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.

Q: Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally efficient. With wide recognition of potential advantages, why is it that variational Bayes has seen very limited practical use for BNNs in real applications? We argue that variational inference in neural networks is fragile: successful implementations require careful initialization and tuning of prior variances, as well as controlling the variance of Monte Carlo gradient estimates. We provide two innovations that aim to turn VB into a robust inference tool for Bayesian neural networks: first, we introduce a novel deterministic method to approximate moments in neural networks, eliminating gradient variance; second, we introduce a hierarchical prior for parameters and a novel Empirical Bayes procedure for automatically selecting prior variances. Combining these two innovations, the resulting method is highly efficient and robust. On the application of heteroscedastic regression we demonstrate good predictive performance over alternative approaches.

A: A method for eliminating gradient variance and automatically tuning priors for effective training of bayesian neural networks
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Q: Hierarchical label structures widely exist in many machine learning tasks, ranging from those with explicit label hierarchies such as image classification to the ones that have latent label hierarchies such as semantic segmentation. Unfortunately, state-of-the-art methods often utilize cross-entropy loss which in-explicitly assumes the independence among class labels. Motivated by the fact that class members from the same hierarchy need to be similar to each others, we design a new training diagram called Hierarchical Complement Objective Training (HCOT). In HCOT, in addition to maximizing the probability of the ground truth class, we also neutralize the probabilities of rest of the classes in a hierarchical fashion, making the model take advantage of the label hierarchy explicitly. We conduct our method on both image classification and semantic segmentation. Results show that HCOT outperforms state-of-the-art models in CIFAR100, Imagenet, and PASCAL-context. Our experiments also demonstrate that HCOT can be applied on tasks with latent label hierarchies, which is a common characteristic in many machine learning tasks.

A: We propose Hierarchical Complement Objective Training, a novel training paradigm to effectively leverage category hierarchy in the labeling space on both image classification and semantic segmentation.
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Q: There has recently been a heated debate (e.g. Schwartz-Ziv & Tishby (2017), Saxe et al. (2018), Noshad et al. (2018), Goldfeld et al. (2018)) about measuring the information flow in Deep Neural Networks using techniques from information theory. It is claimed that Deep Neural Networks in general have good generalization capabilities since they not only learn how to map from an input to an output but also how to compress information about the training data input (Schwartz-Ziv & Tishby, 2017). That is, they abstract the input information and strip down any unnecessary or over-specific information. If so, the message compression method, Information Bottleneck (IB), could be used as a natural comparator for network performance, since this method gives an optimal information compression boundary. This claim was then later denounced as well as reaffirmed (e.g.  Saxe et al. (2018), Achille et al. (2017), Noshad et al. (2018)), as the employed method of mutual information measuring is not actually measuring information but clustering of the internal layer representations (Goldfeld et al. (2018)). In this paper, we will present a detailed explanation of the development in the Information Plain (IP), which is a plot-type that compares mutual information to judge compression (Schwartz-Ziv & Tishby (2017)), when noise is retroactively added (using binning estimation).   We also explain why different activation functions show different trajectories on the IP. Further, we have looked into the effect of clustering on the network loss through early and perfect stopping using the Information Plane and how clustering can be used to help network pruning.

A:
We give a detailed explanation of the trajectories in the information plane and investigate its usage for neural network design (pruning)
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