全球有吸引力的集为四次数值的神经网络与中立项目的集
Xili Wu1, Zhengwen Tu2, Tao Peng1
1School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404100, China.
Scientific reports
|August 2, 2024
概括
本研究建立了具有复杂延迟和中性项目的四次数值神经网络 (QVNNs) 的全球有吸引力的集合. 新的方法确保了实际应用,即使具有无限的中性激活功能.
科学领域:
- * 计算神经科学 计算神经科学
- *复杂系统分析 复杂系统分析
- * 神经网络理论 * 神经网络理论
背景情况:
- * 四次值神经网络 (QVNNs) 提供了处理复杂数据的高级功能.
- *分析具有各种延迟和中性项目的QVNN的稳定性和趋同性至关重要.
- *现有的方法往往需要限制性条件或网络分解.
研究的目的:
- * 调查QVNN的全球吸引力集,包括泄漏延迟,时间变化延迟和中性项目.
- * 开发新的分析技术来确定全球指数吸引力集合.
- *为了更广泛的适用性,放松激活功能的限制.
主要方法:
- * 应用利亚普诺夫理论和新的分析技术.
- * 没有分解的QVNN的直接分析.
- *考虑非差异化和时间变化的延迟.
主要成果:
- *为研究的QVNNs建立了全球吸引力集和全球指数吸引力集.
- * 证明了直接分析方法的有效性.
- * 通过两个模拟示例验证了理论结果.
结论:
- * 提出的方法为分析具有复杂动态的QVNN提供了强大的框架.
- * 中性激活功能的放松条件增强了发现的实用性.
- *这项研究有助于更深入地了解QVNN的稳定性和收性质.
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