Instituto de Ciencias Físicas, Universdad Nacional Autónoma de México, Cuernavaca, Morelos, México.
PLoS One. 2012;7(8):e42348. doi: 10.1371/journal.pone.0042348. Epub 2012 Aug 10.
We study the properties of the dynamical phase transition occurring in neural network models in which a competition between associative memory and sequential pattern recognition exists. This competition occurs through a weighted mixture of the symmetric and asymmetric parts of the synaptic matrix. Through a generating functional formalism, we determine the structure of the parameter space at non-zero temperature and near saturation (i.e., when the number of stored patterns scales with the size of the network), identifying the regions of high and weak pattern correlations, the spin-glass solutions, and the order-disorder transition between these regions. This analysis reveals that, when associative memory is dominant, smooth transitions appear between high correlated regions and spurious states. In contrast when sequential pattern recognition is stronger than associative memory, the transitions are always discontinuous. Additionally, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of the same set of patterns, there is a discontinuous transition between associative memory and sequential pattern recognition. In contrast, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of independent sets of patterns, the network is able to perform both associative memory and sequential pattern recognition for a wide range of parameter values.
我们研究了在神经网络模型中发生的动力学相变的性质，其中存在联想记忆和序列模式识别之间的竞争。这种竞争通过突触矩阵的对称部分和非对称部分的加权混合来实现。通过生成泛函形式主义，我们确定了非零温度和接近饱和时（即存储模式的数量与网络大小成比例）参数空间的结构，确定了高和弱模式相关性、自旋玻璃解和这些区域之间的有序无序转变的区域。这项分析表明，当联想记忆占主导地位时，在高相关区域和虚假状态之间会出现平滑的转变。相反，当序列模式识别强于联想记忆时，转变总是不连续的。此外，当突触矩阵的对称部分和非对称部分都根据相同的模式集定义时，联想记忆和序列模式识别之间存在不连续的转变。相反，当突触矩阵的对称部分和非对称部分根据独立的模式集定义时，网络能够在广泛的参数值范围内执行联想记忆和序列模式识别。
