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Causal density and integrated information as measures of conscious level

Erik P. Causal interactions within complex systems such as the brain can be analyzed at multiple spatiotemporal levels. It is widely assumed that the micro level is causally complete, thus excluding causation at the macro level. In this work, we go beyond effective information and consider additional requirements of a proper measure of causal power from the intrinsic perspective of a system: composition the cause—effect power of the parts , state-dependency the cause—effect power of the system in a specific state ; integration the causal irreducibility of the whole to its parts , and exclusion the causal borders of the system.

This happens if coarse-graining micro elements produces macro mechanisms with high irreducible causal selectivity. These results are relevant to a theoretical account of consciousness, because for integrated information theory the spatiotemporal maximum of integrated information fixes the spatiotemporal scale of consciousness.

More generally, these results show that the notions of macro causal emergence and micro causal exclusion hold when causal power is assessed in full and from the intrinsic perspective of a system.

The causal structure of physical systems can be analyzed at various spatial or temporal levels, from the most fine-grained micro level to any coarse-grained macro level.

For example, the brain can be analyzed, in space, at the level of neurons, neuronal groups, macro-columns, and areas; and in time, over tens, hundreds, and thousands of milliseconds Sporns et al. Thus, neuroimaging studies of effective connectivity in the brain examine interactions at the spatial level of voxels, which contain millions of neurons, and at the temporal level of blood-oxygen fluctuations, on the order of seconds. While such coarse-grained investigations are useful, it is widely assumed that the causal structure of a system is only fully captured by the most fine-grained causal model.

This view of causal power denies the possibility of genuine causal emergence. IIT is a theory of consciousness that starts from the essential properties of phenomenal experience and derives the requirements that must be satisfied by its PSC. A direct implication of the theory is that the spatiotemporal grain of the physical elements and intervals constituting the PSC must be the one that maximizes cause—effect power.

Hence, IIT predicts that the PSC must have maximum intrinsic cause—effect power at the level of macro elements and macro intervals, rather than at the level of micro elements and micro intervals Tononi, ; Marom, ; Chalmers, The quantitative assessment of cause—effect power is a prerequisite for determining whether and under what conditions the macro can indeed beat the micro.

Importantly, IIT provides the conceptual and mathematical tools to fully assess cause—effect power, at least for idealized, simple systems that can be manipulated, observed, and partitioned systematically.

In recent work, we provided a first proof of principle that, once causal interactions are quantified, causal power at the macro level can surpass that at the micro level Hoel et al.

However, this evaluation was done using an average measure of causal interactions within a predefined system taken as a whole.

According to IIT, these requirements postulates correspond to the causal properties that must be satisfied by the PSC, in turn are derived from the essential phenomenal properties of consciousness axioms : experience exists intrinsically, is structured, specific, unitary, and definite Tononi, , ; Oizumi et al. This measure of integrated information has already been applied to classify the causal structure of discrete dynamical systems, such as cellular automata Albantakis and Tononi, , and to track how the causal structure of simulated organisms, called animats, evolves in a simulated environment Albantakis et al.

Such demonstration constitutes a necessary first step toward a principled account of the spatiotemporal scale of consciousness. Moreover, it provides the theoretical foundation for empirical studies aimed at characterizing the neural elements and intervals constituting the neural substrate of consciousness and at testing a key prediction of IIT. For example, if in the brain a maximum of intrinsic cause—effect power were to obtain at the more macro spatial scale of neuronal groups, rather than at the more micro scale of neurons, IIT would predict that only changes in the average activity of a group of neurons, and not of individual neurons, should make a difference to the content of experience Tononi et al.

A detailed description of IIT 3. In the following, we first outline the IIT 3. Given a collection of such micro elements in a particular state, the IIT 3. Due to computational constraints, we restrict our examples to those where the micro elements are small collections of binary logic gates. For a given physical system S , we first perturb the elements of S into all possible states with equal probability Tononi et al.

These state transitions define the transition probability matrix TPM of the physical system, from which all IIT measures can be derived. Perturbing a physical system into a state means to physically intervene on the system, and to explicitly set its elements into that state. This procedure is akin to the calculus of interventions and the do x operator introduced by Pearl , to identify causal relationships.

A part of the system is a set of elements in a state m t that is a subset of S. To determine the cause—effect structure of a system, we consider every part of the system as a candidate mechanism.

