在正规的随机神经网络中不连续地过渡到混乱
1<a href="https://ror.org/040kx1j83">Instituto de Física de Cantabria (IFCA)</a>, Universidad de Cantabria-CSIC, 39005 Santander, Spain.
Physical review. E
|August 20, 2024
概括
研究人员探索了一个随机反复的神经网络模型. 他们发现,改变转移函数可以导致突然,不连续的过渡到混乱的行为,与原始模型的逐渐变化不同.
科学领域:
- 计算神经科学是一种计算神经科学.
- 理论物理学的理论物理.
- 动态系统是动态系统.
背景情况:
- 索波林斯基,克里桑蒂和索默斯 (SCS) 模型描述了一个范式性的随机循环神经网络.
- 在其标准形式中,SCS模型显示了随着网络尺寸的增加,从静止状态到混乱状态的直接,连续的过渡.
- 在这种过渡中,利亚普诺夫指数,一种混乱的度量,从零逐渐上升.
研究的目的:
- 通过将各种奇数和非线性转移函数纳入标准tanh(x) 之外的SCS模型进行概括.
- 研究这些通用转移函数对过渡到混乱动态的性质的影响.
- 分析过渡到混乱变得不连续的条件.
主要方法:
- 用新型转移函数对通用的SCS模型进行数学分析.
- 在无限大小限制中对系统的行为进行调查.
- 使用利亚普诺夫指数和稳定性分析,描述过渡到混乱的过程.
主要成果:
- 当转移函数在零点的斜率是局部最小值时 (特别是当第三个导数是正值时),观察到一个不连续的混乱过渡.
- 在这种情况下,混乱通过吸引力-排斥力折叠分叉突然出现.
- 在混乱开始时,利亚普诺夫指数仍然不是零,这表明复杂动态的突然出现.
结论:
- 非线性转移函数的选择对随机循环神经网络中的过渡动态产生了关键影响.
- 不连续的过渡到混乱是可能的,并以转移函数的导数在起源的特定属性为特征.
- 这种概括扩大了神经网络模型中混乱动态的理解.
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