Cooperation-Induced Topological Complexity: A Promising Road to Fault Tolerance and Hebbian Learning

Abstract

According to an increasing number of researchers intelligence emerges from criticality as a consequence of locality breakdown and long-range correlation, well known properties of phase transition processes. We study a model of interacting units, as an idealization of real cooperative systems such as the brain or a flock of birds, for the purpose of discussing the emergence of long-range correlation from the coupling of any unit with its nearest neighbors. We focus on the critical condition that has been recently shown to maximize information transport and we study the topological structure of the network of dynamically linked nodes. Although the topology of this network depends on the arbitrary choice of correlation threshold, namely the correlation intensity selected to establish a link between two nodes; the numerical calculations of this paper afford some important indications on the dynamically induced topology. The first important property is the emergence of a perception length as large as the flock size, thanks to some nodes with a large number of links, thus playing the leadership role. All the units are equivalent and leadership moves in time from one to another set of nodes, thereby insuring fault tolerance. Then we focus on the correlation threshold generating a scale-free topology with power index ν ≈ 1 and we find that if this topological structure is selected to establish consensus through the linked nodes, the control parameter necessary to generate criticality is close to the critical value corresponding to the all-to-all coupling condition. We find that criticality in this case generates also a third state, corresponding to a total lack of consensus. However, we make a numerical analysis of the dynamically induced network, and we find that it consists of two almost independent structures, each of which is equivalent to a network in the all-to-all coupling condition. This observation confirms that cooperation makes the system evolve toward favoring consensus topological structures. We argue that these results are compatible with both Hebbian learning and fault tolerance.

Cooperation in neural systems: Bridging complexity and periodicity

“…However, while the cooperative model used in Ref. [47] is Ising-like, and is renewal for both low and high values of the cooperation parameter [24], by contrast, the model of this paper shows a transition from the renewal condition (at the emergence of criticality) to a predictable nonrenewal coherent regime as the cooperation parameter K increases.…”

“…On the basis of the results of the recent work of Ref. [47] we make the plausible conjecture that the adoption of different network topologies generates temporal complexity, locality breakdown, and perfect synchronization upon changing the values of K. There may be scale-free networks where all the results of this paper are recovered at lower values of K. In fact, the work of Ref. [47] shows that the cooperative system generates dynamical links with a scale-free structure that has the important effect of facilitating the transition from the Poisson condition to the criticality-induced long-range correlation regime.…”

Self‐Organized Temporal Criticality: Bottom‐Up Resilience versus Top‐Down Vulnerability

“…To explain this choice notice that in the conventional case of criticality, generated by the choice of a proper control parameter , with = 100, = 1.5 is the value at which the onset of phase transition occurs. This is the value making the mean field ( ) of the conventional DMM fluctuate around = 0 with complex fluctuations and which generates criticality-induced intelligence [37,38]. In the case of the SOTC model this condition of criticalityinduced intelligence, with fluctuations of ( ) around 1.5, is spontaneously generated.…”

Network Theory of Human Decision Making

“…If the dynamically generated correlation is interpreted as a stable link, a complex scale-free network is generated, thereby implying that some unit (hubs) may play a role more important that the others [24]. This process, however, is the result of dynamics, all the units are equivalent and leadership moves in time from one to another unit.…”