Phase diagram and storage capacity of sequence processing neural networks
Phase diagram and storage capacity of sequence processing neural networks
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DOI：
10.1088/0305-4470/31/43/005
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发表时间：
1998-10-30
期刊：
影响因子：
--
通讯作者：
Sherrington, D
中科院分区：
文献类型：
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作者：
During, A;Coolen, ACC;Sherrington, D
我们解决了hopfield型神经网络的动力学问题，该网络存储接近饱和的模式序列。这种模型中相互作用矩阵的不对称性导致了详细平衡的破坏，从而排除了平衡统计力学分析。利用生成泛函方法，导出了在热力学极限下的动态序参量的精确闭方程，即序列重叠、相关函数和响应函数。我们计算了这些方程的时间平移不变解，描述了平稳极限环，得到了相图。通常在对称模型中出现的有效延迟自相互作用在这里消失了，这导致与存储静态模式的Hopfield网络的α (c)相似的0.269的存储容量相比，α (c)相似的0.139的存储容量显着增加。我们的结果与大量的计算机模拟进行了测试，结果非常吻合。
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium statistical mechanical analysis. Using generating functional methods we derive exact closed equations for dynamical order parameters, namely the sequence overlap and correlation and response functions, in the thermodynamic limit. We calculate the time translation invariant solutions of these equations, describing stationary limit cycles, which leads to a phase diagram. The effective retarded self-interaction usually appearing in symmetric models is here found to vanish, which causes a significantly enlarged storage capacity of alpha(c) similar to 0.269, compared with alpha(c) similar to 0.139 for Hopfield networks storing static patterns. Our results are tested against extensive computer simulations and excellent agreement is found.