[dharma1]

Afaik the Google TPU does inference only, at 8 bits. I don't think it's possible to train a neural network at 8 bit precision at this point in time. FP16 works for training though, and is twice as fast as FP32 on certain nvidia chips

[Houshalter]

Backpropagation can work with any precision, as long as you use stochastic rounding (so that the rounding errors are not correlated.) Without stochastic rounding even 16 bits will have rounding error bias.

http://arxiv.org/abs/1412.7024

[dharma1]

OK. I was going by this - https://petewarden.com/2016/05/03/how-to-quantize-neural-net...

I haven't seen 8bit training implemented in any (public) frameworks yet - that's not to say it's not possible. If it works then that's great, especially for specialised hardware.