In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: Finding inclusion-minimal hitting sets for a given collection of sets is a fundamental combinatorial problem with applications in domains as diverse as Boolean algebra, computational biology, and data mining. Much of the algorithmic literature focuses on the problem of recognizing the collection of minimal hitting sets; however, in many of the applications, it is more important to generate these hitting sets. We survey twenty algorithms from across a variety of domains, considering their history, classification, useful features, and computational performance on a variety of synthetic and real-world inputs. We also provide a suite of implementations of these algorithms with a ready-to-use, platform-agnostic interface based on Docker containers and the AlgoRun framework, so that interested computational scientists can easily perform similar tests with inputs from their own research areas on their own computers or through a convenient Web interface.

A: The minimal hitting set generation problem: algorithms and computation
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Q: An emerging way to deal with highdimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work aims to elevate the notion of joint harmonic analysis to a full-fledged framework denoted as Time-Vertex Signal Processing, that links together the time-domain signal processing techniques with the new tools of graph signal processing. This entails three main contributions: (a) We provide a formal motivation for harmonic time-vertex analysis as an analysis tool for the state evolution of simple Partial Differential Equations on graphs. (b) We improve the accuracy of joint filtering operators by up-to two orders of magnitude. (c) Using our joint filters, we construct time-vertex dictionaries analyzing the different scales and the local time-frequency content of a signal. The utility of our tools is illustrated in numerous applications and datasets, such as dynamic mesh denoising and classification, still-video inpainting, and source localization in seismic events. Our results suggest that joint analysis of time-vertex signals can bring benefits to regression and learning.

A: A Time-Vertex Signal Processing Framework Scalable processing and meaningful representations for time-series on graphs
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Q: The significant computational costs of deploying neural networks in large-scale or resource constrained environments, such as data centers and mobile devices, has spurred interest in model compression, which can achieve a reduction in both arithmetic operations and storage memory. Several techniques have been proposed for reducing or compressing the parameters for feed-forward and convolutional neural networks, but less is understood about the effect of parameter compression on recurrent neural networks (RNN). In particular, the extent to which the recurrent parameters can be compressed and the impact on short-term memory performance, is not well understood. In this paper, we study the effect of complexity reduction, through singular value decomposition rank reduction, on RNN and minimal gated recurrent unit (MGRU) networks for several tasks. We show that considerable rank reduction is possible when compressing recurrent weights, even without fine tuning. Furthermore, we propose a perturbation model for the effect of general perturbations, such as a compression, on the recurrent parameters of RNNs. The model is tested against a noiseless memorization experiment that elucidates the short-term memory performance. In this way, we demonstrate that the effect of compression of recurrent parameters is dependent on the degree of temporal coherence present in the data and task. This work can guide on-the-fly RNN compression for novel environments or tasks, and provides insight for applying RNN compression in low-power devices, such as hearing aids. Keywords—compression; recurrent neural networks; complexity reduction; SVD; RNN; MGRU; MRU

A:
Parameter Compression of Recurrent Neural Networks and Degredation of Short-term Memory
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