Do you happen to know if the Tesla approach is fundamentally different from say the method Waymo and Mobileye are using? I presume they all use neural net processing.
They're all using NNs, though how they use them, for what they use them, and how they train them, is obviously different.
Fundamentally Tesla is trying to build a generalized vision-only solution that works everywhere. Having maps "helps" for general navigation, and to provide high level info like not-visible-at-distance traffic control locations or lane information, but they don't need to know where every single curb and tree is in the maps.
The rest are using fusion of multiple sensors (generally radar, lidar, and vision at minimum) and also HD maps that do provide super fine detail, the using the fused sensors to know where in that ultra-high-res map they are. As a result, so far anyway, none of these folks have been able to scale their systems, and they typically offer nothing more than "pilot" test programs in a single city (with promises, now years late, to offer them in a very few other cities... though some are at least private-testing in a few other cities).
@diplomat33 can probably give you a deeper dive into the weeds on the differences in each of the "we need lidar" companies approaches, I think he mentioned for example between Waymo and Mobileye that Waymo does their fusion much earlier in the process for example.
Teslas theory in contrast is if you solve vision, there's nothing LIDAR can add....and if you haven't solved vision then LIDAR and super-HD-maps is just a crutch for a sub-optimal vision system.
(personally I think Teslas thinking here is GENERALLY correct-- but I disagree with them on radar... because Radar objectively
can add info that vision can't... the problem is most cheap "we need a million+ of these a year" car radars are very low resolution so trying to fuse that data with vision is difficult--- and Tesla ended up deciding the relatively few edge cases where it does add useful info you can't get with cameras are outweighed by the many more cases where it makes the system worse)