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Register a new userError Analysis and Improving the Accuracy of Winograd Convolution for Deep Neural Networks
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Added by
Barbara Barabasz
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is present in many DNN software frameworks. However, the performance gain is at the expense of a reduction in floating point (FP) numerical accuracy. In this paper, we analyse the worst case FP error and prove the estimation of norm and conditioning of the algorithm. We show that the bound grows exponentially with the size of the convolution, but the error bound of the textit{modified} algorithm is smaller than the original one. We propose several methods for reducing FP error. We propose a canonical evaluation ordering based on Huffman coding that reduces summation error. We study the selection of sampling points experimentally and find empirically good points for the most important sizes. We identify the main factors associated with good points. In addition, we explore other methods to reduce FP error, including mixed-precision convolution, and pairwise summation across DNN channels. Using our methods we can significantly reduce FP error for a given block size, which allows larger block sizes and reduced computation.
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Deep convolutional neural networks (CNNs) are deployed in various applications but demand immense computational requirements. Pruning techniques and Winograd convolution are two typical methods to reduce the CNN computation. However, they cannot be directly combined because Winograd transformation fills in the sparsity resulting from pruning. Li et al. (2017) propose sparse Winograd convolution in which weights are directly pruned in the Winograd domain, but this technique is not very practical because Winograd-domain retraining requires low learning rates and hence significantly longer training time. Besides, Liu et al. (2018) move the ReLU function into the Winograd domain, which can help increase the weight sparsity but requires changes in the network structure. To achieve a high Winograd-domain weight sparsity without changing network structures, we propose a new pruning method, spatial-Winograd pruning. As the first step, spatial-domain weights are pruned in a structured way, which efficiently transfers the spatial-domain sparsity into the Winograd domain and avoids Winograd-domain retraining. For the next step, we also perform pruning and retraining directly in the Winograd domain but propose to use an importance factor matrix to adjust weight importance and weight gradients. This adjustment makes it possible to effectively retrain the pruned Winograd-domain network without changing the network structure. For the three models on the datasets of CIFAR10, CIFAR-100, and ImageNet, our proposed method can achieve the Winograd domain sparsities of 63%, 50%, and 74%, respectively.
Compression techniques for deep neural network models are becoming very important for the efficient execution of high-performance deep learning systems on edge-computing devices. The concept of model compression is also important for analyzing the generalization error of deep learning, known as the compression-based error bound. However, there is still huge gap between a practically effective compression method and its rigorous background of statistical learning theory. To resolve this issue, we develop a new theoretical framework for model compression and propose a new pruning method called {it spectral pruning} based on this framework. We define the ``degrees of freedom to quantify the intrinsic dimensionality of a model by using the eigenvalue distribution of the covariance matrix across the internal nodes and show that the compression ability is essentially controlled by this quantity. Moreover, we present a sharp generalization error bound of the compressed model and characterize the bias--variance tradeoff induced by the compression procedure. We apply our method to several datasets to justify our theoretical analyses and show the superiority of the the proposed method.
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We present a probabilistic variant of the recently introduced maxout unit. The success of deep neural networks utilizing maxout can partly be attributed to favorable performance under dropout, when compared to rectified linear units. It however also depends on the fact that each maxout unit performs a pooling operation over a group of linear transformations and is thus partially invariant to changes in its input. Starting from this observation we ask the question: Can the desirable properties of maxout units be preserved while improving their invariance properties ? We argue that our probabilistic maxout (probout) units successfully achieve this balance. We quantitatively verify this claim and report classification performance matching or exceeding the current state of the art on three challenging image classification benchmarks (CIFAR-10, CIFAR-100 and SVHN).
Malaria is a female anopheles mosquito-bite inflicted life-threatening disease which is considered endemic in many parts of the world. This article focuses on improving malaria detection from patches segmented from microscopic images of red blood cell smears by introducing a deep convolutional neural network. Compared to the traditional methods that use tedious hand engineering feature extraction, the proposed method uses deep learning in an end-to-end arrangement that performs both feature extraction and classification directly from the raw segmented patches of the red blood smears. The dataset used in this study was taken from National Institute of Health named NIH Malaria Dataset. The evaluation metric accuracy and loss along with 5-fold cross validation was used to compare and select the best performing architecture. To maximize the performance, existing standard pre-processing techniques from the literature has also been experimented. In addition, several other complex architectures have been implemented and tested to pick the best performing model. A holdout test has also been conducted to verify how well the proposed model generalizes on unseen data. Our best model achieves an accuracy of almost 97.77%.
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