I didn't know about Theano, thanks for the hint. I have been focused on C++ libraries only, apparently missing a huge body of work.
CPU is supported through OpenCL by these libraries. Remember, OpenCL code can run on CPUs. As for Aura, it is pre-alpha, not a lot of functionality there yet, I'm still figuring out the interface. So not usable yet, but keep an eye on it, it will be.
Oh, I wasn't aware that OpenCL also can run on the CPU, I always thought that it is GPU-only, thanks for pointing that out! How fast is that? Is that comparable to uBLAS or ATLAS or so? Can that scale to multiple CPU cores? Does it use SSE or similar technics? Or does that depend on the implementation? What can I expect in common desktop PCs?
I'm not overly familiar with OpenCL on the CPU myself, I only know it works. But people are doing this [0,1]. Whether or no it uses SSE/multiple cores depends on the specific OpenCL backend that is used. But it should use both multiple cores and SSE. I know Intel does this for both their Phi and regular CPUs.
For me, the most important thing in both CUDA and OpenCL is the programming model. It allows us to describe data parallel problems and related data (in)dependence explicitly. Compilers should be (and already are) able to generate efficient code from this. It is not as nice as it could be, we have to write kernels by hand etc. But there are libraries that make our lives easier (we discussed them earlier). And there is also C++ AMP which tries to integrate better. Yet still, while we have all these options and we can solve most of our problems with more or less effort and elegance, I believe there must be something better out there: the right way to describe data parallel and task parallel problems as well as concurrency etc. Maybe the FP guys are on to something, I don't know. I'll be on the lookout.
CPU is supported through OpenCL by these libraries. Remember, OpenCL code can run on CPUs. As for Aura, it is pre-alpha, not a lot of functionality there yet, I'm still figuring out the interface. So not usable yet, but keep an eye on it, it will be.