The forward pass of a neural network is an Euler step of a relaxation PDE: the activation function is the local equilibrium and the weights act as advection-diffusion coefficients.
Anderson, The end of theory: the data deluge makes the scie ntific method obsolete
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A note on the physical interpretation of neural PDE's
The forward pass of a neural network is an Euler step of a relaxation PDE: the activation function is the local equilibrium and the weights act as advection-diffusion coefficients.