AI 中文总结
该研究提出在简单线性循环神经网络模型中添加动态循环反馈增益的机制，无需精细调节即可产生长时标与无标度关联，通过解析和数值方法验证了该机制的有效性。
AI 中文摘要
大脑动力学中的长时标会产生实验中测得的幂律关联。简单的循环神经网络模型可重现这种幂律行为，但需对循环相互作用强度进行精细调节，使其处于稳定边缘。我们表明，通过在该简单线性模型中添加动态循环反馈增益，可消除精细调节的需求，因为该增益会自组织，使得有效循环矩阵的谱始终无间隙，且无论循环强度如何，其最大特征值都落在稳定边缘上。因此，长时标和无标度关联会普遍出现，我们通过解析和数值两种方式对此进行了验证。
英文摘要
Long timescales in brain dynamics give rise to power law correlations measured in experiments. A simple linear recurrent neural network model can reproduce this power law behavior, but the recurrent interaction strength needs to be fine tuned in order to sit at the edge of stability. We show that by adding a dynamical recurrent feedback gain to the simple linear model removes the need for fine tuning, because the gain self-organizes so that the spectrum of the effective recurrent matrix is always gapless with the top eigenvalue landing on the stability edge for any recurrent strength. As a consequence, long timescales and scale free correlations arise generically, as we demonstrate both analytically and numerically.
Comments4 pages, 3 figures, 35 references
