Strengths:
This paper unifies a number of straight through estimators under a common framework which helps in motivating previously considered 'ad-hoc' rules for gradient backpropagation, and helps understanding of the conditions which may affect the bias/performance of the estimators.
The paper is technical but written in such a way that it is still relatively easy to follow, by keeping notations simple (yet clear) and deferring detailed derivations/proofs to the appendix (which I did not go through in detail).
The paper shows theoretically and experimentally that different design choices for the estimator are possible, as long as different parts (model, initialization and training) are well aligned. Weaknesses:
As a weakness, the paper feels a bit as an enumeration of related but separate contributions (summed up in the paragraph 'contributions'). The experiments mainly concern section 4 and show somewhat the effect of Bias Analysis IV), but it would improve the paper if (toy) experiments would have been conducted relating to the other analysis in section 2.2 as well, which could then justify the practical relevance of these results.
While the paper motivates the reintroduction of ST as principled methods, the experiments give some insights but do not fully convince of the practical use of the proposed extensions.
It is positive that the paper is largely self-contained, but this makes it a bit difficult to distinguish novel derivations from recapitulations of results from previous work. Also, the paper lacks a discussion section and as a result feels a bit unfinished.
3. Recommendation
My current recommendation is to accept the paper.
4. Arguments for recommendation
This paper helps in the theoretical understanding and unifying view of a variety of straight through estimators, which may help advancing these estimators for training networks with binary weights and activations, which is a relevant and difficult problem.
5. Questions to authors
Why is a discussion section omitted?
Figure 1: looking at the y-axis for the top row, it seems that both ARM and ST get worse results with 256 bits than 8 or 64 bits, which hints at underfitting. How does this affect the conclusions?
Additional feedback
Minor comments
Line 152: where does the symbol f for loss come from?
Line 305: a reference is missing: ??
Line 331,5: reminder -> remainder?
Line 372: ELOB -> ELBO? Or -ELBO (negative ELBO)?
Some grammar could be improved, e.g. in abstract 'we … obtains, …, explains'
5. Questions to authors Why is a discussion section omitted? Figure 1: looking at the y-axis for the top row, it seems that both ARM and ST get worse results with 256 bits than 8 or 64 bits, which hints at underfitting. How does this affect the conclusions? Additional feedback Minor comments Line 152: where does the symbol f for loss come from? Line 305: a reference is missing: ?? Line 331,5: reminder -> remainder? Line 372: ELOB -> ELBO? Or -ELBO (negative ELBO)? Some grammar could be improved, e.g. in abstract 'we … obtains, …, explains'