Alpha, an alternative parameter for consciousness measurement based on Integration Information Theory

Abstract

Integration Information Theory of Tononi contends that calculation of integrated information can give an account of consciousness. One "weakness" of IIT is the massive computation needed for the integration of information. Alpha born as an alternative to this calculation based on the thesis of natural computationalism, and Principle of Computational Equivalence, that roughly contends that small or simple rules can reproduce complex behaviors. Alpha is a kind of reduction of behaviors into small rules based on biology studies that accelerate the integration information calculus

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Integration Information Theory

According to Tononi ”Integration Information Theory (IIT) attempts to identify essential properties of consciousness, and from there, infers the properties of physical systems that can be account for it (postulates) Based on the postulates, it permits in principle to derive, for any particular system of elements in a state, whether it has consciousness, how much, and which particular experience it is having. IIT offers a parsimonious explanation for empirical evidence, makes testable predictions, and permits inferences and extrapolations”.

IIT define five essential axioms of consciousness: 1) existence, 2) composition, 3) information, 4) integration and 5) exclusion. Based on axioms, postulates are defined, this is, IIT extends axioms to characteristics of physical substrate in order to test empirically that the substratum itself is capable or it is no capable to have real experiences experiences.

According to Tononi [4] “consciousness corresponds to the capacity of a system to integrate information”. Such claim –According with himself– is motivated by two phenomenological properties of consciousness: differentiation, this is, the availability of a very large number of conscious experiences; and integration, the unity of each such experience–.

The IIT states that the quantity of consciousness available to a system can be measured as the F value of a complex of elements. F is the amount of causally effective information that can be integrated across the informational weakest link of a subset of elements. A complex is a subset of elements with F>0 that is not part of a subset of higher F. The theory also claims that the quality of consciousness is determined by the informational relationships among the elements of a complex, which are specified by the values of effective information among them. Finally, each particular conscious experience is specified by the value, at any given time, of the variables mediating informational interactions among the elements of a complex”.

In the next section 2 a resume of phi calculus according to version 3.0 of IIT is introduced.

Alpha

Alpha is fully inspired in IIT, and is introduced as alternative to phi as measurement of information integration in big networks. Alpha is based on the view of basins of attraction for construction of the map of all possible states that a network can be reach in the evolution of time. In order to simplify and then to speed up the information integration calculus an analysis based on the schemata theorem [1, 2] is applied. Roughly, Holland’s schemata theorem states that in strings (of DNA) some constant patterns cause all complexity if phenotypes. This idea, joined to the one proposed by principles of irreducibility, computational equivalence and an algorithmic nature of nature [6] allow us to propose that integration of information is a function of topology and dynamic of systems (among other factors). In addition, in order to explore big networks, a set of bioinformatic tools as samSPECTRAL [5], k-means and spectral clustering algorithms are applied in two possible ways: reduction or division of networks. In both cases an adaptation of alpha parameter calculus is proposed.

Alpha calculus

1. Candidate set and current state are defined.

2. Search for main complex by means connectivity analysis of candidate set.

3. Input repertoire calculation.

4. TPM (transition probability matrix) calculation.

5. Computation of basins of attraction of the candidate set, as results here is obtained a set of attractors or final states corresponding to all possible outputs of the candidate set.

6. Construction of schemata in set of inputs related with specific attractors. As result of this analysis the set of “valid” associations mechanism-purview is obtained. This is, by means this computation is possible to identify who affects to who.

7. Calculation of integration information as in IIT from step number 3 in above list of steps.

Calculating basins of attraction. As is possible to observe in figure 4, since this is a highly integrated system, there is a marked tendency towards a relatively small set of outputs (attractors).

Finding schemata. This is, finding patterns in inputs that leads to an attractor

According to Holland [2] “A schema is a template that identifies a subset of strings with similarities at certain string positions”. In Alpha, schemata analysis allows to find the footprint of the sets of inputs that lead to specific attractors (the set of all possible outputs of the network). Such points of attraction can be identified in basins of attraction (Figure 2) as the points where inputs go through. In figure 3, schemata or patterns of inputs are shown in the left side, where ’*’ symbol, as in Holland’s schemata, is used as wildcard symbol, which means that in this position can have value of either 1 or 0. Then it does not care what value it takes, always it will lead to specific output or attractor.

The interpretation of schemata in Alpha’s context is that, a network, being in a specific state, and given a perturbation over specific nodes, it results in changes in specific nodes of the same system. In other words, it is possible to characterise who affects who, or how and how much the system is integrated. The analysis showed here results on 84 (possible/valid) comparisons or couples mechanism-purview, unlikely phi calculus that need at least of 2^16 * 2^16 comparisons where 2^16 is the number of possible mechanisms or possible subsets in a network of 16 nodes. From Alpha’s view, phi exhaustive search of all possible combinations perform unnecessary calculations, because it is easy to see that the influence of nodes over a set of nodes depend not only on the number of nodes, but also depends on the network’s dynamic and topology.

In a network with high integration of information, we expect to see a map of basins of attraction with highest concentration of attractors, or in other words, we expect to see very dense areas that confluence to a single area as it is possible to observe in figure 2. Another characteristic of high integrated system is that the effect of a change over a set of nodes cause effects on the most part of the candidate set.

Conclusion

Alpha calculus is faster than phi calculus, and keeps faithful to the account of integration of information proposed by Tononi. Also, as a consequence, it is possible to respond to the Aaronson challenge against IIT, where value of integration of information does not depends only on the size of the analyzed system in such way that the bigger systems the bigger information integration value. As Alpha has shown integration information depends on topology, dynamic, current and past state of the system.