As traditional neural network consumes a significant amount of computing resources during back propagation, propose a simple yet effective technique to alleviate this problem. In this technique, only a small subset of the full gradients are computed to update the model parameters. In this paper we extend this technique into the Convolutional Neural Network(CNN) to reduce calculation in back propagation, and the surprising results verify its validity in CNN: only 5 of the gradients are passed back but the model still achieves the same effect as the traditional CNN, or even better. We also show that the top- @math selection of gradients leads to a sparse calculation in back propagation, which may bring significant computational benefits for high computational complexity of convolution operation in CNN.
The methods @cite_2 are limited to the softmax layer (output layer) and are only based on random sampling, while our method does not have those limitations. The sparsely-gated mixture-of-experts @cite_3 only sparsifies the mixture-of-experts gated layer and it is limited to the specific setting of mixture-of-experts, while our method does not have those limitations. There are also prior studies focusing on reducing the communication cost in distributed systems @cite_12 @cite_10 , by quantizing each value of the gradient from 32-bit float to only 1-bit. Those settings are also different from ours.
@cite_10 @cite_12 @cite_3 @cite_2
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Mixtures of Experts combine the outputs of several “expert” networks, each of which specializes in a different part of the input space. This is achieved by training a “gating” network that maps each input to a distribution over the experts. Such models show promise for building larger networks that are still cheap to compute at test time, and more parallelizable at training time. In this this work, we extend the Mixture of Experts to a stacked model, the Deep Mixture of Experts, with multiple sets of gating and experts. This exponentially increases the number of effective experts by associating each input with a combination of experts at each layer, yet maintains a modest model size. On a randomly translated version of the MNIST dataset, we find that the Deep Mixture of Experts automatically learns to develop location-dependent (“where”) experts at the first layer, and class-specific (“what”) experts at the second layer. In addition, we see that the different combinations are in use when the model is applied to a dataset of speech monophones. These demonstrate effective use of all expert combinations. The capacity of a neural network to absorb information is limited by its number of parameters. Conditional computation, where parts of the network are active on a per-example basis, has been proposed in theory as a way of dramatically increasing model capacity without a proportional increase in computation. In practice, however, there are significant algorithmic and performance challenges. In this work, we address these challenges and finally realize the promise of conditional computation, achieving greater than 1000x improvements in model capacity with only minor losses in computational efficiency on modern GPU clusters. We introduce a Sparsely-Gated Mixture-of-Experts layer (MoE), consisting of up to thousands of feed-forward sub-networks. A trainable gating network determines a sparse combination of these experts to use for each example. We apply the MoE to the tasks of language modeling and machine translation, where model capacity is critical for absorbing the vast quantities of knowledge available in the training corpora. We present model architectures in which a MoE with up to 137 billion parameters is applied convolutionally between stacked LSTM layers. On large language modeling and machine translation benchmarks, these models achieve significantly better results than state-of-the-art at lower computational cost. Mixture of experts (ME) is one of the most popular and interesting combining methods, which has great potential to improve performance in machine learning. ME is established based on the divide-and-conquer principle in which the problem space is divided between a few neural network experts, supervised by a gating network. In earlier works on ME, different strategies were developed to divide the problem space between the experts. To survey and analyse these methods more clearly, we present a categorisation of the ME literature based on this difference. Various ME implementations were classified into two groups, according to the partitioning strategies used and both how and when the gating network is involved in the partitioning and combining procedures. In the first group, The conventional ME and the extensions of this method stochastically partition the problem space into a number of subspaces using a special employed error function, and experts become specialised in each subspace. In the second group, the problem space is explicitly partitioned by the clustering method before the experts' training process starts, and each expert is then assigned to one of these sub-spaces. Based on the implicit problem space partitioning using a tacit competitive process between the experts, we call the first group the mixture of implicitly localised experts (MILE), and the second group is called mixture of explicitly localised experts (MELE), as it uses pre-specified clusters. The properties of both groups are investigated in comparison with each other. Investigation of MILE versus MELE, discussing the advantages and disadvantages of each group, showed that the two approaches have complementary features. Moreover, the features of the ME method are compared with other popular combining methods, including boosting and negative correlation learning methods. As the investigated methods have complementary strengths and limitations, previous researches that attempted to combine their features in integrated approaches are reviewed and, moreover, some suggestions are proposed for future research directions. As communication systems scale up in speed and bandwidth, the cost and power consumption of high-precision (e.g., 8-12 bits) analog-to-digital conversion (ADC) becomes the limiting factor in modern transceiver architectures based on digital signal processing. In this work, we explore the impact of lowering the precision of the ADC on the performance of the communication link. Specifically, we evaluate the communication limits imposed by low-precision ADC (e.g., 1-3 bits) for transmission over the real discrete-time additive white Gaussian noise (AWGN) channel, under an average power constraint on the input. For an ADC with K quantization bins (i.e., a precision of log2 K bits), we show that the input distribution need not have any more than K+1 mass points to achieve the channel capacity. For 2-bin (1-bit) symmetric quantization, this result is tightened to show that binary antipodal signaling is optimum for any signal-to- noise ratio (SNR). For multi-bit quantization, a dual formulation of the channel capacity problem is used to obtain tight upper bounds on the capacity. The cutting-plane algorithm is employed to compute the capacity numerically, and the results obtained are used to make the following encouraging observations : (a) up to a moderately high SNR of 20 dB, 2-3 bit quantization results in only 10-20 reduction of spectral efficiency compared to unquantized observations, (b) standard equiprobable pulse amplitude modulated input with quantizer thresholds set to implement maximum likelihood hard decisions is asymptotically optimum at high SNR, and works well at low to moderate SNRs as well.