Since the 1980s, and particularly with the Hopfield model, recurrent neural networks or RNN became a topic of great interest. The first works of neural networks consisted of simple systems of a few neurons that were commonly simulated through analogue electronic circuits. The passage from the equations to the circuits was carried out directly without justification and subsequent formalisation. The present work shows a way to formally obtain the equivalence between an analogue circuit and a neural network and formalizes the connection between both systems. We also show which are the properties that these electrical networks must satisfy. We can have confidence that the representation in terms of circuits is mathematically equivalent to the equations that represent the network.

翻译：自20世纪80年代以来，特别是随着Hopfield模型的出现，递归神经网络（RNN）成为备受关注的研究课题。早期神经网络研究由简单系统构成，仅包含少数神经元，通常通过模拟电子电路进行仿真。从方程到电路的转换过程缺乏严格论证，也未得到后续的形式化处理。本研究展示了一种能够正式建立模拟电路与神经网络等价性的方法，并系统阐述了两者之间的联系。我们还揭示了这些电路网络必须满足的物理特性。研究证实，基于电路的表示形式在数学上与表征网络的方程具有等价性。