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.

Ex Input:
Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lowerand upper-bounds showing that the sample complexity scales with the representation dimension when no assumptions are made about the underlying data distribution. However, by leveraging the structure of the data distribution, we show that one can achieve rates that are fine-tuned to a specific notion of intrinsic complexity for a given dataset. Our analysis reveals that augmenting the metric learning optimization criterion with a simple norm-based regularization can help adapt to a dataset’s intrinsic complexity, yielding better generalization. Experiments on benchmark datasets validate our analysis and show that regularizing the metric can help discern the signal even when the data contains high amounts of noise.

Ex Output:
Sample Complexity of Learning Mahalanobis Distance Metrics


Ex Input:
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

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


Ex Input:
In Pawlak’s rough set theory, a set is approximated by a pair of lower and upper approximations. To measure numerically the roughness of an approximation, Pawlak introduced a quantitative measure of roughness by using the ratio of the cardinalities of the lower and upper approximations. Although the roughness measure is effective, it has the drawback of not being strictly monotonic with respect to the standard ordering on partitions. Recently, some improvements have been made by taking into account the granularity of partitions. In this paper, we approach the roughness measure in an axiomatic way. After axiomatically defining roughness measure and partition measure, we provide a unified construction of roughness measure, called strong Pawlak roughness measure, and then explore the properties of this measure. We show that the improved roughness measures in the literature are special instances of our strong Pawlak roughness measure and introduce three more strong Pawlak roughness measures as well. The advantage of our axiomatic approach is that some properties of a roughness measure follow immediately as soon as the measure satisfies the relevant axiomatic definition.

Ex Output:

An axiomatic approach to the roughness measure of rough sets