Summary:

only use caffe with GPU but without cudnn, you could use  NVIDIA GPUs of compute capability less than 2.0 is ok;

But with cudnn, you must make sure your  NVIDIA GPUs of compute capability 3.0 and higher.

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Proof1(comes from nvidia official pdf):

2.6. GPU and driver requirements

cuDNN v3.0 supports NVIDIA GPUs of compute capability 3.0 and higher and requires

an NVIDIA Driver compatible with CUDA Toolkit 7.0.

This is ref  cuDNN v3 user guide. In cudnn_library.pdf. 

You could download this pdf from https://developer.nvidia.com/rdp/cudnn-archive .

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Proof2(comes from caffe official website info):

Caffe need :

CUDA compute capability: devices with compute capability <= 2.0 may have to reduce CUDA thread numbers and batch sizes due to hardware constraints. Brew with caution; we recommend compute capability >= 3.0. 

ref:

http://caffe.berkeleyvision.org/installation.html

Note:

You could refer to the Wikipedia page supported GPUs to know which compute capability your GPU has (a similar list is available on Nvidia's compute capability webpage).

Referenced blogs:

https://github.com/botonchou/libdnn/issues/20

http://stackoverflow.com/questions/33760192/how-to-know-which-cudnn-version-one-should-use