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Register a new userThe Effects of Approximate Multiplication on Convolutional Neural Networks
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Min Soo Kim
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This paper analyzes the effects of approximate multiplication when performing inferences on deep convolutional neural networks (CNNs). The approximate multiplication can reduce the cost of the underlying circuits so that CNN inferences can be performed more efficiently in hardware accelerators. The study identifies the critical factors in the convolution, fully-connected, and batch normalization layers that allow more accurate CNN predictions despite the errors from approximate multiplication. The same factors also provide an arithmetic explanation of why bfloat16 multiplication performs well on CNNs. The experiments are performed with recognized network architectures to show that the approximate multipliers can produce predictions that are nearly as accurate as the FP32 references, without additional training. For example, the ResNet and Inception-v4 models with Mitch-$w$6 multiplication produces Top-5 errors that are within 0.2% compared to the FP32 references. A brief cost comparison of Mitch-$w$6 against bfloat16 is presented, where a MAC operation saves up to 80% of energy compared to the bfloat16 arithmetic. The most far-reaching contribution of this paper is the analytical justification that multiplications can be approximated while additions need to be exact in CNN MAC operations.
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We investigate filter level sparsity that emerges in convolutional neural networks (CNNs) which employ Batch Normalization and ReLU activation, and are trained with adaptive gradient descent techniques and L2 regularization or weight decay. We conduct an extensive experimental study casting our initial findings into hypotheses and conclusions about the mechanisms underlying the emergent filter level sparsity. This study allows new insight into the performance gap obeserved between adapative and non-adaptive gradient descent methods in practice. Further, analysis of the effect of training strategies and hyperparameters on the sparsity leads to practical suggestions in designing CNN training strategies enabling us to explore the tradeoffs between feature selectivity, network capacity, and generalization performance. Lastly, we show that the implicit sparsity can be harnessed for neural network speedup at par or better than explicit sparsification / pruning approaches, with no modifications to the typical training pipeline required.
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Graph convolution networks have recently garnered a lot of attention for representation learning on non-Euclidean feature spaces. Recent research has focused on stacking multiple layers like in convolutional neural networks for the increased expressive power of graph convolution networks. However, simply stacking multiple graph convolution layers lead to issues like vanishing gradient, over-fitting and over-smoothing. Such problems are much less when using shallower networks, even though the shallow networks have lower expressive power. In this work, we propose a novel Multipath Graph convolutional neural network that aggregates the output of multiple different shallow networks. We train and test our model on various benchmarks datasets for the task of node property prediction. Results show that the proposed method not only attains increased test accuracy but also requires fewer training epochs to converge. The full implementation is available at https://github.com/rangan2510/MultiPathGCN
Although group convolution operators are increasingly used in deep convolutional neural networks to improve the computational efficiency and to reduce the number of parameters, most existing methods construct their group convolution architectures by a predefined partitioning of the filters of each convolutional layer into multiple regular filter groups with an equal spatial group size and data-independence, which prevents a full exploitation of their potential. To tackle this issue, we propose a novel method of designing self-grouping convolutional neural networks, called SG-CNN, in which the filters of each convolutional layer group themselves based on the similarity of their importance vectors. Concretely, for each filter, we first evaluate the importance value of their input channels to identify the importance vectors, and then group these vectors by clustering. Using the resulting emph{data-dependent} centroids, we prune the less important connections, which implicitly minimizes the accuracy loss of the pruning, thus yielding a set of emph{diverse} group convolution filters. Subsequently, we develop two fine-tuning schemes, i.e. (1) both local and global fine-tuning and (2) global only fine-tuning, which experimentally deliver comparable results, to recover the recognition capacity of the pruned network. Comprehensive experiments carried out on the CIFAR-10/100 and ImageNet datasets demonstrate that our self-grouping convolution method adapts to various state-of-the-art CNN architectures, such as ResNet and DenseNet, and delivers superior performance in terms of compression ratio, speedup and recognition accuracy. We demonstrate the ability of SG-CNN to generalise by transfer learning, including domain adaption and object detection, showing competitive results. Our source code is available at https://github.com/QingbeiGuo/SG-CNN.git.
Two networks are equivalent if they produce the same output for any given input. In this paper, we study the possibility of transforming a deep neural network to another network with a different number of units or layers, which can be either equivalent, a local exact approximation, or a global linear approximation of the original network. On the practical side, we show that certain rectified linear units (ReLUs) can be safely removed from a network if they are always active or inactive for any valid input. If we only need an equivalent network for a smaller domain, then more units can be removed and some layers collapsed. On the theoretical side, we constructively show that for any feed-forward ReLU network, there exists a global linear approximation to a 2-hidden-layer shallow network with a fixed number of units. This result is a balance between the increasing number of units for arbitrary approximation with a single layer and the known upper bound of $lceil log(n_0+1)rceil +1$ layers for exact representation, where $n_0$ is the input dimension. While the transformed network may require an exponential number of units to capture the activation patterns of the original network, we show that it can be made substantially smaller by only accounting for the patterns that define linear regions. Based on experiments with ReLU networks on the MNIST dataset, we found that $l_1$-regularization and adversarial training reduces the number of linear regions significantly as the number of stable units increases due to weight sparsity. Therefore, we can also intentionally train ReLU networks to allow for effective loss-less compression and approximation.
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