The way a candidate mechanism constrains the potential past and future states of a purview is described by its cause—effect repertoire Tononi The difference the partition makes is the distance between the repertoire and the corresponding partitioned repertoire. For a cause—effect repertoire to be irreducible, all possible partitions must make a difference to the repertoire.

The partition that makes the least difference to the repertoire is the minimum information partition MIP , and the difference it makes defines the irreducibility of the candidate mechanism over its particular purview. According to IIT, a concept specifies a phenomenal distinction that contributes to what it is like to be a physical system in its current state. This means that its borders are set by its own intrinsic cause—effect structure, as opposed to being set by an external observer.

According to IIT, there is an identity between the conceptual structure specified by a complex in its current state and its subjective experience—what it is like to be the complex Oizumi et al. A discrete, finite system constituted of elements in a state can be considered at various spatiotemporal levels, from the most fine-grained micro level S m to a multitude of coarse-grainings S M. For simplicity, without loss of generality, we confine our analysis to coarse-grains in which macro elements are also binary.

First, one chooses a candidate system S m of micro elements and its associated bipartitions. Second, disjoint subsets of micro elements from S m are grouped into macro elements.

Third, the associated micro states are mapped into binary macro states. In order to be a valid mapping, S M must be such that mappings of micro states into macro states are limited to those in which the identity of the individual micro elements within a macro element is irrelevant to determine the macro state or else the macro level would not be a true coarse-grain as micro-level information would still be available at the macro level; moreover, from the intrinsic perspective of the macro system this information is not available.

The TPM of a candidate system is thus assessed independently at each spatiotemporal level: perturbing S M into all possible macro states with equal probability typically corresponds to a non-uniform distribution of all possible micro perturbations except if all macro states are composed of the same number of micro states.

This reshaping of micro perturbations at the macro level is what makes the causal analysis sensitive to the higher-level causal structure Hoel et al.

Macro cause—effect structures are then calculated from the macro TPM of a candidate system of macro elements S M as described above. All binary coarse-grains of discrete systems of logic gates were created with a custom-made Python program PyPhi, see Mayner and Marshall, , available for download at www.

To better understand the causal ramifications of coarse-graining, it is helpful to decompose this difference into three components: i the repertoire size of cause or effect repertoires, ii the change in how selective the mechanism is about its possible causes and effects post-partition, and iii the shift in which states are selected as possible causes and effects post-partition Fig. A Consider a hypothetical isolated system constituted of three interconnected binary elements.

The unpartitioned cause—effect repertoires of the system can change in several ways following a partition. There can be a loss of selectivity, moving the partition closer to maximum entropy top , a shift in which states are selected in the partitioned repertoire middle , or a mix of both bottom.

B Consider a simpler system of just two connected binary elements left. Compare degeneracy and determinism to selectivity: the minimum distance of either the cause or effect repertoires from the maximum entropy distribution H. In both cases, selectivity accurately reflects determinism and degeneracy B, bottom.

Note that the definition of repertoire size given here is a special case for systems of binary elements, and that in general, one needs to consider the maximum EMD distance between repertoires, which depends both on the number of elements in the purview and the distance between states of those elements. Irreducible selectivity values can range between 0. Selectivity can be related to the notion of determinism and degeneracy as described in Hoel et al. There, we demonstrated that the effective information EI in a causal model depends on how deterministic and degenerate its mechanisms are on average.

Here, this search is expanded to include all possible binary coarse-grains. In Hoel et al. The results of applying the additional causal criteria required by IIT can be seen in Fig. To visualize the cause—effect structure of the system, each concept is plotted as a star in cause—effect space Fig. In cause—effect space, each dimension is a possible past or future state of the system. The four concepts of S m each occupy a position based on the probability distributions of its maximally irreducible cause—effect repertoires.

Spatial causal emergence of integrated information increasing determinism. A The micro-level S m is constituted of noisy elements.

C A 3D projection of the 32D cause—effect space. The one past blue and two future green dimensions chosen were those with the greatest variance of probabilities so the visualization maximizes the distances between concepts. D The elements at the macro level of the system S M are less noisy than those in S m. E The two macro elements each generate a concept.

