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I've been working with fpgas for about 15 years. In that time, the projects have gone from pld style logic as you've described, to process algorithms, and now we're implementing machine learning trained neural nets in hardware and running Linux on board.
It's really wild. They are pretty neat.
Man, no kidding. We've got SoCs, we've got processors running on the FPGA fabric, we've got communications to Ethernet, PCIe, any AXI you like really. They can talk to RAM, storage, other processors, output graphics, kiss me on the forehead, and tuck me in at night. (I think.)
A coworker was telling me about the big shots in New York trading companies that are starting to implement FPGA architectures into their high-frequency trading algorithms, as the blazing high speed and great parallelization helps them squeeze out a couple extra microseconds in their algorithms. I think that's a good sign of people wising up to this potential here.
I don't know of any ML training on FPGAs, but I have no doubt that it can be / it is being done.
Edit: I just remembered the other day, I was shown a module that could take in a grey scale image, do edge dection, and output the edges as a new image file. Which isn't that hard, it's convolution on a sliding window, but what baffled me is that it was done in fewer cycles than could be compiled through C code, and the pipeline wasn't even that deep. It's crazy!
Ya, it's fun stuff. We're using ML for particle identification and tracking in high-energy physics. It's magnitudes faster than anything a CPU/GPU can do..
your eyes do this, the cells in your eyes do a variety of edge detection and orientation detection before passing on this preprocessed image to the brain where the brain processes it further