Deep Epitome for Unravelling Generalized Hamming Network: A Fuzzy Logic Interpretation of Deep Learning
This paper gives a rigorous analysis of trained Generalized Hamming Networks (GHN) proposed by Fan (2017) and discloses an interesting finding about GHNs, i.e. stacked convolution layers in a GHN is equivalent to a single yet wide convolution layer. The revealed equivalence, on the theoretical side, can be regarded as a constructive manifestation of the universal approximation theorem Cybenko (1989); Hornik (1991). In practice, it has profound and multi-fold implications. For network visualization, the constructed deep epitomes at each layer provide a visualization of network internal representation that does not rely on the input data. Moreover, deep epitomes allows the direct extraction of features in just one step, without resorting to regularized optimizations used in existing visualization tools.
 pros : - interesting topic cons : - experiments are not convincing - writing & clarity could be improved sometimes The paper is a bit hard to read sometimes, because it does not refer to usual notions. First of all, the Equation (1) of the subsection 3.1 could be more precise. Use and not and define the "dot" operation. I have assumed the paper was using real valued networks and the euclidean scalar product. I do not see the interest to use the notation "g" if the circplus is used. The definitions 1 and 2 of 3.2 do not help the reader so maybe they could be removed.. Secondly, it is shown that the operations performed by the network are associative, and equivalent to a single "epitome convolution". I dot not agree with (on page 7) the "manifestation of the universal approximation" theorem. The formulations are rigorously different (2 linear+point wise non linearity), or I do not see the link and thus a comment would be appreciated. Thirdly, there is the "data independent" and "data dependent" visualisation, which correspond, if I*m correct, to a visualisation of the filters and the representations respectively. I do not understand what are the histograms of the normalised deep epitoms, or to which quantity they refer to. Similarly, I do not understand what is displayed on the Figures in the appendix: if I am correct, the equivalent {g_n} are visualised, but this is not specified and there are a lot of redundant filters, which could be commented. The figures of the appendix should be put in the main paper. I am finally very concerned with the experimental section. No classification accuracy is reported. It is important to report it, as one can not judge the technique: it is possible to reach 80% with mathematically predefined filters (wavelets) on CIFAR10, which are interpretable. It is very important to have competitive results w.r.t. classification to convince a reader that the technique is well-founded to study CNN.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Deep Epitome for Unravelling Generalized Hamming Network: A Fuzzy Logic Interpretation of Deep Learning
This paper gives a rigorous analysis of trained Generalized Hamming Networks (GHN) proposed by Fan (2017) and discloses an interesting finding about GHNs, i.e. stacked convolution layers in a GHN is equivalent to a single yet wide convolution layer. The revealed equivalence, on the theoretical side, can be regarded as a constructive manifestation of the universal approximation theorem Cybenko (1989); Hornik (1991). In practice, it has profound and multi-fold implications. For network visualization, the constructed deep epitomes at each layer provide a visualization of network internal representation that does not rely on the input data. Moreover, deep epitomes allows the direct extraction of features in just one step, without resorting to regularized optimizations used in existing visualization tools.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 pros : - interesting topic cons : - experiments are not convincing - writing & clarity could be improved sometimes The paper is a bit hard to read sometimes, because it does not refer to usual notions. First of all, the Equation (1) of the subsection 3.1 could be more precise. Use and not and define the "dot" operation. I have assumed the paper was using real valued networks and the euclidean scalar product. I do not see the interest to use the notation "g" if the circplus is used. The definitions 1 and 2 of 3.2 do not help the reader so maybe they could be removed.. Secondly, it is shown that the operations performed by the network are associative, and equivalent to a single "epitome convolution". I dot not agree with (on page 7) the "manifestation of the universal approximation" theorem. The formulations are rigorously different (2 linear+point wise non linearity), or I do not see the link and thus a comment would be appreciated. Thirdly, there is the "data independent" and "data dependent" visualisation, which correspond, if I*m correct, to a visualisation of the filters and the representations respectively. I do not understand what are the histograms of the normalised deep epitoms, or to which quantity they refer to. Similarly, I do not understand what is displayed on the Figures in the appendix: if I am correct, the equivalent {g_n} are visualised, but this is not specified and there are a lot of redundant filters, which could be commented. The figures of the appendix should be put in the main paper. I am finally very concerned with the experimental section. No classification accuracy is reported. It is important to report it, as one can not judge the technique: it is possible to reach 80% with mathematically predefined filters (wavelets) on CIFAR10, which are interpretable. It is very important to have competitive results w.r.t. classification to convince a reader that the technique is well-founded to study CNN.
assistant
 pros : - interesting topic cons : - experiments are not convincing - writing & clarity could be improved sometimes The paper is a bit hard to read sometimes, because it does not refer to usual notions. First of all, the Equation (1) of the subsection 3.1 could be more precise. Use and not and define the "dot" operation. I have assumed the paper was using real valued networks and the euclidean scalar product. I do not see the interest to use the notation "g" if the circplus is used. The definitions 1 and 2 of 3.2 do not help the reader so maybe they could be removed.. Secondly, it is shown that the operations performed by the network are associative, and equivalent to a single "epitome convolution". I dot not agree with (on page 7) the "manifestation of the universal approximation" theorem. The formulations are rigorously different (2 linear+point wise non linearity), or I do not see the link and thus a comment would be appreciated. Thirdly, there is the "data independent" and "data dependent" visualisation, which correspond, if I*m correct, to a visualisation of the filters and the representations respectively. I do not understand what are the histograms of the normalised deep epitoms, or to which quantity they refer to. Similarly, I do not understand what is displayed on the Figures in the appendix: if I am correct, the equivalent {g_n} are visualised, but this is not specified and there are a lot of redundant filters, which could be commented. The figures of the appendix should be put in the main paper. I am finally very concerned with the experimental section. No classification accuracy is reported. It is important to report it, as one can not judge the technique: it is possible to reach 80% with mathematically predefined filters (wavelets) on CIFAR10, which are interpretable. It is very important to have competitive results w.r.t. classification to convince a reader that the technique is well-founded to study CNN.