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.

In this paper, we present a layer-wise learning of stochastic neural networks (SNNs) in an information-theoretic perspective. In each layer of an SNN, the compression and the relevance are defined to quantify the amount of information that the layer contains about the input space and the target space, respectively. We jointly optimize the compression and the relevance of all parameters in an SNN to better exploit the neural network's representation. Previously, the Information Bottleneck (IB) framework (\cite{Tishby99}) extracts relevant information for a target variable. Here, we propose Parametric Information Bottleneck (PIB) for a neural network by utilizing (only) its model parameters explicitly to approximate the compression and the relevance. We show that, as compared to the maximum likelihood estimate (MLE) principle, PIBs : (i) improve the generalization of neural networks in classification tasks, (ii) push the representation of neural networks closer to the optimal information-theoretical representation in a faster manner.
Learning a better neural networks' representation with Information Bottleneck principle

Metric embeddings are immensely useful representations of associations between entities (images, users, search queries, words, and more). Embeddings are learned by optimizing a loss objective of the general form of a sum over example associations. Typically, the optimization uses stochastic gradient updates over minibatches of examples that are arranged independently at random. In this work, we propose the use of {\em structured arrangements} through randomized {\em microbatches} of examples that are more likely to include similar ones. We make a principled argument for the properties of our arrangements that accelerate the training and present efficient algorithms to generate microbatches that respect the marginal distribution of training examples. Finally, we observe experimentally that our structured arrangements accelerate training by 3-20\%. Structured arrangements emerge as a powerful and novel performance knob for SGD that is independent and complementary to other SGD hyperparameters and thus is a candidate for wide deployment.
Accelerating SGD by arranging examples differently

L1 and L2 regularizers are critical tools in machine learning due to their ability to simplify solutions. However, imposing strong L1 or L2 regularization with gradient descent method easily fails, and this limits the generalization ability of the underlying neural networks. To understand this phenomenon, we investigate how and why training fails for strong regularization. Specifically, we examine how gradients change over time for different regularization strengths and provide an analysis why the gradients diminish so fast. We find that there exists a tolerance level of regularization strength, where the learning completely fails if the regularization strength goes beyond it. We propose a simple but novel method, Delayed Strong Regularization, in order to moderate the tolerance level. Experiment results show that our proposed approach indeed achieves strong regularization for both L1 and L2 regularizers and improves both accuracy and sparsity on public data sets. Our source code is published.
We investigate how and why strong L1/L2 regularization fails and propose a method than can achieve strong regularization.