The WBP problem is related to the optimal transport (OT) problem, in that both are based on the Wassersteindistance, buttheWBP issignificantly harder.

In Appendix B, we provide proofs of the theorems. In Table 6, we provide a list of oracle functions of three basic operation types, including affine transformation, unary nonlinear function, and binary nonlinear function. This lower bound can be used for training ReLU networks with loss fusion. Figure 4 compares the linear bounds in LiRP A and IBP respesctively. We refer readers to those existing works for details.

Training certifiably robust neural networks remains a notoriously hard problem.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes a novel model selection criterion for binary latent feature models. It is like variational Bayes, except that rather than assuming a factorized posterior over latent variables and parameters, it approximately integrates out the parameters using the BIC. They demonstrate improved held-out likelihood scores compared to several existing IBP implementations. The proposed approach seems like a reasonable thing to do, and is motivated by a plausible asymptotic argument.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This is an interesting paper describing mechanism to introduce constraints of the priors 1) I have two concerns with how the discussion is formulated: 1.1) The introduction of the paper talks about preserving exchangeability, and a substantial effort is devoted to showing that restrictions on the predictive distributions do not necessarily lead to exchangeable rows. However, given that the authors are working with priors on array-valued processes, they should have framed the discussion in terms of separate exchangeability (Aldous, 1981), which is what we really desired from the model. I think that all the proofs works and the models described are indeed separately exchangeable (rather than unrestrictedly exchangeable), but the current presentation is not really adequate.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Spectral methods are based on decomposing moment tensors. If data are generated from latent variable models, their empirical moment tensors have a kind of (approximate) low-rank decomposition (approximate due to both noisy observations and finite sample estimation error in the empirical moments). These decompositions can be computed from the moment tensors, e.g. using a kind of power iteration method on related (symmetrized) tensors. The basic ideas of these spectral methods are fairly well established and many examples have been explored, especially in [6]. This paper applies spectral fitting methods to data modeled as being generated from an IBP, including two common emission models (a linear gaussian model and a sparse factor analysis model, described in Section 2). The main ingredients are a calculation of the appropriate moment tensors and corresponding symmetrized versions (Section 3), an application of the standard tensor power decomposition method (Section 4), and concentration proofs to offer recovery guarantees when data are generated from the model (Section 5).