Paper: Graph Lottery Ticket Automated (ICLR-2024)

Reviewer comment (Theory):
The assumption of Theorem 1 may not be true for $G^{(l)}$ in most cases, since $G^{(l)}$ should be different due to the layer-adaptive pruning.

Author response:
Thanks for your insightful question. We would like to clarify that $\mathbf{G}^{(l)}$ differs across the layer index $l$. In our setting, the key distinction is in the smallest singular value $\sigma^{(l)}_0 = 1 - \alpha^l$, which varies with the layer index. This setting of the smallest singular value is in accordance with *layer-adaptive pruning*. Additionally, other singular values can also differ within $\mathbf{G}^{(l)}$. Consequently, the operation matrix $\mathbf{G}^{(l)}$ varies from layer to layer.

Reviewer comment (Theory):
Could the author describe how to get the equation 10?

Author response:
Please refer to our response to Weakness 3 :)