On the influence of roundoff errors on the convergence of the gradient descent method with low-precision floating-point computation. (arXiv:2202.12276v1 [cs.LG])

The employment of stochastic rounding schemes helps prevent stagnation of
convergence, due to vanishing gradient effect when implementing the gradient
descent method in low precision. Conventional stochastic rounding achieves zero
bias by preserving small updates with probabilities proportional to their
relative magnitudes. In this study, we propose a new stochastic rounding scheme
that trades the zero bias property with a larger probability to preserve small
gradients. Our method yields a constant rounding bias that, at each iteration,
lies in a …

arxiv computation convergence errors gradient precision