In this paper, we introduce the pseudo-extended MCMC method as a simple approach for improving the mixing of the MCMC sampler for multi-modal posterior distributions.

All of the reviewers' minor comments and corrections have been added to Below, we address the reviewers' main questions. The paper focuses on HMC sampling. Unfortunately, HMC can't be applied in the discrete setting due to discontinuous How do you recommend setting π and g to best estimate β? Therefore, it's quite straightforward to implement pseudo-extended HMC within Stan by As a minor comment in line 58, it would be good to state that delta is an arbitrary differentiable function. This is a good point and we've corrected this in the paper. The experiments in 4.1 and 4.2 use the RMSE error of the target variables which is quite unusual.

In this article, we study binary classification for large-scale data sets.

We also use our approach for estimating covariance structure for a number of real-world datasets and show that it consistently outperforms state-of-the-art estimators at a fraction of the computational cost.

CFCNet learns to capture, to the largest extent, the semantically correlated features between RGB and depth information.

Adversarial examples have attracted significant attention in machine learning, but the reasons for their existence and pervasiveness remain unclear. We demonstrate that adversarial examples can be directly attributed to the presence of non-robust features: features (derived from patterns in the data distribution) that are highly predictive, yet brittle and (thus) incomprehensible to humans. After capturing these features within a theoretical framework, we establish their widespread existence in standard datasets. Finally, we present a simple setting where we can rigorously tie the phenomena we observe in practice to a misalignment between the (human-specified) notion of robustness and the inherent geometry of the data.

Rather than changing the learning rate at each iteration, we propose an approach that automates the most common hand-tuning heuristic: use a constant learning rate until "progress stops", then drop. We design an explicit statistical test that determines when the dynamics of stochastic gradient descent reach a stationary distribution.

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The presence of the threshold comes from statistics.

We propose simple and fast approximations for its expectation, which serves as an essential role in our proposed policy.