Modern discrete GPUs also have IOMMUs and per-context page tables. It's a large attack surface which has received relatively little attention from hackers so far compared to CPUs, but there are hardware-level security features in place.
Other than the framebuffer there's not even any data of worth on the GPU.
The attack of note that's been mitigated is DoS attacks through webgl, but GPU preemption is a thing now which largely solves the infinite loop in a shader to lock up the machine.
(And re the MMU features upthread, it's just a building block. Just like CPU having a MMU doesn't make your OS magically secure)
If you want to attack the shader compiler go for it, but since that lives in your own process anyway so you could skip that step and go straight to attacking whatever it is you wanted to attack.
> WebGL history (it's been much worse, not DoS only etc).
Such as? All I'm finding are DoS attacks. But regardless WebGL's problems were more due to WebGL and its designs than in vulnerabilities in the drivers or GPUs.
Regarding WebGL vulnerabilities, you can use your favourite search engine to look up vulnerabilities, here are some first hits for RCE bugs: https://www.cvedetails.com/cve/CVE-2012-3968/ https://bugs.chromium.org/p/chromium/issues/detail?id=740603 https://nvd.nist.gov/vuln/detail/CVE-2017-5128