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摘要: 目前受限玻尔兹曼机网络训练算法主要是基于采样的算法.当用采样算法进行梯度计算时，得到的采样梯度是真实梯度的近似值，采样梯度和真实梯度之间存在较大的误差，这严重影响了网络的训练效果.针对该问题，本文首先分析了采样梯度和真实梯度之间的数值误差和方向误差，以及它们对网络训练性能的影响，然后从马尔科夫采样的角度对以上问题进行了理论分析，并建立了梯度修正模型，通过修正梯度对采样梯度进行数值和方向的调节，并提出了基于改进并行回火算法的训练算法，即GFPT（Gradient fixing parallel tempering）算法.最后给出GFPT算法与现有算法的对比实验，仿真结果表明，GFPT算法可以极大地减小采样梯度和真实梯度之间的误差，大幅度提升受限玻尔兹曼机网络的训练效果.Abstract: Currently, most algorithms for training restricted Boltzmann machines (RBMs) are based on multi-step Gibbs sampling. When the sampling algorithm is used to calculate gradient, the sampling gradient is an approximate value of the true gradient, and there is a big error between the sampling gradient and the true gradient, which seriously affects training effect of network. This article focuses on the problems mentioned above. Firstly, numerical error and direction error between gradient and true gradient sampling are analyzed, as well as their influences on the performance of network training. The problems are theoretically analyzed from the angle of Markov sampling. Then a gradient modification model is established to adjust the numerical value and direction of sampling gradient. Furthermore, improved tempering learning based algorithm is put forward, that is, GFPT (Gradient fixing parallel tempering) algorithm. Finally, a comparative experiment on the GFPT algorithm and existing algorithms is given. It demonstrated that GFPT algorithm can greatly reduce the sampling error between sampling gradient and true gradient, and improve RBM network training precision.1) 本文责任编委 乔俊飞
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表 1 训练算法及参数
Table 1 Training algorithms and parameters
CD1 CD5 CD10 PT5 PT10 GFPT5 GFPT10 η 0.1 0.1 0.1 0.1 0.1 0.1 0.1 k 1 5 10 1 1 1 1 T - - - 20 20 20 20 M - - - 5 10 5 10 λ 0.1 0.1 batch 60 60 60 60 60 60 60 iter 1 000 1 000 1 000 1 000 1 000 1 000 1000 
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