On reaction network implementations of neural networks

This paper is concerned with the utilization of deterministically modelled chemical reaction networks for implementation (feed-forward) neural networks. We develop a general mathematical framework and prove that ordinary differential equations (ODEs) associated certain network implementations have desirable properties including (i) existence unique positive fixed points are smooth in parameters model (necessary gradient descent) (ii) fast convergence to point regardless initial condition efficient implementation). do so by first making connection between systems ODEs, then constructing correct set ODEs. demonstrate theory implements smoothed ReLU activation function, though we also how generalize construction allow other functions (each listed previously). As there multiple types ‘networks’ used this paper, give careful introduction both networks, order disambiguate overlapping vocabulary two settings clearly highlight role each network’s properties.