Low Precision Training
We can filter through quantization noise by combining weights that have been rounded down with weights that have been rounded up. Moreover, by averaging weights to find a flat region of the loss surface, large perturbations of the weights will not affect the quality of the solution (Figures 9 and 10). Recent work shows that by adapting SWA to the low precision setting, in a method called SWALP, one can match the performance of full-precision SGD even with all training in 8 bits [5]. This is quite a practically important result, given that (1) SGD training in 8 bits performs notably worse than full precision SGD, and (2) low precision training is significantly harder than predictions in low precision after training (the usual setting). For example, a ResNet-164 trained on CIFAR-100 with float (16-bit) SGD achieves 22.2% error, while 8-bit SGD achieves 24.0% error. By contrast, SWALP with 8 bit training achieves 21.8% error.