Charged Point Normalization: An Efficient Solution to the Saddle Point Problem
Recently, the problem of local minima in very high dimensional non-convex optimization has been challenged and the problem of saddle points has been introduced. This paper introduces a dynamic type of normalization that forces the system to escape saddle points. Unlike other saddle point escaping algorithms, second order information is not utilized, and the system can be trained with an arbitrary gradient descent learner. The system drastically improves learning in a range of deep neural networks on various data-sets in comparison to non-CPN neural networks.
This paper proposes a novel method for accelerating optimization near saddle points. The basic idea is to repel the current parameter vector from a running average of recent parameter values. This method is shown to optimize faster than a variety of other methods in a variety of datasets and architectures. On the surface, the proposed method seems extremely close to momentum. It would be very valuable to think of a clear diagram illustrating how it differs from momentum and why it might be better near a saddle point. The illustration of better convergence on the toy saddle example is not what I mean here—optimization speed comparisons are always difficult due to the many details and hyper parameters involved, so seeing it work faster in one specific application is not as useful as a conceptual diagram which shows a critical case where CPN will behave differently from—and clearly qualitatively better than—momentum. Another way of getting at the relationship to momentum would be to try to find a form for R_t(f) that yields the exact momentum update. You could then compare this with the R_t(f) used in CPN. The overly general notation etc should be dropped—Eqn 8 is enough. The theoretical results (Eqn 1 and Thm 1) should be removed, they are irrelevant until the joint density can be specified. Experimentally, it would be valuable to standardize the results to allow comparison to other methods. For instance, recreating Figure 4 of Dauphin et al, but engaging the CPN method rather than SFN, would clearly demonstrate that CPN can escape something that momentum cannot. I think the idea here is potentially very valuable, but needs more rigorous comparison and a clear relation to momentum and other work.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Charged Point Normalization: An Efficient Solution to the Saddle Point Problem
Recently, the problem of local minima in very high dimensional non-convex optimization has been challenged and the problem of saddle points has been introduced. This paper introduces a dynamic type of normalization that forces the system to escape saddle points. Unlike other saddle point escaping algorithms, second order information is not utilized, and the system can be trained with an arbitrary gradient descent learner. The system drastically improves learning in a range of deep neural networks on various data-sets in comparison to non-CPN neural networks.
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>



This paper proposes a novel method for accelerating optimization near saddle points. The basic idea is to repel the current parameter vector from a running average of recent parameter values. This method is shown to optimize faster than a variety of other methods in a variety of datasets and architectures. On the surface, the proposed method seems extremely close to momentum. It would be very valuable to think of a clear diagram illustrating how it differs from momentum and why it might be better near a saddle point. The illustration of better convergence on the toy saddle example is not what I mean here—optimization speed comparisons are always difficult due to the many details and hyper parameters involved, so seeing it work faster in one specific application is not as useful as a conceptual diagram which shows a critical case where CPN will behave differently from—and clearly qualitatively better than—momentum. Another way of getting at the relationship to momentum would be to try to find a form for R_t(f) that yields the exact momentum update. You could then compare this with the R_t(f) used in CPN. The overly general notation etc should be dropped—Eqn 8 is enough. The theoretical results (Eqn 1 and Thm 1) should be removed, they are irrelevant until the joint density can be specified. Experimentally, it would be valuable to standardize the results to allow comparison to other methods. For instance, recreating Figure 4 of Dauphin et al, but engaging the CPN method rather than SFN, would clearly demonstrate that CPN can escape something that momentum cannot. I think the idea here is potentially very valuable, but needs more rigorous comparison and a clear relation to momentum and other work.
assistant
This paper proposes a novel method for accelerating optimization near saddle points. The basic idea is to repel the current parameter vector from a running average of recent parameter values. This method is shown to optimize faster than a variety of other methods in a variety of datasets and architectures. On the surface, the proposed method seems extremely close to momentum. It would be very valuable to think of a clear diagram illustrating how it differs from momentum and why it might be better near a saddle point. The illustration of better convergence on the toy saddle example is not what I mean here—optimization speed comparisons are always difficult due to the many details and hyper parameters involved, so seeing it work faster in one specific application is not as useful as a conceptual diagram which shows a critical case where CPN will behave differently from—and clearly qualitatively better than—momentum. Another way of getting at the relationship to momentum would be to try to find a form for R_t(f) that yields the exact momentum update. You could then compare this with the R_t(f) used in CPN. The overly general notation etc should be dropped—Eqn 8 is enough. The theoretical results (Eqn 1 and Thm 1) should be removed, they are irrelevant until the joint density can be specified. Experimentally, it would be valuable to standardize the results to allow comparison to other methods. For instance, recreating Figure 4 of Dauphin et al, but engaging the CPN method rather than SFN, would clearly demonstrate that CPN can escape something that momentum cannot. I think the idea here is potentially very valuable, but needs more rigorous comparison and a clear relation to momentum and other work.