Matrix capsules with EM routing
A capsule is a group of neurons whose outputs represent different properties of the same entity. Each layer in a capsule network contains many capsules. We describe a version of capsules in which each capsule has a logistic unit to represent the presence of an entity and a 4x4 matrix which could learn to represent the relationship between that entity and the viewer (the pose). A capsule in one layer votes for the pose matrix of many different capsules in the layer above by multiplying its own pose matrix by trainable viewpoint-invariant transformation matrices that could learn to represent part-whole relationships. Each of these votes is weighted by an assignment coefficient. These coefficients are iteratively updated for each image using the Expectation-Maximization algorithm such that the output of each capsule is routed to a capsule in the layer above that receives a cluster of similar votes. The transformation matrices are trained discriminatively by backpropagating through the unrolled iterations of EM between each pair of adjacent capsule layers. On the smallNORB benchmark, capsules reduce the number of test errors by 45\% compared to the state-of-the-art. Capsules also show far more resistance to white box adversarial attacks than our baseline convolutional neural network.
 The paper describes another instantiation of "capsules" which attempt to learn part-whole relationships and the geometric pose transformations between them. Results are presented on the smallNORB test set obtaining impressive performance. Although I like very much this overall approach, this particular paper is so opaquely written that it is difficult to understand exactly what was done and how the network works. It sounds like the main innovation here is using a 4x4 matrix for the pose parameters, and an iterative EM algorithm to find the correspondence between capsules (routing by agreement). But what exactly the pose matrix represents, and how they get transformed from one layer to the next, is left almost entirely to the reader*s imagination. In addition, how EM factors in, what the probabilities P_ih represent, etc. is not clear. I think the authors could do a much better job explaining this model, the rationale behind it, and how it works. Perhaps the most interesting and compelling result is Figure 2, which shows how ambiguity in object class assignment is resolved with each iteration. This is very intriguing, but it would be great to understand what is going on and how this is happening. Although the results are impressive, if one can*t understand how this was achieved it is hard to know what to make of it.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Matrix capsules with EM routing
A capsule is a group of neurons whose outputs represent different properties of the same entity. Each layer in a capsule network contains many capsules. We describe a version of capsules in which each capsule has a logistic unit to represent the presence of an entity and a 4x4 matrix which could learn to represent the relationship between that entity and the viewer (the pose). A capsule in one layer votes for the pose matrix of many different capsules in the layer above by multiplying its own pose matrix by trainable viewpoint-invariant transformation matrices that could learn to represent part-whole relationships. Each of these votes is weighted by an assignment coefficient. These coefficients are iteratively updated for each image using the Expectation-Maximization algorithm such that the output of each capsule is routed to a capsule in the layer above that receives a cluster of similar votes. The transformation matrices are trained discriminatively by backpropagating through the unrolled iterations of EM between each pair of adjacent capsule layers. On the smallNORB benchmark, capsules reduce the number of test errors by 45\% compared to the state-of-the-art. Capsules also show far more resistance to white box adversarial attacks than our baseline convolutional neural network.
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>



 The paper describes another instantiation of "capsules" which attempt to learn part-whole relationships and the geometric pose transformations between them. Results are presented on the smallNORB test set obtaining impressive performance. Although I like very much this overall approach, this particular paper is so opaquely written that it is difficult to understand exactly what was done and how the network works. It sounds like the main innovation here is using a 4x4 matrix for the pose parameters, and an iterative EM algorithm to find the correspondence between capsules (routing by agreement). But what exactly the pose matrix represents, and how they get transformed from one layer to the next, is left almost entirely to the reader*s imagination. In addition, how EM factors in, what the probabilities P_ih represent, etc. is not clear. I think the authors could do a much better job explaining this model, the rationale behind it, and how it works. Perhaps the most interesting and compelling result is Figure 2, which shows how ambiguity in object class assignment is resolved with each iteration. This is very intriguing, but it would be great to understand what is going on and how this is happening. Although the results are impressive, if one can*t understand how this was achieved it is hard to know what to make of it.
assistant
 The paper describes another instantiation of "capsules" which attempt to learn part-whole relationships and the geometric pose transformations between them. Results are presented on the smallNORB test set obtaining impressive performance. Although I like very much this overall approach, this particular paper is so opaquely written that it is difficult to understand exactly what was done and how the network works. It sounds like the main innovation here is using a 4x4 matrix for the pose parameters, and an iterative EM algorithm to find the correspondence between capsules (routing by agreement). But what exactly the pose matrix represents, and how they get transformed from one layer to the next, is left almost entirely to the reader*s imagination. In addition, how EM factors in, what the probabilities P_ih represent, etc. is not clear. I think the authors could do a much better job explaining this model, the rationale behind it, and how it works. Perhaps the most interesting and compelling result is Figure 2, which shows how ambiguity in object class assignment is resolved with each iteration. This is very intriguing, but it would be great to understand what is going on and how this is happening. Although the results are impressive, if one can*t understand how this was achieved it is hard to know what to make of it.