  Uncertainty quantification for deep neural networks has recently evolved
through many techniques. In this work, we revisit Laplace approximation, a
classical approach for posterior approximation that is computationally
attractive. However, instead of computing the curvature matrix, we show that,
under some regularity conditions, the Laplace approximation can be easily
constructed using the gradient second moment. This quantity is already
estimated by many exponential moving average variants of Adagrad such as Adam
and RMSprop, but is traditionally discarded after training. We show that our
method (L2M) does not require changes in models or optimization, can be
implemented in a few lines of code to yield reasonable results, and it does not
require any extra computational steps besides what is already being computed by
optimizers, without introducing any new hyperparameter. We hope our method can
open new research directions on using quantities already computed by optimizers
for uncertainty estimation in deep neural networks.
