>Until now, there were three known ways that neurons “talk” to each other in the brain: via synaptic transmission, axonal transmission and what are known as “gap junctions” between the neurons.

I know about chemical synapses (the "usual" synapses with gain, and which we model with weights in artificial neural networks, and which transmit information in forward mode), I also know about electrical synapses (fast, no gain, bidirectional, possibly mediator of the backpropagation signal?) but I don't know what they refer to with "axonal transmission" ? surely they don't just mean pulse propagation along the axon, can someone point me to the accepted mechanism of axonal transmission across neurons? from cell body to synapse is just transmission line along the same neuron...

also correlation is not necessarily propagation, consider for example shining a laser dot on a distant wall, and rotating the beam such that the spot moves faster than light: this is perfectly possible, but no physical signal is moving faster than light, rather the dot at some initial time and the dot at a later time are correlated, but are both the result of a laser reflecting of a rotating mirror.

in order to eliminate a mutual cause, you dont make a local cut in some neuronal tissue, you fully separate the tissue, and then measure their electrical activity (preferably optically using a nematic liquid crystal as they used in the past to inspect voltage levels on chips under microscopes) while mounted on micron precision translation stage, and starting from a distance, slowly have the samples approach and measure their correlation, and do the same experiment without a neuron culture, because the correlation may be due to stray electric fields from the environment (another common cause, like the laser for the lightspeed dots)

use 2 different wavelengths (and corresponding filters at the detectors) of light to measure the optical activity of the nematic liquid crystal sensors, in order to make sure no light is leaking through...

According to wikipedia https://en.wikipedia.org/wiki/Axonal_transport :

>Since some axons are on the order of meters long, neurons cannot rely on diffusion to carry products of the nucleus and organelles to the end of their axons.

and:

>Vesicular cargoes move relatively fast (50–400 mm/day) whereas transport of soluble (cytosolic) and cytoskeletal proteins takes much longer (moving at less than 8 mm/day).

note that the flow of material in axonal transport is retrograde (i.e. in the opposite direction of pulse transmission), so any feedback, adjoint sensitivity or backpropagation signal - if it exists - to implement Automatic Differentiation in a physical manner, might move at such speeds. I don't know the typical axon lengths (please tell me if you know or can refer me to measured distributions of axon length), but this maximum of about 1000mm implies 125 days (8mm/day) or 2.5 days (400mm/day). If we assume the dimension of the brain as a typical axon length i.e. 10cm = 100mm then this becomes 12.5 days (400mm/day) and 0.25 days or six hours (8mm/day). For 1cm we have 30 hours (8mm/d) and 36 minutes (400mm/d). For 1cm to 10cm typical axon lengths and shorter indeed seem like the kind of time frame of learning, i.e. the weights may be modified during sleep, and the delay line of materials undergoing axonal transport in each axon contain echoes or memories of synaptic activity during the day.