Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks
The point estimates of ReLU classification networks, arguably the most widely used neural network architecture, have recently been shown to have arbitrarily high confidence far away from the training data. This architecture is thus not robust, e.g., against out-of-distribution data. Approximate Bayesian posteriors on the weight space have been empirically demonstrated to improve predictive uncertainty in deep learning. The theoretical analysis of such Bayesian approximations is limited, including for ReLU classification networks. We present an analysis of approximate Gaussian posterior distributions on the weights of ReLU networks. We show that even a simplistic (thus cheap), non-Bayesian Gaussian distribution fixes the asymptotic overconfidence issue. Furthermore, when a Bayesian method, even if a simple one, is employed to obtain the Gaussian, the confidence becomes better calibrated. This theoretical result motivates a range of Laplace approximations along a fidelity-cost trade-off. We validate these findings empirically via experiments using common deep ReLU networks.
The paper presents the argument that ReLU networks do not have accurate estimates of confidence in areas that are far from the training data. They suggest explicitly estimating the Covariance of the final layer of a network as a way to more accurately estimate the confidence. They provide theoretical results that bound the logit predictions and use this to choose their covariance matrix. The clarity of the paper is not great. They do not discuss the relevance of many of their theoretical results and instead present them in a large list. The experiments are limited, but the results are promising, particularly Figure 3. Overall the paper feels like it has a lot of content without a lot of substance. This may be because they spent a lot of time listing all their theorems, but not as much motivating why these theoretical results add novelty and are important. Many of their theoretical results are rather obvious (and use well-studied techniques), but they have not been presented explicitly for neural networks.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks
The point estimates of ReLU classification networks, arguably the most widely used neural network architecture, have recently been shown to have arbitrarily high confidence far away from the training data. This architecture is thus not robust, e.g., against out-of-distribution data. Approximate Bayesian posteriors on the weight space have been empirically demonstrated to improve predictive uncertainty in deep learning. The theoretical analysis of such Bayesian approximations is limited, including for ReLU classification networks. We present an analysis of approximate Gaussian posterior distributions on the weights of ReLU networks. We show that even a simplistic (thus cheap), non-Bayesian Gaussian distribution fixes the asymptotic overconfidence issue. Furthermore, when a Bayesian method, even if a simple one, is employed to obtain the Gaussian, the confidence becomes better calibrated. This theoretical result motivates a range of Laplace approximations along a fidelity-cost trade-off. We validate these findings empirically via experiments using common deep ReLU 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>



The paper presents the argument that ReLU networks do not have accurate estimates of confidence in areas that are far from the training data. They suggest explicitly estimating the Covariance of the final layer of a network as a way to more accurately estimate the confidence. They provide theoretical results that bound the logit predictions and use this to choose their covariance matrix. The clarity of the paper is not great. They do not discuss the relevance of many of their theoretical results and instead present them in a large list. The experiments are limited, but the results are promising, particularly Figure 3. Overall the paper feels like it has a lot of content without a lot of substance. This may be because they spent a lot of time listing all their theorems, but not as much motivating why these theoretical results add novelty and are important. Many of their theoretical results are rather obvious (and use well-studied techniques), but they have not been presented explicitly for neural networks.
assistant
The paper presents the argument that ReLU networks do not have accurate estimates of confidence in areas that are far from the training data. They suggest explicitly estimating the Covariance of the final layer of a network as a way to more accurately estimate the confidence. They provide theoretical results that bound the logit predictions and use this to choose their covariance matrix. The clarity of the paper is not great. They do not discuss the relevance of many of their theoretical results and instead present them in a large list. The experiments are limited, but the results are promising, particularly Figure 3. Overall the paper feels like it has a lot of content without a lot of substance. This may be because they spent a lot of time listing all their theorems, but not as much motivating why these theoretical results add novelty and are important. Many of their theoretical results are rather obvious (and use well-studied techniques), but they have not been presented explicitly for neural networks.