Diversity and Depth in Per-Example Routing Models
Routing models, a form of conditional computation where examples are routed through a subset of components in a larger network, have shown promising results in recent works. Surprisingly, routing models to date have lacked important properties, such as architectural diversity and large numbers of routing decisions. Both architectural diversity and routing depth can increase the representational power of a routing network. In this work, we address both of these deficiencies. We discuss the significance of architectural diversity in routing models, and explain the tradeoffs between capacity and optimization when increasing routing depth. In our experiments, we find that adding architectural diversity to routing models significantly improves performance, cutting the error rates of a strong baseline by 35% on an Omniglot setup. However, when scaling up routing depth, we find that modern routing techniques struggle with optimization. We conclude by discussing both the positive and negative results, and suggest directions for future research.
 The major contribution of this work is extending routing networks (Rosenbaum et al., ICLR 2018) to use diverse architectures across routed modules. I view this as an important contribution and am very impressed by the experiment on Omniglot where it shows big performance gain on a split with very few examples. This idea of incorporating in architectural bias and not just parameter bias for small data problems is very compelling and intuitive to me on the surface. The ablation study was also very interesting in this regard. I really like the discourse and found it to be filled with interesting insights throughout ranging from the connection between routing networks and neural architecture search to the heuristic for selecting k. However, after the great discourse, I was quite disappointed by the breadth of the experiments. The paper is positioned as exploring two parallel ideas that are independently interesting 1) diversity in the architecture of modules in routing models 2) the effect of increasing depth in routing models. For the first idea, this is shown very well by the Omniglot experiment but is not evaluated in any other setting. Showing this in a few other experiments would have really driven this point home in my opinion. The second idea is not really executed in a convincing way to me. The authors call it a ‘negative result’ in the end, but I’m not sure I really feel like I learned anything from this experiment. I wonder about statistical significance. I also feel like the authors are trying to turn it into a commentary that this is a pain point for all variants of routing models while they only actually tried it for their proposed architecture which makes quite a few decisions along the way. I would have liked to see more model variants and datasets before really feeling like I can make any empirical determinations about the fundamental limitations of all routing models in this regard. Additionally, if there were such a fundamental scaling limitation, you would imagine that an experiment could be constructed that really highlighted this fact where all routing models do way worse. In short, I think there are some really good idea in this paper and vote for acceptance on that basis. Had the authors provided more empirical evidence about architectural diversity, I would have given it a very high score. The analysis of depth is also a very interesting topic, but it could possibly even serve as another paper considering that the current results don’t really come to concrete conclusions for the community.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Diversity and Depth in Per-Example Routing Models
Routing models, a form of conditional computation where examples are routed through a subset of components in a larger network, have shown promising results in recent works. Surprisingly, routing models to date have lacked important properties, such as architectural diversity and large numbers of routing decisions. Both architectural diversity and routing depth can increase the representational power of a routing network. In this work, we address both of these deficiencies. We discuss the significance of architectural diversity in routing models, and explain the tradeoffs between capacity and optimization when increasing routing depth. In our experiments, we find that adding architectural diversity to routing models significantly improves performance, cutting the error rates of a strong baseline by 35% on an Omniglot setup. However, when scaling up routing depth, we find that modern routing techniques struggle with optimization. We conclude by discussing both the positive and negative results, and suggest directions for future research.
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 major contribution of this work is extending routing networks (Rosenbaum et al., ICLR 2018) to use diverse architectures across routed modules. I view this as an important contribution and am very impressed by the experiment on Omniglot where it shows big performance gain on a split with very few examples. This idea of incorporating in architectural bias and not just parameter bias for small data problems is very compelling and intuitive to me on the surface. The ablation study was also very interesting in this regard. I really like the discourse and found it to be filled with interesting insights throughout ranging from the connection between routing networks and neural architecture search to the heuristic for selecting k. However, after the great discourse, I was quite disappointed by the breadth of the experiments. The paper is positioned as exploring two parallel ideas that are independently interesting 1) diversity in the architecture of modules in routing models 2) the effect of increasing depth in routing models. For the first idea, this is shown very well by the Omniglot experiment but is not evaluated in any other setting. Showing this in a few other experiments would have really driven this point home in my opinion. The second idea is not really executed in a convincing way to me. The authors call it a ‘negative result’ in the end, but I’m not sure I really feel like I learned anything from this experiment. I wonder about statistical significance. I also feel like the authors are trying to turn it into a commentary that this is a pain point for all variants of routing models while they only actually tried it for their proposed architecture which makes quite a few decisions along the way. I would have liked to see more model variants and datasets before really feeling like I can make any empirical determinations about the fundamental limitations of all routing models in this regard. Additionally, if there were such a fundamental scaling limitation, you would imagine that an experiment could be constructed that really highlighted this fact where all routing models do way worse. In short, I think there are some really good idea in this paper and vote for acceptance on that basis. Had the authors provided more empirical evidence about architectural diversity, I would have given it a very high score. The analysis of depth is also a very interesting topic, but it could possibly even serve as another paper considering that the current results don’t really come to concrete conclusions for the community.
assistant
 The major contribution of this work is extending routing networks (Rosenbaum et al., ICLR 2018) to use diverse architectures across routed modules. I view this as an important contribution and am very impressed by the experiment on Omniglot where it shows big performance gain on a split with very few examples. This idea of incorporating in architectural bias and not just parameter bias for small data problems is very compelling and intuitive to me on the surface. The ablation study was also very interesting in this regard. I really like the discourse and found it to be filled with interesting insights throughout ranging from the connection between routing networks and neural architecture search to the heuristic for selecting k. However, after the great discourse, I was quite disappointed by the breadth of the experiments. The paper is positioned as exploring two parallel ideas that are independently interesting 1) diversity in the architecture of modules in routing models 2) the effect of increasing depth in routing models. For the first idea, this is shown very well by the Omniglot experiment but is not evaluated in any other setting. Showing this in a few other experiments would have really driven this point home in my opinion. The second idea is not really executed in a convincing way to me. The authors call it a ‘negative result’ in the end, but I’m not sure I really feel like I learned anything from this experiment. I wonder about statistical significance. I also feel like the authors are trying to turn it into a commentary that this is a pain point for all variants of routing models while they only actually tried it for their proposed architecture which makes quite a few decisions along the way. I would have liked to see more model variants and datasets before really feeling like I can make any empirical determinations about the fundamental limitations of all routing models in this regard. Additionally, if there were such a fundamental scaling limitation, you would imagine that an experiment could be constructed that really highlighted this fact where all routing models do way worse. In short, I think there are some really good idea in this paper and vote for acceptance on that basis. Had the authors provided more empirical evidence about architectural diversity, I would have given it a very high score. The analysis of depth is also a very interesting topic, but it could possibly even serve as another paper considering that the current results don’t really come to concrete conclusions for the community.