That is assuming you restrict yourself to a radical simplified model of each neuron. The actual biochemical processes going on in a single synaptic density go w

That is assuming you restrict yourself to a radical simplified model of each neuron. The actual biochemical processes going on in a single synaptic density go way beyond something that could be represented by a scalar weight that assemble into a linear transformation. Instead we are talking about 10^15 dynamical systems. This then still neglects most of the time /spatial extended nature of neurons, the fact that calcium stores in the endoplasmatic reticulum play a role etc. Some of this might be only relevant to learning, but non-linear dendritic processing is believed to be relevant for example for inference aswell.