Review for NeurIPS paper: ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA

Weaknesses: This work falls on the periphery of my area of expertise, so I'll try to offer the perspective of someone who is interested and somewhat familiar with this family of methods, but who does not have intricate knowledge of it. I agree that seeking identifiable representations, as defined in the manuscript, is a worthwhile goal, and a promising way to improve downstream processing. The authors came very close to proving full identifiability for the proposed model family, having achieved weak (linear mapping) and strong (permutation) identifiability conditions. However, I'm not sure I follow why strong identifiability represents a substantial step after weak identifiability, in the sense that I struggle to think of a downstream task that can handle strong representations, but not weak. As I understand it, the idea of identifiability explored here was introduced in Khemakem er at.