Iterative neural networks for improving memory capacity

IF 6 1区计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Neural Networks Pub Date : 2024-11-23 DOI:10.1016/j.neunet.2024.106936

Xiaofeng Chen , Dongyuan Lin , Zhongshan Li , Weikai Li

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Abstract

In recent years, the problem of the multistability of neural networks has been studied extensively. From the research results obtained, the number of stable equilibrium points depends only on a power form of the network dimension. However, in practical applications, the number of stable equilibrium points needed is often not expressed in power form. Therefore, can we determine an appropriate activation function so that the neural network has exactly the required number of stable equilibrium points? This paper provides a new way to study this problem by means of an iteration method. The necessary activation function is constructed by an appropriate iteration method, and the neural network model is established. Based on the mathematical theories of matrix analysis and functional analysis and on the inequality method, the number and distribution of the network equilibrium points are determined by dividing the state space reasonably, and some multistability criteria that are related to the number of iterations and are independent of the network dimension are established.

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提高记忆容量的迭代神经网络

近年来，人们对神经网络的多稳定性问题进行了广泛的研究。从已取得的研究成果来看，稳定平衡点的数量只取决于网络维度的幂形式。然而，在实际应用中，所需的稳定平衡点数量往往无法用幂形式表示。因此，我们能否确定一个合适的激活函数，使神经网络恰好具有所需的稳定平衡点数呢？本文提供了一种通过迭代法研究这一问题的新方法。通过适当的迭代法构建了必要的激活函数，并建立了神经网络模型。基于矩阵分析和函数分析的数学理论以及不等式方法，通过合理划分状态空间，确定了网络平衡点的数量和分布，并建立了一些与迭代次数相关且与网络维度无关的多稳性准则。

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来源期刊

Neural Networks 工程技术-计算机：人工智能

CiteScore

13.90

自引率

7.70%

发文量

425

审稿时长

67 days

期刊介绍： Neural Networks is a platform that aims to foster an international community of scholars and practitioners interested in neural networks, deep learning, and other approaches to artificial intelligence and machine learning. Our journal invites submissions covering various aspects of neural networks research, from computational neuroscience and cognitive modeling to mathematical analyses and engineering applications. By providing a forum for interdisciplinary discussions between biology and technology, we aim to encourage the development of biologically-inspired artificial intelligence.