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PyTorch uses CuBLAS [1] under the hood, among other libraries, so basic linear algebra ops should be fast.

You might also look at CuPy [2], especially if you like NumPy.

[1] https://developer.nvidia.com/cublas [2] https://cupy.chainer.org/



Now I'm wondering if anybody wrote a DL library on top of CuPy, and if such library could be competitive with PyTorch in terms of performance.


Yes, it is called Chainer and it's quite competitive.




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