneous local connectivity pattern. The only hyper-parameters of a fabric are the number of channels and layers. While individual architectures can be recovered as paths, the fabric can in addition ensemble all embedded architectures together, sharing their weights where their paths overlap. Parameters can be learned using standard methods based on back-propagation, at a cost that scales linearly in the fabric size. We present benchmark results competitive with the state of the art for image classification on MNIST and CIFAR10, and for semantic segmentation on the Part Labels dataset.Comment: Corrected typos (In proceedings of NIPS16

Deep Epitomic Convolutional Neural Networks

Deep convolutional neural networks have recently proven extremely competitive in challenging image recognition tasks. This paper proposes the epitomic convolution as a new building block for deep neural networks. An epitomic convolution layer replaces a pair of consecutive convolution and max-pooling layers found in standard deep convolutional neural networks. The main version of the proposed model uses mini-epitomes in place of filters and computes responses invariant to small translations by epitomic search instead of max-pooling over image positions. The topographic version of the proposed model uses large epitomes to learn filter maps organized in translational topographies. We show that error back-propagation can successfully learn multiple epitomic layers in a supervised fashion. The effectiveness of the proposed method is assessed in image classification tasks on standard benchmarks. Our experiments on Imagenet indicate improved recognition performance compared to standard convolutional neural networks of similar architecture. Our models pre-trained on Imagenet perform excellently on Caltech-101. We also obtain competitive image classification results on the small-image MNIST and CIFAR-10 datasets.Comment: 9 page