Kronecker-factored Curvature Approximations for Recurrent Neural Networks
Kronecker-factor Approximate Curvature (Martens & Grosse, 2015) (K-FAC) is a 2nd-order optimization method which has been shown to give state-of-the-art performance on large-scale neural network optimization tasks (Ba et al., 2017). It is based on an approximation to the Fisher information matrix (FIM) that makes assumptions about the particular structure of the network and the way it is parameterized. The original K-FAC method was applicable only to fully-connected networks, although it has been recently extended by Grosse & Martens (2016) to handle convolutional networks as well. In this work we extend the method to handle RNNs by introducing a novel approximation to the FIM for RNNs. This approximation works by modelling the covariance structure between the gradient contributions at different time-steps using a chain-structured linear Gaussian graphical model, summing the various cross-covariances, and computing the inverse in closed form. We demonstrate in experiments that our method significantly outperforms general purpose state-of-the-art optimizers like SGD with momentum and Adam on several challenging RNN training tasks.
 In this paper, the authors present a second-order method that is specifically designed for RNNs. The paper overall is well-written and I enjoyed reading the paper. The main idea of the paper is to extend the existing kronecker-factored algorithms to RNNs. In order to obtain a tractable formulation, the authors impose certain assumptions and provide detailed derivations. Even though the gain in the convergence speed is not very impressive and the algorithm is quite complicated and possibly not very accessible by deep learning practitioners, I still believe this is a novel and valuable contribution and will be of interest to the community. I only have some minor corrections: 1) Sec 2.1: typo "is is" 2) Sec 2.2: typo "esstentiallybe" 3) Sec 2.2: (F+lambda I) --> should be inverse 4) The authors should include a proper conclusion
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Kronecker-factored Curvature Approximations for Recurrent Neural Networks
Kronecker-factor Approximate Curvature (Martens & Grosse, 2015) (K-FAC) is a 2nd-order optimization method which has been shown to give state-of-the-art performance on large-scale neural network optimization tasks (Ba et al., 2017). It is based on an approximation to the Fisher information matrix (FIM) that makes assumptions about the particular structure of the network and the way it is parameterized. The original K-FAC method was applicable only to fully-connected networks, although it has been recently extended by Grosse & Martens (2016) to handle convolutional networks as well. In this work we extend the method to handle RNNs by introducing a novel approximation to the FIM for RNNs. This approximation works by modelling the covariance structure between the gradient contributions at different time-steps using a chain-structured linear Gaussian graphical model, summing the various cross-covariances, and computing the inverse in closed form. We demonstrate in experiments that our method significantly outperforms general purpose state-of-the-art optimizers like SGD with momentum and Adam on several challenging RNN training tasks.
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>



 In this paper, the authors present a second-order method that is specifically designed for RNNs. The paper overall is well-written and I enjoyed reading the paper. The main idea of the paper is to extend the existing kronecker-factored algorithms to RNNs. In order to obtain a tractable formulation, the authors impose certain assumptions and provide detailed derivations. Even though the gain in the convergence speed is not very impressive and the algorithm is quite complicated and possibly not very accessible by deep learning practitioners, I still believe this is a novel and valuable contribution and will be of interest to the community. I only have some minor corrections: 1) Sec 2.1: typo "is is" 2) Sec 2.2: typo "esstentiallybe" 3) Sec 2.2: (F+lambda I) --> should be inverse 4) The authors should include a proper conclusion
assistant
 In this paper, the authors present a second-order method that is specifically designed for RNNs. The paper overall is well-written and I enjoyed reading the paper. The main idea of the paper is to extend the existing kronecker-factored algorithms to RNNs. In order to obtain a tractable formulation, the authors impose certain assumptions and provide detailed derivations. Even though the gain in the convergence speed is not very impressive and the algorithm is quite complicated and possibly not very accessible by deep learning practitioners, I still believe this is a novel and valuable contribution and will be of interest to the community. I only have some minor corrections: 1) Sec 2.1: typo "is is" 2) Sec 2.2: typo "esstentiallybe" 3) Sec 2.2: (F+lambda I) --> should be inverse 4) The authors should include a proper conclusion