L-SR1: A Second Order Optimization Method for Deep Learning
We describe L-SR1, a new second order method to train deep neural networks. Second order methods hold great promise for distributed training of deep networks. Unfortunately, they have not proven practical. Two significant barriers to their success are inappropriate handling of saddle points, and poor conditioning of the Hessian. L-SR1 is a practical second order method that addresses these concerns. We provide experimental results showing that L-SR1 performs at least as well as Nesterov*s Accelerated Gradient Descent, on the MNIST and CIFAR10 datasets. For the CIFAR10 dataset, we see competitive performance on shallow networks like LeNet5, as well as on deeper networks like residual networks. Furthermore, we perform an experimental analysis of L-SR1 with respect to its hyper-parameters to gain greater intuition. Finally, we outline the potential usefulness of L-SR1 in distributed training of deep neural networks.
It is an interesting idea to go after saddle points in the optimization with an SR1 update and a good start in experiments, but missing important comparisons to recent 2nd order optimizations such as Adam, other Hessian free methods (Martens 2012), Pearlmutter fast exact multiplication by the Hessian. From the mnist/cifar curves it is not really showing an advantage to AdaDelta/Nag (although this is stated), and much more experimentation is needed to make a claim about mini-batch insensitivity to performance, can you show error rates on a larger scale task?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
L-SR1: A Second Order Optimization Method for Deep Learning
We describe L-SR1, a new second order method to train deep neural networks. Second order methods hold great promise for distributed training of deep networks. Unfortunately, they have not proven practical. Two significant barriers to their success are inappropriate handling of saddle points, and poor conditioning of the Hessian. L-SR1 is a practical second order method that addresses these concerns. We provide experimental results showing that L-SR1 performs at least as well as Nesterov*s Accelerated Gradient Descent, on the MNIST and CIFAR10 datasets. For the CIFAR10 dataset, we see competitive performance on shallow networks like LeNet5, as well as on deeper networks like residual networks. Furthermore, we perform an experimental analysis of L-SR1 with respect to its hyper-parameters to gain greater intuition. Finally, we outline the potential usefulness of L-SR1 in distributed training of deep 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>



It is an interesting idea to go after saddle points in the optimization with an SR1 update and a good start in experiments, but missing important comparisons to recent 2nd order optimizations such as Adam, other Hessian free methods (Martens 2012), Pearlmutter fast exact multiplication by the Hessian. From the mnist/cifar curves it is not really showing an advantage to AdaDelta/Nag (although this is stated), and much more experimentation is needed to make a claim about mini-batch insensitivity to performance, can you show error rates on a larger scale task?
assistant
It is an interesting idea to go after saddle points in the optimization with an SR1 update and a good start in experiments, but missing important comparisons to recent 2nd order optimizations such as Adam, other Hessian free methods (Martens 2012), Pearlmutter fast exact multiplication by the Hessian. From the mnist/cifar curves it is not really showing an advantage to AdaDelta/Nag (although this is stated), and much more experimentation is needed to make a claim about mini-batch insensitivity to performance, can you show error rates on a larger scale task?