用于稀疏重建的正竞争网络

IF 2.7 4区 计算机科学 Q3 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Veronica Centorrino;Anand Gokhale;Alexander Davydov;Giovanni Russo;Francesco Bullo
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引用次数: 0

摘要

我们提出并分析了一种连续时间发射率神经网络--正发射率竞争网络(PFCN),用于解决具有非负性约束的稀疏重构问题。这些问题涉及使用一组稀疏(活跃)神经元从字典中逼近给定的输入刺激,在神经科学、信号处理和机器学习等广泛领域发挥着关键作用。首先,我们利用近算子理论,将连续时间发射率神经网络家族的均衡点与稀疏重构问题的最优解联系起来。然后,我们证明了 PFCN 是一个正系统,并给出了收敛到均衡的严格条件。具体来说,我们证明了收敛只取决于字典的一个属性,并且是线性-指数收敛,即最初的收敛率在最坏情况下是线性的,然后在瞬态之后变成指数收敛。我们还证明了一系列技术结果,以评估相关神经动力学的收缩特性。我们的分析利用了收缩理论来描述有非负性约束和无非负性约束的稀疏重构的发射率竞争网络家族的行为特征。最后,我们通过一个数值示例验证了我们方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Positive Competitive Networks for Sparse Reconstruction
We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (PFCN), to tackle sparse reconstruction problems with non-negativity constraints. These problems, which involve approximating a given input stimulus from a dictionary using a set of sparse (active) neurons, play a key role in a wide range of domains, including, for example, neuroscience, signal processing, and machine learning. First, by leveraging the theory of proximal operators, we relate the equilibria of a family of continuous-time firing-rate neural networks to the optimal solutions of sparse reconstruction problems. Then we prove that the PFCN is a positive system and give rigorous conditions for the convergence to the equilibrium. Specifically, we show that the convergence depends only on a property of the dictionary and is linear-exponential in the sense that initially, the convergence rate is at worst linear and then, after a transient, becomes exponential. We also prove a number of technical results to assess the contractivity properties of the neural dynamics of interest. Our analysis leverages contraction theory to characterize the behavior of a family of firing-rate competitive networks for sparse reconstruction with and without non-negativity constraints. Finally, we validate the effectiveness of our approach via a numerical example.
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来源期刊
Neural Computation
Neural Computation 工程技术-计算机:人工智能
CiteScore
6.30
自引率
3.40%
发文量
83
审稿时长
3.0 months
期刊介绍: Neural Computation is uniquely positioned at the crossroads between neuroscience and TMCS and welcomes the submission of original papers from all areas of TMCS, including: Advanced experimental design; Analysis of chemical sensor data; Connectomic reconstructions; Analysis of multielectrode and optical recordings; Genetic data for cell identity; Analysis of behavioral data; Multiscale models; Analysis of molecular mechanisms; Neuroinformatics; Analysis of brain imaging data; Neuromorphic engineering; Principles of neural coding, computation, circuit dynamics, and plasticity; Theories of brain function.
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