vandal-vpr/vg-transformers

Is there a problem with the representation of L in Formula 1 of your paper?

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Is there a problem with the representation of L in Formula 1 of your paper? In the paper, L represents the sequence length. Should L in Formula 2 be changed to represent the number of clusters in the NetVLAD algorithm?
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in that formula, the netvlad cluster index is $k$. Therefor for each cluster in this formula we compute the assignment, on all descriptors ($M$ is the number of descriptors in an image), for all frames in the sequence; with $L$ sequence length

Think you for your help!