All knowledgeable referees have confirmed the novelty parts and contributions of this work. I recommend acceptance of this paper and suggest the authors refine the paper before publication. Particularly, the concerns and suggestions raised by R#4 & R#3 should be addressed. AC and SAC discussed this paper on the issues raised by R3 and converged to accept. The authors are encouraged to discuss whether CNN belongs to the models that can be explained by the method proposed.

Weaknesses: Weaknesses Evaluating feature interactions - I think the synthetic dataset experiment in Section 4.1 is a good step towards evaluating the efficacy of PID. Looking at the AUC numbers, the performance of PID, AG, and NID seems quite close. Given these are synthetic data results, and the testbed is quite controlled, I would encourage the authors to provide more insights on why the performance is similar/close. For instance, the authors note AG is "tree-based", but it is not immediately clear how or why this may the main reason PID to perform better in F5, F6, and F8. Furthermore, with NID being a similar (in spirit) baseline, I would expect more in-depth analysis and discussion on the benefits that PID brings comparatively.

Detecting statistical interactions between input features is a crucial and challenging task. Recent advances demonstrate that it is possible to extract learned interactions from trained neural networks. It has also been observed that, in neural networks, any interacting features must follow a strongly weighted connection to common hidden units. Motivated by the observation, in this paper, we propose to investigate the interaction detection problem from a novel topological perspective by analyzing the connectivity in neural networks. Specially, we propose a new measure for quantifying interaction strength, based upon the well-received theory of persistent homology.