Recurrent Neural Networks as Electrical Networks, a formalization
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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Fourier-Enhanced Recurrent Neural Networks for Electrical Load Time Series Downscaling
We present a Fourier-enhanced recurrent neural network (RNN) for downscaling electrical loads. The model combines (i) a recurrent backbone driven by low-resolution inputs, (ii) explicit Fourier seasonal embeddings fused …
Modeling Electrical Motor Dynamics using Encoder-Decoder with Recurrent Skip Connection
Electrical motors are the most important source of mechanical energy in the industrial world. Their modeling traditionally relies on a physics-based approach, which aims at taking their complex internal dynamics into acc…
DecoderDomain AdaptationFormalized Hopfield Networks and Boltzmann Machines
Neural networks are widely used, yet their analysis and verification remain challenging. We present a Lean~4 formalization covering both deterministic and stochastic models. We first formalize Hopfield networks -- recurr…
Physical Modeling using Recurrent Neural Networks with Fast Convolutional Layers
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms …
Recurrent Neural Networks for Forecasting Time Series with Multiple Seasonality: A Comparative Study
This paper compares recurrent neural networks (RNNs) with different types of gated cells for forecasting time series with multiple seasonality. The cells we compare include classical long short term memory (LSTM), gated …
Load ForecastingTime SeriesTime Series Analysis