布尔网络中通过自适应信息处理的紧急临界性
Emergent Criticality Through Adaptive Information Processing in Boolean Networks
摘要：
我们研究了布尔网络中具有不断发展的连通性的群体的信息处理，并系统地探索了学习能力，鲁棒性，网络拓扑结构和任务复杂性之间的相互作用。我们解决了一个长期悬而未决的问题，并发现计算，对于大系统尺寸$N$，自适应信息处理驱动网络的关键连接$K_{c}=2$。对于有限规模的网络，其连通性以系统规模$N$的幂律逼近临界值。我们表明，网络学习和泛化在临界点附近进行了优化，给定任务复杂度和提供阈值的信息量。随机网络和演化网络都在$K_{c}$附近表现出最大的拓扑多样性。我们假设，这支持有效的探索和鲁棒性的解决方案。在我们的观察中还反映出，值的方差在关键网络种群中是最大的。最后，我们讨论了我们的研究结果的影响，以确定最佳的拓扑结构的自适应动态网络，解决计算任务。
英文摘要：
We study information processing in populations of Boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a long-standing open question and find computationally that, for large system sizes $N$, adaptive information processing drives the networks to a critical connectivity $K_{c}=2$. For finite size networks, the connectivity approaches the critical value with a power-law of the system size $N$. We show that network learning and generalization are optimized near criticality, given task complexity and the amount of information provided threshold values. Both random and evolved networks exhibit maximal topological diversity near $K_{c}$. We hypothesize that this supports efficient exploration and robustness of solutions. Also reflected in our observation is that the variance of the values is maximal in critical network populations. Finally, we discuss implications of our results for determining the optimal topology of adaptive dynamical networks that solve computational tasks.
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