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摘要: 动量算法理论上可以加速受限玻尔兹曼机（Restricted Boltzmann machine，RBM）网络的训练速度.本文通过对现有动量算法进行仿真研究，发现现有动量算法在受限玻尔兹曼机网络训练中加速效果较差，且在训练后期逐渐失去了加速性能.针对以上问题，本文首先基于Gibbs采样收敛性定理对现有动量算法进行了理论分析，证明了现有动量算法的加速效果是以牺牲网络权值为代价的；然后，本文进一步对网络权值进行研究，发现网络权值中包含大量真实梯度的方向信息，这些方向信息可以用来对网络进行训练；基于此，本文提出了基于网络权值的权值动量算法，最后给出了仿真实验.实验结果表明，本文提出的动量算法具有更好的加速效果，并且在训练后期仍然能够保持较好的加速性能，可以很好地弥补现有动量算法的不足.Abstract: Momentum algorithms can accelerate the training speed of restricted Boltzmann machine theoretically. Through a simulation study on existing momentum algorithms, it is found that existing momentum algorithms for training restricted Boltzmann machine have a poor accelerating effect and they began to lose acceleration performance. In the latter part of training process. Focusing on this problem, firstly, this paper gives a theoretical analysis of the algorithms based on Gibbs sampling convergence theorem. It is proved that the acceleration effect of existing momentum algorithms is at the expense of enlarging network weights. Then, a further investigation on network weights shows that the network weights contain a lot of information of the true gradient direction which can be used to train the network. According to this, a weight momentum algorithm is proposed based on the weight of the network. Finally, simulation results demonstrate that the proposed algorithm has a better acceleration effect and has the accelerating ability even in the end of the training process. Therefore the proposed algorithm can well make up for the weaknesses of existing momentum algorithms.
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Key words:
- Deep learning /
- restricted Boltzmann machine (RBM) /
- momentum algorithm /
- weight momentum
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图 23 迭代初期梯度差值对比图
Fig. 23 Compassion of the difference of the gradients in initial stages of iteration
图 24 迭代中期梯度差值对比图
Fig. 24 Compassion of the difference of the gradients in mid-term of iteration
表 1 网络参数值
Table 1 The value of network parameters
网络参数 初始值 $a$ zeros $(1, 784) $ $b$ zeros $(1, 500) $ $w$ $0.1\times randn(784,500)$ $\eta $ $0.1$ $\mu $ $0.9 $ 
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表 2 训练参数
Table 2 Training parameters
算法参数 $\mu $ $\lambda$ $\alpha $ CD 0.9 CM 0.9 NM 0.9 CMD 0.9 0.00001 NMD 0.9 0.00001 CDW 0.9 0.0001 CMW 0.9 0.0001 NMW 0.9 0.0001
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表 3 记号示意图
Table 3 Sign diagram
代号 差值项 A CM-CD B NM-CD C CMW-CD D NMW-CD E CDW-CD F CMW-CD G NMW-CD
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表 4 网络参数值
Table 4 The value of network parameters
网络参数 初始值 $a$ zeros $(1, 1024) $ $b$ zeros $(1, 800) $ $w$ $0.1\times randn(1024,800)$ $\eta $ $0.01$ $\mu $ $0.9$
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表 5 网络参数值
Table 5 The value of network parameters
网络参数 初始值 $a$ zeros $(1, 3072) $ $b$ zeros $(1, 2000) $ $w$ $0.1\times randn(3072,2000)$ $\eta $ $0.01$ $\mu $ $0.9$
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表 6 网络参数值
Table 6 The value of network parameters
网络参数 初始值 $a$ zeros $(1, 3072) $ $b$ zeros $(1, 2000) $ $w$ $0.1\times randn(3072,2000)$ $\eta $ $0.01$ $\mu $ $0.9 $
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表 7 网络参数值
Table 7 The value of network parameters
网络参数 初始值 $a$ zeros $(1, 4096) $ $b$ zeros $(1, 3000) $ $w$ $0.1\times randn(4096,3000)$ $\eta $ $0.01$ $\mu $ $0.9 $
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