Metric (mathematics)

About: Metric (mathematics) is a research topic. Over the lifetime, 42617 publications have been published within this topic receiving 836571 citations. The topic is also known as: distance function & metric.

Some Recent Results in Metric Temporal Logic

Abstract: Metric Temporal Logic ( MTL ) is a widely-studied real-time extension of Linear Temporal Logic. In this paper we survey results about the complexity of the satisfiability and model checking problems for fragments of MTL with respect to different semantic models. We show that these fragments have widely differing complexities: from polynomial space to non-primitive recursive and even undecidable. However we show that the most commonly occurring real-time properties, such as invariance and bounded response, can be expressed in fragments of MTL for which model checking, if not satisfiability, can be decided in polynomial or exponential space.

Distribution Consistency Based Covariance Metric Networks for Few-Shot Learning

Abstract: Few-shot learning aims to recognize new concepts from very few examples. However, most of the existing few-shot learning methods mainly concentrate on the first-order statistic of concept representation or a fixed metric on the relation between a sample and a concept. In this work, we propose a novel end-to-end deep architecture, named Covariance Metric Networks (CovaMNet). The CovaMNet is designed to exploit both the covariance representation and covariance metric based on the distribution consistency for the few-shot classification tasks. Specifically, we construct an embedded local covariance representation to extract the second-order statistic information of each concept and describe the underlying distribution of this concept. Upon the covariance representation, we further define a new deep covariance metric to measure the consistency of distributions between query samples and new concepts. Furthermore, we employ the episodic training mechanism to train the entire network in an end-to-end manner from scratch. Extensive experiments in two tasks, generic few-shot image classification and fine-grained fewshot image classification, demonstrate the superiority of the proposed CovaMNet. The source code can be available from https://github.com/WenbinLee/CovaMNet.git.

A generative modeling approach for benchmarking and training shallow quantum circuits

Abstract: Hybrid quantum-classical algorithms provide ways to use noisy intermediate-scale quantum computers for practical applications. Expanding the portfolio of such techniques, we propose a quantum circuit learning algorithm that can be used to assist the characterization of quantum devices and to train shallow circuits for generative tasks. The procedure leverages quantum hardware capabilities to its fullest extent by using native gates and their qubit connectivity. We demonstrate that our approach can learn an optimal preparation of the Greenberger-Horne-Zeilinger states, also known as “cat states”. We further demonstrate that our approach can efficiently prepare approximate representations of coherent thermal states, wave functions that encode Boltzmann probabilities in their amplitudes. Finally, complementing proposals to characterize the power or usefulness of near-term quantum devices, such as IBM’s quantum volume, we provide a new hardware-independent metric called the qBAS score. It is based on the performance yield in a specific sampling task on one of the canonical machine learning data sets known as Bars and Stripes. We show how entanglement is a key ingredient in encoding the patterns of this data set; an ideal benchmark for testing hardware starting at four qubits and up. We provide experimental results and evaluation of this metric to probe the trade off between several architectural circuit designs and circuit depths on an ion-trap quantum computer.

Musicians and the metric structure of words

Abstract: The present study aimed to examine the influence of musical expertise on the metric and semantic aspects of speech processing. In two attentional conditions (metric and semantic tasks), musicians listened to short sentences ending in trisyllabic words that were semantically and/or metrically congruous or incongruous. Both ERPs and behavioral data were analyzed and the results were compared to previous nonmusicians' data. Regarding the processing of meter, results showed that musical expertise influenced the automatic detection of the syllable temporal structure (P200 effect), the integration of metric structure and its influence on word comprehension (N400 effect), as well as the reanalysis of metric violations (P600 and late positivities effects). By contrast, results showed that musical expertise did not influence the semantic level of processing. These results are discussed in terms of transfer of training effects from music to speech processing.