Where is the Information in a Deep Network?
Whatever information a deep neural network has gleaned from past data is encoded in its weights. How this information affects the response of the network to future data is largely an open question. In fact, even how to define and measure information in a network entails some subtleties. We measure information in the weights of a deep neural network as the optimal trade-off between accuracy of the network and complexity of the weights relative to a prior. Depending on the prior, the definition reduces to known information measures such as Shannon Mutual Information and Fisher Information, but in general it affords added flexibility that enables us to relate it to generalization, via the PAC-Bayes bound, and to invariance. For the latter, we introduce a notion of effective information in the activations, which are deterministic functions of future inputs. We relate this to the Information in the Weights, and use this result to show that models of low (information) complexity not only generalize better, but are bound to learn invariant representations of future inputs. These relations hinge not only on the architecture of the model, but also on how it is trained.
This paper presents a theoretical account of information encoded within deep neural networks subject to information theoretic measures. In contrast to other efforts that examine information encoded in weights, this work emphasizes the effective information in the activations. This characterization is further related to information in the weights, and a theoretical justification is made for what this means with respect to properties of generalization and invariance in the network. The notion of attaching the weights that represent the training set to the activations that accord with the test set in a theoretical framework is interesting. In practice, I would have liked to see a bit more attachment of the theoretical formalisms to the empirical justification that follows the references. This, however, is a matter of personal bias as I don*t typically produce papers that are principally theoretical contributions in my own work. Overall, the content of the paper seems sound and the theoretical and empirical justifications seem well founded but I also can*t claim to be an expert in this area.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Where is the Information in a Deep Network?
Whatever information a deep neural network has gleaned from past data is encoded in its weights. How this information affects the response of the network to future data is largely an open question. In fact, even how to define and measure information in a network entails some subtleties. We measure information in the weights of a deep neural network as the optimal trade-off between accuracy of the network and complexity of the weights relative to a prior. Depending on the prior, the definition reduces to known information measures such as Shannon Mutual Information and Fisher Information, but in general it affords added flexibility that enables us to relate it to generalization, via the PAC-Bayes bound, and to invariance. For the latter, we introduce a notion of effective information in the activations, which are deterministic functions of future inputs. We relate this to the Information in the Weights, and use this result to show that models of low (information) complexity not only generalize better, but are bound to learn invariant representations of future inputs. These relations hinge not only on the architecture of the model, but also on how it is trained.
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 presents a theoretical account of information encoded within deep neural networks subject to information theoretic measures. In contrast to other efforts that examine information encoded in weights, this work emphasizes the effective information in the activations. This characterization is further related to information in the weights, and a theoretical justification is made for what this means with respect to properties of generalization and invariance in the network. The notion of attaching the weights that represent the training set to the activations that accord with the test set in a theoretical framework is interesting. In practice, I would have liked to see a bit more attachment of the theoretical formalisms to the empirical justification that follows the references. This, however, is a matter of personal bias as I don*t typically produce papers that are principally theoretical contributions in my own work. Overall, the content of the paper seems sound and the theoretical and empirical justifications seem well founded but I also can*t claim to be an expert in this area.
assistant
This paper presents a theoretical account of information encoded within deep neural networks subject to information theoretic measures. In contrast to other efforts that examine information encoded in weights, this work emphasizes the effective information in the activations. This characterization is further related to information in the weights, and a theoretical justification is made for what this means with respect to properties of generalization and invariance in the network. The notion of attaching the weights that represent the training set to the activations that accord with the test set in a theoretical framework is interesting. In practice, I would have liked to see a bit more attachment of the theoretical formalisms to the empirical justification that follows the references. This, however, is a matter of personal bias as I don*t typically produce papers that are principally theoretical contributions in my own work. Overall, the content of the paper seems sound and the theoretical and empirical justifications seem well founded but I also can*t claim to be an expert in this area.