The best-fit Gaussian distribution is denoted with adashed line.

Understanding convergence of stochastic gradient descent (SGD) based optimization algorithms can help deal with enormous machine learning problems.

Finally, we develop an efficient implementation that translates these computational savings into actual wall-clock speedup.

We refer to them astarget-causing confounders.

We show that adversarial training is unnecessary and sometimes counter-productive; we instead cast invariant representation learning asasingle information-theoretic objectivethat can bedirectly optimized.

The proof can be found in Chapter 27 of [6]. For the non-flat version, the update is similar to the mini-batch SGD except that we add small Gaussian noises to the particle models. In Section 4.2 of the main paper, we provide a comprehensive analysis of the performance concerning In the experiments presented in Tables 1 and 2 in the main paper, we train all models for 300 epochs using SGD, with a learning rate of 0.1 and a cosine schedule. For the baseline of the Deep-Ensemble, SGLD, SGVB and SGVB-LRT methods, we reproduce results following the hyper-parameters and processes as our flat versions. ImageNet: This is a large and challenging dataset with 1000 classes.