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.

Deep neural networks have led to a series of breakthroughs, dramatically improving the state-of-the-art in many domains. The techniques driving these advances, however, lack a formal method to account for model uncertainty. While the Bayesian approach to learning provides a solid theoretical framework to handle uncertainty, inference in Bayesian-inspired deep neural networks is difficult. In this paper, we provide a practical approach to Bayesian learning that relies on a regularization technique found in nearly every modern network, batch normalization. We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty. Using our approach, it is possible to make meaningful uncertainty estimates using conventional architectures without modifying the network or the training procedure. Our approach is thoroughly validated in a series of empirical experiments on different tasks and using various measures, showing it to outperform baselines on a majority of datasets with strong statistical significance.
We show that training a deep network using batch normalization is equivalent to approximate inference in Bayesian models, and we demonstrate how this finding allows us to make useful estimates of the model uncertainty in conventional networks.

Empirical risk minimization (ERM), with proper loss function and regularization, is the common practice of supervised classification. In this paper, we study training arbitrary (from linear to deep) binary classifier from only unlabeled (U) data by ERM. We prove that it is impossible to estimate the risk of an arbitrary binary classifier in an unbiased manner given a single set of U data, but it becomes possible given two sets of U data with different class priors. These two facts answer a fundamental question---what the minimal supervision is for training any binary classifier from only U data. Following these findings, we propose an ERM-based learning method from two sets of U data, and then prove it is consistent. Experiments demonstrate the proposed method could train deep models and outperform state-of-the-art methods for learning from two sets of U data.
Three class priors are all you need to train deep models from only U data, while any two should not be enough.

We explore the role of multiplicative interaction as a unifying framework to describe a range of classical and modern neural network architectural motifs, such as gating, attention layers, hypernetworks, and dynamic convolutions amongst others.
 Multiplicative interaction layers as primitive operations have a long-established presence in the literature, though this often not emphasized and thus under-appreciated. We begin by showing that such layers strictly enrich the representable function classes of neural networks. We conjecture that multiplicative interactions offer a particularly powerful inductive bias when fusing multiple streams of information or when conditional computation is required. We therefore argue that they should be considered in many situation where multiple compute or information paths need to be combined, in place of the simple and oft-used concatenation operation. Finally, we back up our claims and demonstrate the potential of multiplicative interactions by applying them in large-scale complex RL and sequence modelling tasks, where their use allows us to deliver state-of-the-art results, and thereby provides new evidence in support of multiplicative interactions playing a more prominent role when designing new neural network architectures.

We explore the role of multiplicative interaction as a unifying framework to describe a range of classical and modern neural network architectural motifs, such as gating, attention layers, hypernetworks, and dynamic convolutions amongst others.