TensorFlow GPU: is cudnn optional? Couldn't open CUDA library libcudnn.so

cuDNN is used to speedup a few TensorFlow operations such as the convolution. I noticed in your log file that you're training on the MNIST dataset. The reference MNIST model provided with TensorFlow is built around 2 fully connected layers and a softmax. Therefore TensorFlow won't attempt to call cuDNN when training this model.

I'm not sure that TensorFlow will automatically fallback to a slower convolution algorithm when cuDNN isn't available. If it doesn't you can always disable the use of cuDNN by setting the TF_USE_CUDNN environment variable to 0 before running TensorFlow.