Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6) and JARA-Institute Brain Structure-Function Relationships (INM-10), Jülich Research Centre, 52425 Jülich, Germany.
Institute for Theoretical Solid State Physics, RWTH Aachen University, 52074 Aachen, Germany.
Phys Rev Lett. 2022 Apr 22;128(16):168301. doi: 10.1103/PhysRevLett.128.168301.
Criticality is deeply related to optimal computational capacity. The lack of a renormalized theory of critical brain dynamics, however, so far limits insights into this form of biological information processing to mean-field results. These methods neglect a key feature of critical systems: the interaction between degrees of freedom across all length scales, required for complex nonlinear computation. We present a renormalized theory of a prototypical neural field theory, the stochastic Wilson-Cowan equation. We compute the flow of couplings, which parametrize interactions on increasing length scales. Despite similarities with the Kardar-Parisi-Zhang model, the theory is of a Gell-Mann-Low type, the archetypal form of a renormalizable quantum field theory. Here, nonlinear couplings vanish, flowing towards the Gaussian fixed point, but logarithmically slowly, thus remaining effective on most scales. We show this critical structure of interactions to implement a desirable trade-off between linearity, optimal for information storage, and nonlinearity, required for computation.
关键性质与最优计算能力密切相关。然而，由于缺乏规范的临界脑动力学理论，目前对这种生物信息处理形式的认识仅限于平均场结果。这些方法忽略了临界系统的一个关键特征：跨越所有尺度的自由度之间的相互作用，这是复杂非线性计算所必需的。我们提出了一个原型神经场理论——随机威尔逊-科旺方程的规范理论。我们计算了耦合流，这些耦合流参数化了不断增加的长度尺度上的相互作用。尽管与卡达诺-帕里西-张模型有相似之处，但该理论属于杰尔曼-洛模型类型，是规范可重整化量子场论的典型形式。在这里，非线性耦合消失，流向高斯不动点，但对数缓慢，因此在大多数尺度上仍然有效。我们展示了这种相互作用的临界结构，在信息存储所需的线性和计算所需的非线性之间实现了理想的权衡。
