I think the question is about how the kernel can use the GPU. Linux probably doesn't need to train hidden Markov models. It might, however, need to do crypto (e.g., for an encrypted filesystem).
Oh gosh you're right. I wasn't thinking about the context in which the question was posed. Anyway, hopefully someone will find those examples interesting. NVIDIA's CUDA developer zone is chock full of great resources for GPGPU (like video lectures and tools and code examples).