Crossover between neural networks is considered disruptive due to the strong functional dependency between connection weights. We propose a modularity-based linkage model at the weight level to preserve functionally dependent communities (building blocks) in neural networks during mixing. A proximity matrix is built by estimating the dependency between weights, then a community detection algorithm maximizing modularity is run on the graph described by such matrix. The resulting communities/groups of parameters are considered to be mutually independent and used as crossover masks in an optimal mixing EA. A variant is tested with an operator that neutralizes the permutation problem of neural networks to a degree. Experiments were performed on 8 and 10-bit parity problems as the intrinsic hierarchical nature of the dependencies in these problems are challenging to learn. The results show that our algorithm finds better, more functionally dependent linkage which leads to more successful crossover and better performance.

翻译：神经网络间的交叉常被认为具有破坏性，因为连接权重之间存在强烈的功能依赖性。我们提出了一种基于权重级模块化的链接模型，以在混合过程中保留神经网络中功能依赖的社区（构建块）。通过估计权重之间的依赖性构建邻近矩阵，然后在该矩阵描述的图上运行最大化模块化的社区检测算法。所得参数社区/组被视为相互独立，并用作最优混合进化算法中的交叉掩码。我们测试了一个变体，该变体使用一种算子在一定程度上消除了神经网络的排列问题。实验在8位和10位奇偶校验问题上进行，因为这些问题中依赖关系的固有层级性质具有学习挑战性。结果表明，我们的算法能发现更好、功能依赖更强的链接，从而带来更成功的交叉和更优的性能。