Spontaneous Symmetry Breaking in Deep Neural Networks
We propose a framework to understand the unprecedented performance and robustness of deep neural networks using field theory. Correlations between the weights within the same layer can be described by symmetries in that layer, and networks generalize better if such symmetries are broken to reduce the redundancies of the weights. Using a two parameter field theory, we find that the network can break such symmetries itself towards the end of training in a process commonly known in physics as spontaneous symmetry breaking. This corresponds to a network generalizing itself without any user input layers to break the symmetry, but by communication with adjacent layers. In the layer decoupling limit applicable to residual networks (He et al., 2015), we show that the remnant symmetries that survive the non-linear layers are spontaneously broken based on empirical results. The Lagrangian for the non-linear and weight layers together has striking similarities with the one in quantum field theory of a scalar. Using results from quantum field theory we show that our framework is able to explain many experimentally observed phenomena, such as training on random labels with zero error (Zhang et al., 2017), the information bottleneck and the phase transition out of it (Shwartz-Ziv & Tishby, 2017), shattered gradients (Balduzzi et al., 2017), and many more.
 The paper promises quite a few intriguing connections between information bottleneck, phase transitions and deep learning. While we think that this is a worthwhile bridge to build between machine learning and statistical field theory, the exposition of the paper leaves much to be desired. Had it been a clean straightforward application of QFT, as well-trained theoretical physicists, we would have been able to evaluate the paper. Generally, it would help the reader to have an overall map and indication of the steps that would be taken formally. Specifically, starting from Section 2.3, especially around the transition to continuous layers, very little information is provided how one is dealing with the cost function and the results are derived. Section 2.3 would benefit from expanded discussion with examples and detailed explanations. Minor: The following sentence in third paragraph of the Introduction is incomplete: Because the ResNet does not contain such symmetry breaking layers in the architecture.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Spontaneous Symmetry Breaking in Deep Neural Networks
We propose a framework to understand the unprecedented performance and robustness of deep neural networks using field theory. Correlations between the weights within the same layer can be described by symmetries in that layer, and networks generalize better if such symmetries are broken to reduce the redundancies of the weights. Using a two parameter field theory, we find that the network can break such symmetries itself towards the end of training in a process commonly known in physics as spontaneous symmetry breaking. This corresponds to a network generalizing itself without any user input layers to break the symmetry, but by communication with adjacent layers. In the layer decoupling limit applicable to residual networks (He et al., 2015), we show that the remnant symmetries that survive the non-linear layers are spontaneously broken based on empirical results. The Lagrangian for the non-linear and weight layers together has striking similarities with the one in quantum field theory of a scalar. Using results from quantum field theory we show that our framework is able to explain many experimentally observed phenomena, such as training on random labels with zero error (Zhang et al., 2017), the information bottleneck and the phase transition out of it (Shwartz-Ziv & Tishby, 2017), shattered gradients (Balduzzi et al., 2017), and many more.
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 paper promises quite a few intriguing connections between information bottleneck, phase transitions and deep learning. While we think that this is a worthwhile bridge to build between machine learning and statistical field theory, the exposition of the paper leaves much to be desired. Had it been a clean straightforward application of QFT, as well-trained theoretical physicists, we would have been able to evaluate the paper. Generally, it would help the reader to have an overall map and indication of the steps that would be taken formally. Specifically, starting from Section 2.3, especially around the transition to continuous layers, very little information is provided how one is dealing with the cost function and the results are derived. Section 2.3 would benefit from expanded discussion with examples and detailed explanations. Minor: The following sentence in third paragraph of the Introduction is incomplete: Because the ResNet does not contain such symmetry breaking layers in the architecture.
assistant
 The paper promises quite a few intriguing connections between information bottleneck, phase transitions and deep learning. While we think that this is a worthwhile bridge to build between machine learning and statistical field theory, the exposition of the paper leaves much to be desired. Had it been a clean straightforward application of QFT, as well-trained theoretical physicists, we would have been able to evaluate the paper. Generally, it would help the reader to have an overall map and indication of the steps that would be taken formally. Specifically, starting from Section 2.3, especially around the transition to continuous layers, very little information is provided how one is dealing with the cost function and the results are derived. Section 2.3 would benefit from expanded discussion with examples and detailed explanations. Minor: The following sentence in third paragraph of the Introduction is incomplete: Because the ResNet does not contain such symmetry breaking layers in the architecture.