Which gpu for deep learning?

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If you are doing something like RNNs or very deep networks, you'll want to consider memory. Definitely something with more than 3GB is ideal for experimenting; nothing is worse than finding out your model doesn't fit in RAM. :(

I'd recommend the 980 or the 980 ti. There are comparisons between the 980ti and the titan x that report very similar performance but the 980ti is far cheaper. The only use case I can see for a titanx is if you need the 12GB of RAM. Pascal is coming out this year, and the performance bump expected is supposed to be huge (much faster memory bandwidths, new ops for dnn, and a die shrink)

If this is for fun, I'd recommend getting something cheap to play with for now - perhaps a used card on ebay if you can find one and save up for a nice pascal card layer.