Asymptotics of Wide Networks from Feynman Diagrams
Understanding the asymptotic behavior of wide networks is of considerable interest. In this work, we present a general method for analyzing this large width behavior. The method is an adaptation of Feynman diagrams, a standard tool for computing multivariate Gaussian integrals. We apply our method to study training dynamics, improving existing bounds and deriving new results on wide network evolution during stochastic gradient descent. Going beyond the strict large width limit, we present closed-form expressions for higher-order terms governing wide network training, and test these predictions empirically.
This paper proposes a new tool based on Feynman diagrams to analyze wide networks (e.g., feed-forward networks with one or more large hidden layers or CNNs with a large number of filters). The main contributions of the paper are: - a new method (using Feynman diagrams) to bound the asymptotic behavior of correlation functions (ensemble averages of the network functions and its derivatives). The method is presented as a conjecture. - tighter bounds for gradient flow of wide networks - an extended analysis of SGD for wide networks - a formalism for deriving finite-width corrections The study of (infinitely) wide networks has been active over the last few years. A better understanding of wide networks could, amongst other things, shed light on recent empirical results related to over-parametrized networks. As such, improving our theoretical understanding of wide networks and especially properties of finite-width networks, which is what this paper explores, seems significant and potentially very impactful.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Asymptotics of Wide Networks from Feynman Diagrams
Understanding the asymptotic behavior of wide networks is of considerable interest. In this work, we present a general method for analyzing this large width behavior. The method is an adaptation of Feynman diagrams, a standard tool for computing multivariate Gaussian integrals. We apply our method to study training dynamics, improving existing bounds and deriving new results on wide network evolution during stochastic gradient descent. Going beyond the strict large width limit, we present closed-form expressions for higher-order terms governing wide network training, and test these predictions empirically.
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<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 new tool based on Feynman diagrams to analyze wide networks (e.g., feed-forward networks with one or more large hidden layers or CNNs with a large number of filters). The main contributions of the paper are: - a new method (using Feynman diagrams) to bound the asymptotic behavior of correlation functions (ensemble averages of the network functions and its derivatives). The method is presented as a conjecture. - tighter bounds for gradient flow of wide networks - an extended analysis of SGD for wide networks - a formalism for deriving finite-width corrections The study of (infinitely) wide networks has been active over the last few years. A better understanding of wide networks could, amongst other things, shed light on recent empirical results related to over-parametrized networks. As such, improving our theoretical understanding of wide networks and especially properties of finite-width networks, which is what this paper explores, seems significant and potentially very impactful.
assistant
This paper proposes a new tool based on Feynman diagrams to analyze wide networks (e.g., feed-forward networks with one or more large hidden layers or CNNs with a large number of filters). The main contributions of the paper are: - a new method (using Feynman diagrams) to bound the asymptotic behavior of correlation functions (ensemble averages of the network functions and its derivatives). The method is presented as a conjecture. - tighter bounds for gradient flow of wide networks - an extended analysis of SGD for wide networks - a formalism for deriving finite-width corrections The study of (infinitely) wide networks has been active over the last few years. A better understanding of wide networks could, amongst other things, shed light on recent empirical results related to over-parametrized networks. As such, improving our theoretical understanding of wide networks and especially properties of finite-width networks, which is what this paper explores, seems significant and potentially very impactful.