Does later versions of CUDA support older GPUs?

I have an old GeForce 650 GTX, and I see in the list CUDA GPUs - Compute Capability | NVIDIA Developer that the supported CUDA version is 3.0.

If I install CUDA 9.0 or any earlier, but after 3.0, would it work? And should I? Or should I just install the ancient 3.0 version?

Thanks,
Simen

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You should be able to use it with CUDA 9.0 and current display drivers.

The Streaming Multiprocessor (SM) version of your GPU determines which CUDA toolkit still supports it.
The GeForce 650 uses a GK107 which is a Kepler GPU architecture which means it has something in the SM 3.x versions (SM 3.0 according to the list you linked to, which is not the CUDA toolkit version!), which is still supported by CUDA 9.0, and current display drivers for your board containing CUDA 9.0 capable drivers.

Hereā€™s a detailed list of which features the different SM versions support:
[url]Programming Guide :: CUDA Toolkit Documentation

Older SM versions are not supported since CUDA 8.0 anymore and 32-bit is also not recommended.

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Hello! I have a GeForce330M (compute capability 1.2) built in my notebook. My OS is Ubuntu16.04LTS. So, could you please advise me an appropriate version of Cuda Toolkit?

That would be CUDA 6.0 from four years ago, if memory serves. You can download it from the CUDA archives. Note: CUDA 6.0 probably does not support your version of Ubuntu, check the Linux installation guide in CUDA 6.0.

IMHO, you wonā€™t be doing yourself any favors by trying to work with CUDA on utterly outdated hardware which lacks a lot of modern features. You really would want to get started on a GPU with at least compute capability 3.0 at this point and ideally one with compute capability >= 5.0.

Thanks! Iā€™ve found archives and iā€™m going to install Ubuntu 14.04 in addition to my 16.04 to try with Cuda Toolkit 6.5. I think itā€™ll sutisfy me for a first time.

I have the similar problem.
I have an older graphics card of NVIDIA.
By running the command ubuntu-drivers-devices i get -

model : GK107 [GeForce GT 630 OEM]
driver : nvidia-driver-470 - third-party non-free recommended

Does it will support CUDA 11.5 or 11.6 or any other version of CUDA 11??

No. CUDA 11.x does not support devices with compute capability 3.0 (sm_30), of which the GK107 is one. When you upgrade the hardware, keep in mind that sm_35, sm_37, and sm_50 are supported but deprecated in CUDA 11, and therefore support for devices with those compute capabilities is likely to disappear with the next major CUDA release.

Thanks for your response!

Actually I have one more graphics card in my uncleā€™s PC. That has a ASUS TUF Gaming GeForce GTX 1660S 6GB graphic card.

You can follow the above link to get the full specs of graphic card.
Does it will support CUDA 11.6??

Yes, it is compute capability 7.5.