do the cars have some serious computer hardware or is it really good code/cloud assisted computation? Maybe ANN's active while driving?
Yes, that's it. Signal processing for forward looking radar, forward and backward looking cameras, and side-looking sonar sensors. Definitely local.
Cloud wouldn't work. The Teslas have LTE data links, but their latency is grossly unpredictable.
The Tesla vehicles use cameras, ultrasonics and radar. So they are processing graphical data (a video stream) and signal data. That's exactly the kind of task that GPUs are good at.
However, this only gets you as far as perceiving the world. The vehicles also have to decide which action to take -- following the traffic laws of the jurisdiction they are in -- which is exactly the kind of branchy imperative task that CPUs are good at and GPUs are terrible at.
https://blogs.nvidia.com/blog/2016/10/20/tesla-motors-self-d...
Not sure what HW their previous cars had