具有拟Hebbian联络矩阵的二次二元泛函的局部极小
Local Minima of a Quadratic Binary Functional with a Quasi-Hebbian Connection Matrix
摘要：
讨论了依赖于二元变量的二次泛函的局部极小问题。一个任意的连接矩阵可以以准赫布展开的形式表示，其中每个模式都有自己的权重。对于这样的矩阵，统计物理方法允许人们导出描述泛函的局部极小值的方程。详细讨论了只有一个权重与其他权重不同的模型。在这种情况下，方程可以解析地求解。得到了重构能量景观的权重临界值。所得结果得到了计算机模拟的证实。
英文摘要：
The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight. For such matrices statistical physics methods allow one to derive an equation describing local minima of the functional. A model where only one weight differs from other ones is discussed in detail. In this case the equation can be solved analytically. The critical values of the weight, for which the energy landscape is reconstructed, are obtained. Obtained results are confirmed by computer simulations.
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