Recurrent Neural Networks as Electrical Network, a formalization

CARUSO, M.; JARNE, CECILIA

Conferencia; -DCAI: International Symposium on Distributed Computing and Artificial Intelligence; 2022

Since the 1980s, and particularly with the Hopfield model, recurrent neural networks became a topic of great interest. It is well known that any finite-time trajectory of a given n−dimensional dynamical system can be approximately realized by the internal state of the output units of a continuous-time recurrent neural network with output units. From this idea, and with the advance of the last ten years which includes current computing algorithms, the new hardware and the theory of neural networks, we have enormous developments in various areas related to natural language, dynamical systems, neurosciences and time series analysis. 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 circuit was carried out directly without formalism. The present work shows a way to formally obtain the equivalence between an analogue circuit anda neural network and formalizes the connection between both systems. We can have confidence that the representation in terms of circuits is mathematically equivalent to the equations that represent the network.