In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
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Question: 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.

Answer: It is possible to learn a zero-centered Gaussian distribution over the weights of a neural network by learning only variances, and it works surprisingly well.


Question: The linear transformations in converged deep networks show fast eigenvalue decay. The distribution of eigenvalues looks like a Heavy-tail distribution, where the vast majority of eigenvalues is small, but not actually zero, and only a few spikes of large eigenvalues exist.
 We use a stochastic approximator to generate histograms of eigenvalues. This allows us to investigate layers with hundreds of thousands of dimensions. We show how the distributions change over the course of image net training, converging to a similar heavy-tail spectrum across all intermediate layers.

Answer: We investigate the eigenvalues of the linear layers in deep networks and show that the distributions develop heavy-tail behavior during training.


Question: We introduce CGNN, a framework to learn functional causal models as generative neural networks. These networks are trained using backpropagation to minimize the maximum mean discrepancy to the observed data. Unlike previous approaches, CGNN leverages both conditional independences and distributional asymmetries to seamlessly discover bivariate and multivariate 
 causal structures, with or without hidden variables. CGNN does not only estimate the causal structure, but a full and differentiable generative model of the data. Throughout an extensive variety of experiments, we illustrate the competitive  esults of CGNN w.r.t state-of-the-art alternatives in observational causal discovery on both simulated and real data, in the tasks of cause-effect inference, v-structure identification, and multivariate causal discovery.

Answer:
Discover the structure of functional causal models with generative neural networks