论文标题
分类Hopfield网络
Categorical Hopfield Networks
论文作者
论文摘要
本文讨论了Manin和作者先前作品中引入的分类Hopfield方程的简单明了的玩具模型示例。这些描述了资源对网络的动态分配，其中资源是Unital对称单体类别中的对象和分配，可以通过求和函数来实现。此处讨论的特殊情况基于计算资源（神经元的计算模型）作为DNN类别中的对象，可以简单地选择定义Hopfield方程的内型函数，这些方程将通过梯度下降重现DNNS中的权重通常更新。
This paper discusses a simple and explicit toy-model example of the categorical Hopfield equations introduced in previous work of Manin and the author. These describe dynamical assignments of resources to networks, where resources are objects in unital symmetric monoidal categories and assignments are realized by summing functors. The special case discussed here is based on computational resources (computational models of neurons) as objects in a category of DNNs, with a simple choice of the endofunctors defining the Hopfield equations that reproduce the usual updating of the weights in DNNs by gradient descent.
