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 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，上述方程可以解析求解。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 details. In this case the above-mention equation can be solved analytically. Obtained results are confirmed by computer simulations.
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