Background: Integrated Information Theory (IIT) has been attracting attention as a theory of consciousness. The latest version, IIT3.0, is still at the stage of accumulating knowledge concerning fundamental networks. This paper presents an evaluation of the system-level integrated conceptual information of a major complex, ΦMax, associated with the center of consciousness for a small-scale network containing two small loops in accordance with the IIT3.0 framework. We focus on the following parameters characterizing the system model: 1) number of nodes in the loop, 2) frustration of the loop, and 3) temperature controlling the stochastic ﬂuctuation of the state transition. Speciﬁcally, assuming that the two loops are coupled systems, such as cerebral hemispheres, the eﬀect of these parameters on the values of ΦMax and conditions for major complexes formed by a single loop, rather than the entire network, is investigated.
Results: Our ﬁrst ﬁnding is that parity of the number of nodes forming a loop has a strong eﬀect on the integrated conceptual information ΦMax. For loops with an even number of nodes, the number of concepts tends to decrease, and ΦMax becomes smaller. When the loop is formed with an odd number of nodes, the system without frustration and the system with two frustrated loops can have exactly the same ΦMax. It is also shown that, although counterintuitive, the value of ΦMax can be maximized in the presence of stochastic ﬂuctuations. Our second ﬁnding is that a major complex is more likely to be formed by a small number of nodes under small stochastic ﬂuctuations. In particular, this tendency is enhanced for larger numbers of nodes constituting a loop. On the other hand, the entire network can easily become a major complex under larger stochastic ﬂuctuations, and this tendency can be reinforced by frustration.
Conclusions: Our results indicating that the entire network dominates and maintains a high level of consciousness in the presence of a certain degree of ﬂuctuation and frustration may qualitatively correspond to actual neural behaviors. The results of this study are expected to contribute to the veriﬁcation of the consistency of IIT with the actual nervous system in the future.