Hopfield networks and their ilk are, in essence, two-dimensional.

霍普菲尔德网络及其同类网络本质上是二维的。

Hopfield networks, in which each node is connected to every other except itself, are particularly good at learning to extract patterns from sparse or noisy data.

霍普菲尔德网络中每个节点都与除自身之外的所有其他节点相连，这种网络特别擅长学习从稀疏或嘈杂的数据中提取模式。

Dr Hinton also, for good measure, tweaked Dr Hopfield's networks using a branch of maths called statistical mechanics to create what are known as Boltzmann machines.

此外，Hinton 博士还利用数学的一个分支“统计力学”对 Hopfield 博士的网络进行了改进，创造出了所谓的玻尔兹曼机。

Dr Hopfield was responsible for what has become known as the Hopfield network—a type of artificial neural network that behaves like a physical structure called a spin glass, which gave the academy a tenuous reason to call the field " physics" .

霍普菲尔德博士负责的研究项目后来被称为霍普菲尔德网络， 这是一种人工神经网络， 其行为类似于一种名为自旋玻璃的物理结构，这让科学院有理由将该领域称为“物理学” 。