Paper:
The sophisticated structure of Convolutional Neural Network (CNN) allows for outstanding performance, but at the cost of intensive computation. As significant redundancies inevitably present in such a structure, many works have been proposed to prune the convolutional filters for computation cost reduction. Although extremely effective, most works are based only on quantitative characteristics of the convolutional filters, and highly overlook the qualitative interpretation of individual filter's specific functionality. In this work, we interpreted the functionality and redundancy of the convolutional filters from different perspectives, and proposed a functionality-oriented filter pruning method. With extensive experiment results, we proved the convolutional filters' qualitative significance regardless of magnitude, demonstrated significant neural network redundancy due to repetitive filter functions, and analyzed the filter functionality defection under inappropriate retraining process. Such an interpretable pruning approach not only offers outstanding computation cost optimization over previous filter pruning methods, but also interprets filter pruning process.

Review:
In this paper, the authors propose a method for pruning the convolutional filters. This method first separates the filters into clusters based on similarities defined with both Activation Maximization (AM) and back-propagation gradients. Then pruning is conducted based on the clustering results, and the contribution index that is calculated based on backward-propagation gradients. The proposed method is compared with a baseline method in the experiments. 
I consider the proposed method as novel, since I do not know any filter pruning methods that adopt a similar strategy. Based on my understanding of the proposed method, it might be useful in convolutional filter pruning.
It seems that "interpretable" might not be the most proper word to summarize the method. It looks like that the key concept of this paper, including smilarity defined in Equation (3), and the contribution index defined in Equation (7) are not directly relevant to interpretability. Therefore, I would consider change the title of the paper, for example, to "Convolutional Filter Pruning Based on Functionality ". 
In terms of writing, I have difficulty understanding some details about the method. 
In filter clustering, how can one run k-means based on pair-wise similarity matrix $S_D$? Do you run kernel k-means, or you  apply PCA to $S_D$ before k-means? What is the criterion of choosing the number of clusters in the process of grid search? 
Are filter level pruning, are cluster level pruning and layer level pruning three pruning strategies in the algorithm? It seems to me that you just apply one pruning strategy based on the clusters and contribution index, as shown in Figure 3. 
In the subsubsection "Cluster Level Pruning", by "cluster volume size", denoted with$length(C^l_c)$, do you mean the size of cluster, i.e., the number of elements in each cluster? This is the first time I see the term "volume size". I assume the adaptive pruning rate, denoted by $R_{clt}^{(c,l)}$, is a fraction. But it looks to me that $length(C^l_c)$ is an integer. So how can it be true that $R_{clt}^{(c,l)} = length(C^l_c)$?
In the subsubsection "Layer Level Pruning", how is the value of $r$ determined?
The authors have conducted several experiments. These experiments help me understand the advantages of the proposed method. However, in the experiments, the proposed method is compared to only one baseline method. In recent years, a large number of convolutional filter pruning methods have been proposed, as mentioned in the related work section. I am not convinced that the proposed method is one of the best methods among all these existing methods. I would suggest the authors provide more experimental comparison, or explain why comparing with these existing methods is irrelevant. 
Since the proposed method is heuristic, I would also like the authors to illustrate that each component of the method is important, via experiment. How would the performance of the proposed method be affected, if we define the similarity $S_D$ in Equation (3) using only $V$ or $\gamma$, rather than both $V$ and $\gamma$? How would the performance of the proposed method be affected, if we prune randomly, rather than prune based on the contribution index?
In summary, I think the method proposed in this paper might be reasonable. But I do not suggest acceptance, unless the author can improve the writing and include more experimental results.