Specifically as current is run across it, it builds up more and more resistance. Then as the current is reversed (the plus and minus ends of the resistor is switched) this resistance will go back down.

Thus it can be used as non-volatile memory in the sense that certain tiers of resistance can be designated as a bit.

Note that as it is fundamentally an analog component one can potentially also used this property to emulate a neuron.

That's incredibly interesting, especially the idea that it could be used to emulate neurons. I expect that it'd be hard to fabricate them with a very high branching factor, but as I've amply demonstrated, I know very little about this topic.

Fixed.