Kahan summation2 is a technique to reduce the numerical error of adding multiple low precision numbers by accumulating errors in a separate compensation buffer. The addition of the compensation buffer increases the effective summation precision by the precision of the compensation buffer.
Using Kahan summation to improve low precision model training was first introduced by Zamirai et al in Revisiting BFloat16 Training. Zamirai et al discovered the primary source of numerical error from low precision training is during the optimizer’s model weight update step. They add Kahan summation to the SGD & AdamW weight update steps to reduce the update’s numerical inaccuracy, increasing low precision training to the equivalent of full precision training across tested models.
https://optimi.benjaminwarner.dev/kahan_summation/
Kahan Summation¶
Kahan summation2 is a technique to reduce the numerical error of adding multiple low precision numbers by accumulating errors in a separate compensation buffer. The addition of the compensation buffer increases the effective summation precision by the precision of the compensation buffer.
Using Kahan summation to improve low precision model training was first introduced by Zamirai et al in Revisiting BFloat16 Training. Zamirai et al discovered the primary source of numerical error from low precision training is during the optimizer’s model weight update step. They add Kahan summation to the SGD & AdamW weight update steps to reduce the update’s numerical inaccuracy, increasing low precision training to the equivalent of full precision training across tested models.