cuDNN is a cuda library which provides basic operations like forward and backward passes for neural networks on GPU. This is used by caffe and other toolkits.
You can download cuDNN from : https://developer.nvidia.com/cudnn. Note that you need to login to be able to download.
This post is just for my own reminder on cuDNN installation. Basically untar, and then copy the header and shared-libs to /usr/local/cuda-7.5
cudnn-7.5-linux-x64-v5.0-ga.tgz is downloaded in a directory
$ tar -xvzf cudnn-7.5-linux-x64-v5.0-ga.tgz
$ sudo cp -i include/cudnn.h /usr/local/cuda-7.5/include/
sudo cp -i lib64/libcudnn* /usr/local/cuda-7.5/lib64/
After this, just cmake
caffe and you should see cuDNN found (see my config).
This is it (as of June 2016), possibly NVidia will add instructions/make it easier for installation possibly also extend the library.