在重尾循环神经网络中,缓慢过渡到低维混乱
Eva Yi Xie1,2, Stefan Mihalas1, Łukasz Kuśmierz1
1Allen Institute, Seattle, WA, USA.
bioRxiv : the preprint server for biology
|November 24, 2025
概括
与高斯网络不同,具有重尾突触权重的重复神经网络 (RNN) 显示了强大的混乱过渡. 这种生物现实主义提供了动态稳定性和神经活动丰富性之间的权衡.
科学领域:
- 计算神经科学是一种计算神经科学.
- 理论神经科学理论神经科学
- 机器学习 机器学习
背景情况:
- 大脑中的突触重量通常遵循重尾分布.
- 大多数反复神经网络 (RNN) 的理论分析都假定高斯连接,这可能不是生物学上准确的.
研究的目的:
- 为了研究RNNs的动态与生物学上可信的莱维α-稳定的分布式权重.
- 分析有限大小的重尾RNN中静止和混乱状态之间的过渡.
- 了解神经活动中强度和维度之间的权衡.
主要方法:
- 从莱维α稳定分布中随机权重的RNN系统研究.
- 有限大小分析以确定静止和混乱动态之间的过渡.
- 理论预测和基于模拟的验证过渡收益.
- 分析Lyapunov维度以评估吸引器的维度.
主要成果:
- 有限重尾RNN表现出静止和混乱动态之间的急剧过渡,与平均场预测形成鲜明对比.
- 在重尾RNN中观察到接近混乱边缘的更广泛的增强模式,这表明向混乱的过渡速度更慢.
- 较重的尾巴导致了较小的利亚普诺夫维度,这意味着吸引器的有效维度较低.
- 在动态的稳定性和神经活动的丰富性之间存在着生物学上一致的权衡.
结论:
- 有限大小的效应对于理解重尾RNN中的动态至关重要,其中平均场理论崩.
- 重尾连接为神经电路提供了更现实的模型,为大脑功能提供了洞察力.
- 该研究提供了一个可操作的框架,用于分析现实大小,重尾神经电路中的动力学.
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