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.

Ex Input:
Graph networks have recently attracted considerable interest, and in particular in the context of semi-supervised learning. These methods typically work by generating node representations that are propagated throughout a given weighted graph.

Here we argue that for semi-supervised learning, it is more natural to consider propagating labels in the graph instead. Towards this end, we propose a differentiable neural version of the classic Label Propagation (LP) algorithm. This formulation can be used for learning edge weights, unlike other methods where weights are set heuristically. Starting from a layer implementing a single iteration of LP, we proceed by adding several important non-linear steps that significantly enhance the label-propagating mechanism.

Experiments in two distinct settings demonstrate the utility of our approach.

Ex Output:
Neural net for graph-based semi-supervised learning; revisits the classics and propagates *labels* rather than feature representations

Ex Input:
Deep generative models can emulate the perceptual properties of complex image datasets, providing a latent representation of the data. However, manipulating such representation to perform meaningful and controllable transformations in the data space remains challenging without some form of supervision. While previous work has focused on exploiting statistical independence to extit{disentangle} latent factors, we argue that such requirement can be advantageously relaxed and propose instead a non-statistical framework that relies on identifying a modular organization of the network, based on counterfactual manipulations. Our experiments support that modularity between groups of channels is achieved to a certain degree on a variety of generative models. This allowed the design of targeted interventions on complex image datasets, opening the way to applications such as computationally efficient style transfer and the automated assessment of robustness to contextual changes in pattern recognition systems.

Ex Output:
We develop a framework to find modular internal representations in generative models and manipulate then to generate counterfactual examples.

Ex Input:
State-of-the-art deep neural networks (DNNs) typically have tens of millions of parameters, which might not fit into the upper levels of the memory hierarchy, thus increasing the inference time and energy consumption significantly, and prohibiting their use on edge devices such as mobile phones. The compression of DNN models has therefore become an active area of research recently, with \emph{connection pruning} emerging as one of the most successful strategies. A very natural approach is to prune connections of DNNs via $\ell_1$ regularization, but recent empirical investigations have suggested that this does not work as well in the context of DNN compression. In this work, we revisit this simple strategy and analyze it rigorously, to show that: (a) any \emph{stationary point} of an $\ell_1$-regularized layerwise-pruning objective has its number of non-zero elements bounded by the number of penalized prediction logits, regardless of the strength of the regularization; (b) successful pruning highly relies on an accurate optimization solver, and there is a trade-off between compression speed and distortion of prediction accuracy, controlled by the strength of regularization. Our theoretical results thus suggest that $\ell_1$ pruning could be successful provided we use an accurate optimization solver. We corroborate this in our experiments, where we show that simple $\ell_1$ regularization with an Adamax-L1(cumulative) solver gives pruning ratio competitive to the state-of-the-art.

Ex Output:
We revisit the simple idea of pruning connections of DNNs through $\ell_1$ regularization achieving state-of-the-art results on multiple datasets with theoretic guarantees.