Confusion on Criterion 2

[function2-llx]

Dear authors,

I have read your manuscript, but I cannot understand the definition of of Criterion 2, which is a critical part to understand the contribution of your work. Since public comment on OpenReview is currently inactivated, I have no choice but have to ask here, and I would be grateful if you could help.

What I am seeing is illustrated in the following screenshot:

There are 3 points I am confused:

1. The subscript "k" in the summation term is undefined.
2. "i" is defined as the summation variable, but the statement of "for some i" in the summation term is conflicting.
3. The textual description says this "measures the proportion of code vectors used in VQ". According to my intuition, this should be defined as something like 1/K sum_{k from 1 to K} [there exists some i such that e_k = z'_i]. I believe the Question 2 from Reviewer bT9x concerns the same issue.

I hope my question is clear and thank you for your consideration.