We propose Sparse Neural Network architectures that are based on random or structured bipartite graph topologies. Sparse architectures provide compression of the models learned and speed-ups of computations, they can also surpass their unstructured or fully connected counterparts. As we show, even more compact topologies of the so-called SNN (Sparse Neural Network) can be achieved with the use of structured graphs of connections between consecutive layers of neurons. In this paper, we investigate how the accuracy and training speed of the models depend on the topology and sparsity of the neural network. Previous approaches using sparcity are all based on fully connected neural network models and create sparcity during training phase, instead we explicitly define a sparse architectures of connections before the training. Building compact neural network models is coherent with empirical observations showing that there is much redundancy in learned neural network models. We show experimentally that the accuracy of the models learned with neural networks depends on expander-like properties of the underlying topologies such as the spectral gap and algebraic connectivity rather than the density of the graphs of connections.
It was recently observed @cite_17 , @cite_14 , @cite_12 that imposing specific structure of the linear embedding part of the neural network computations leads to significant speed-ups and memory usage reductions with only minimal loss of the quality of the model. In this approach, the graph of connections between consecutive neural network layers is still dense and the reduction comes from recycling a compact vector of learned weights across the entire matrix. In @cite_18 the authors use a compact multilinear format, called the to represent the dense weight matrix of the fully-connected layers. Even more basic technique relies on using the low-rank representation of the weight matrices. It was empirically tested that restricting the rank of the matrix of neurons connections to be of low rank does not affect much the quality of the model @cite_20 , @cite_3 , @cite_6 , @cite_16 . This setting is more restrictive than the one presented in @cite_17 , since low-rank matrices considered in these papers have in particular low displacement rank.
@cite_18 @cite_14 @cite_3 @cite_6 @cite_16 @cite_12 @cite_20 @cite_17
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We explore the redundancy of parameters in deep neural networks by replacing the conventional linear projection in fully-connected layers with the circulant projection. The circulant structure substantially reduces memory footprint and enables the use of the Fast Fourier Transform to speed up the computation. Considering a fully-connected neural network layer with d input nodes, and d output nodes, this method improves the time complexity from O(d^2) to O(dlogd) and space complexity from O(d^2) to O(d). The space savings are particularly important for modern deep convolutional neural network architectures, where fully-connected layers typically contain more than 90 of the network parameters. We further show that the gradient computation and optimization of the circulant projections can be performed very efficiently. Our experiments on three standard datasets show that the proposed approach achieves this significant gain in storage and efficiency with minimal increase in error rate compared to neural networks with unstructured projections. Recently proposed deep neural network (DNN) obtains significant accuracy improvements in many large vocabulary continuous speech recognition (LVCSR) tasks. However, DNN requires much more parameters than traditional systems, which brings huge cost during online evaluation, and also limits the application of DNN in a lot of scenarios. In this paper we present our new effort on DNN aiming at reducing the model size while keeping the accuracy improvements. We apply singular value decomposition (SVD) on the weight matrices in DNN, and then restructure the model based on the inherent sparseness of the original matrices. After restructuring we can reduce the DNN model size significantly with negligible accuracy loss. We also fine-tune the restructured model using the regular back-propagation method to get the accuracy back when reducing the DNN model size heavily. The proposed method has been evaluated on two LVCSR tasks, with context-dependent DNN hidden Markov model (CD-DNN-HMM). Experimental results show that the proposed approach dramatically reduces the DNN model size by more than 80 without losing any accuracy. Index Terms: deep neural network, singular value decomposition, model restructuring Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves @math accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs. This paper presents results on the memory capacity of a generalized feedback neural network using a circulant matrix. Children are capable of learning soon after birth which indicates that the neural networks of the brain have prior learnt capacity that is a consequence of the regular structures in the brain's organization. Motivated by this idea, we consider the capacity of circulant matrices as weight matrices in a feedback network. We consider the task of building compact deep learning pipelines suitable for deployment on storage and power constrained mobile devices. We propose a unified framework to learn a broad family of structured parameter matrices that are characterized by the notion of low displacement rank. Our structured transforms admit fast function and gradient evaluation, and span a rich range of parameter sharing configurations whose statistical modeling capacity can be explicitly tuned along a continuum from structured to unstructured. Experimental results show that these transforms can significantly accelerate inference and forward backward passes during training, and offer superior accuracy-compactness-speed tradeoffs in comparison to a number of existing techniques. In keyword spotting applications in mobile speech recognition, our methods are much more effective than standard linear low-rank bottleneck layers and nearly retain the performance of state of the art models, while providing more than 3.5-fold compression.