Variance Networks: When Expectation Does Not Meet Your Expectations
Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through test-time averaging. In this paper, we introduce variance layers, a different kind of stochastic layers. Each weight of a variance layer follows a zero-mean distribution and is only parameterized by its variance. It means that each object is represented by a zero-mean distribution in the space of the activations. We show that such layers can learn surprisingly well, can serve as an efficient exploration tool in reinforcement learning tasks and provide a decent defense against adversarial attacks. We also show that a number of conventional Bayesian neural networks naturally converge to such zero-mean posteriors. We observe that in these cases such zero-mean parameterization leads to a much better training objective than more flexible conventional parameterizations where the mean is being learned.
 This paper introduced a new stochastic layer termed variance layer for Bayesian deep learning, where the posterior on weight is a zero-mean symmetric distribution (e.g., Gaussian, Bernoulli, Uniform). The paper showed that under 3 different prior distributions, the Gaussian Dropout layer can converge to variance layer. Experiments verified that it can achieve similar accuracies as conventional binary dropout in image classification and reinforcement learning tasks, is more robust to adversarial attacks, and can be used to sparsify deep models. Pros: (1) Proposed a new type of stochastic layer (variance layer) (2) Competitive performance on a variety of tasks: image classification, robustness to adversarial attacks, reinforcement learning, model compression (3) Theoretically grounded algorithm Cons: (1) My main concern is verification. Most of the comparisons are between variance layer (zero-mean) and conventional binary dropout, while the main argument of the paper is that it’s better to set Gaussian posterior’s mean to zero. So in all the experiments the paper should compare zero-mean variance layer against variational dropout (neuron-wise Eq. 14) and sparse variational dropout (additive Eq. 14), where the mean isn’t zero. (2) The paper applies variance layers to some specific layers. Are there any guidelines to select which layers should be variance layers? Some minor issues: (1) Page 4, equations of Gaussian/Bernoulli/Uniform variance layer, they should be w_ij=…, instead of q(w_ij)= … (2) What’s the prior distribution used in the experiment of Table 1?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Variance Networks: When Expectation Does Not Meet Your Expectations
Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through test-time averaging. In this paper, we introduce variance layers, a different kind of stochastic layers. Each weight of a variance layer follows a zero-mean distribution and is only parameterized by its variance. It means that each object is represented by a zero-mean distribution in the space of the activations. We show that such layers can learn surprisingly well, can serve as an efficient exploration tool in reinforcement learning tasks and provide a decent defense against adversarial attacks. We also show that a number of conventional Bayesian neural networks naturally converge to such zero-mean posteriors. We observe that in these cases such zero-mean parameterization leads to a much better training objective than more flexible conventional parameterizations where the mean is being learned.
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 introduced a new stochastic layer termed variance layer for Bayesian deep learning, where the posterior on weight is a zero-mean symmetric distribution (e.g., Gaussian, Bernoulli, Uniform). The paper showed that under 3 different prior distributions, the Gaussian Dropout layer can converge to variance layer. Experiments verified that it can achieve similar accuracies as conventional binary dropout in image classification and reinforcement learning tasks, is more robust to adversarial attacks, and can be used to sparsify deep models. Pros: (1) Proposed a new type of stochastic layer (variance layer) (2) Competitive performance on a variety of tasks: image classification, robustness to adversarial attacks, reinforcement learning, model compression (3) Theoretically grounded algorithm Cons: (1) My main concern is verification. Most of the comparisons are between variance layer (zero-mean) and conventional binary dropout, while the main argument of the paper is that it’s better to set Gaussian posterior’s mean to zero. So in all the experiments the paper should compare zero-mean variance layer against variational dropout (neuron-wise Eq. 14) and sparse variational dropout (additive Eq. 14), where the mean isn’t zero. (2) The paper applies variance layers to some specific layers. Are there any guidelines to select which layers should be variance layers? Some minor issues: (1) Page 4, equations of Gaussian/Bernoulli/Uniform variance layer, they should be w_ij=…, instead of q(w_ij)= … (2) What’s the prior distribution used in the experiment of Table 1?
assistant
 This paper introduced a new stochastic layer termed variance layer for Bayesian deep learning, where the posterior on weight is a zero-mean symmetric distribution (e.g., Gaussian, Bernoulli, Uniform). The paper showed that under 3 different prior distributions, the Gaussian Dropout layer can converge to variance layer. Experiments verified that it can achieve similar accuracies as conventional binary dropout in image classification and reinforcement learning tasks, is more robust to adversarial attacks, and can be used to sparsify deep models. Pros: (1) Proposed a new type of stochastic layer (variance layer) (2) Competitive performance on a variety of tasks: image classification, robustness to adversarial attacks, reinforcement learning, model compression (3) Theoretically grounded algorithm Cons: (1) My main concern is verification. Most of the comparisons are between variance layer (zero-mean) and conventional binary dropout, while the main argument of the paper is that it’s better to set Gaussian posterior’s mean to zero. So in all the experiments the paper should compare zero-mean variance layer against variational dropout (neuron-wise Eq. 14) and sparse variational dropout (additive Eq. 14), where the mean isn’t zero. (2) The paper applies variance layers to some specific layers. Are there any guidelines to select which layers should be variance layers? Some minor issues: (1) Page 4, equations of Gaussian/Bernoulli/Uniform variance layer, they should be w_ij=…, instead of q(w_ij)= … (2) What’s the prior distribution used in the experiment of Table 1?