This mapping creates the macro element tables seen at the bottom of Fig. The conceptual structure of S M the maximally irreducible cause—effect structure of S is plotted in cause—effect space Fig.

It shows that the two macro-level concepts are more irreducible larger stars and less clustered than those in S m. Here, we show that while the size of the repertoire always decreases with coarse-graining, both irreducible selectivity and selectivity-shift can increase to a degree that outweighs the loss in size, which allows the macro to beat the micro.

However, at the micro level, both the unpartitioned and partitioned distributions are very close to maximum entropy shown in blue and thus the irreducible selectivity of the micro concept is only 0.

By comparison, the irreducible selectivity of the macro concept is 0. The selectivity-shift changes from 0 at the micro level to 0. Thus, while the macro loses 0. Note that most of the gain stems from an increase in irreducible selectivity, rather than selectivity-shift. This is in line with previous results from Hoel et al. How the macro beats the micro.

A comparison of a micro concept of Fig. The unpartitioned repertoires are in solid black, while partitioned repertoires are in red. The dotted blue line shows where the maximum entropy distribution lies. Consider the deterministic micro level of the system shown in Fig. As AND gates in state [0] are highly degenerate see Fig.

The low irreducible selectivity of the concepts 0. The selectivity shift for all micro concepts is 0. In cause—effect space, the micro concepts are clustered Fig. For each macro element, the micro states [00, 01, 10] are considered [OFF] and [11] is considered [ON]. The average distance between the macro concepts is 2, while the average distance between all the micro concepts is 1.

It is this reduction in degeneracy that allows the macro to beat the micro even though the system is completely deterministic. Spatial causal emergence through degeneracy.

C S M is still deterministic but is no longer degenerate. D The conceptual structure is less clustered and more irreducible at the macro level.

Measuring the Complexity of Consciousness

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Seth and A. Barrett and L. Seth , A.

Selected publications. Seth, A. Interoceptive inference, emotion, and the embodied self. Trends in Cognitive Sciences. A predictive processing theory of sensorimotor contingencies: Explaining the puzzle of perceptual presence and its absence in synaesthesia.

Causal density and integrated information as measures of conscious level.

Either your web browser doesn't support Javascript or it is currently turned off. In the latter case, please turn on Javascript support in your web browser and reload this page. Philosophical transactions. Read article at publisher's site DOI : Frontiers in Psychology

Erik P. Causal interactions within complex systems such as the brain can be analyzed at multiple spatiotemporal levels. It is widely assumed that the micro level is causally complete, thus excluding causation at the macro level. In this work, we go beyond effective information and consider additional requirements of a proper measure of causal power from the intrinsic perspective of a system: composition the cause—effect power of the parts , state-dependency the cause—effect power of the system in a specific state ; integration the causal irreducibility of the whole to its parts , and exclusion the causal borders of the system.

Causal density and integrated information as measures of conscious level

Causal density and integrated information as measures of conscious level.

The grand quest for a scientific understanding of consciousness has given rise to many new theoretical and empirical paradigms for investigating the phenomenology of consciousness as well as clinical disorders associated to it. A major challenge in this field is to formalize computational measures that can reliably quantify global brain states from data. In particular, information-theoretic complexity measures such as integrated information have been proposed as measures of conscious awareness. This suggests a new framework to quantitatively classify states of consciousness. However, it has proven increasingly difficult to apply these complexity measures to realistic brain networks.

Either your web browser doesn't support Javascript or it is currently turned off. In the latter case, please turn on Javascript support in your web browser and reload this page. Philosophical transactions. Read article at publisher's site DOI : Frontiers in Psychology

The system can't perform the operation now. Try again later. Citations per year. Duplicate citations. The following articles are merged in Scholar.


Download full-text PDF measures of conscious level. BYANIL K. Keywords: consciousness; causal density; integrated information. 1.


1. Introduction

Curator: Anil Seth. Eugene M. Marc-Oliver Gewaltig. A model of consciousness is a theoretical description that relates brain properties of consciousness e. Because of the diverse nature of these properties Seth et al. While the identification of correlations between aspects of brain activity and aspects of consciousness may constrain the specification of neurobiologically plausible models, such correlations do not by themselves provide explanatory links between neural activity and consciousness. Models should also be distinguished from theories that do not propose any mechanistic implementation e.

Thank you for visiting nature. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript. The neuronal connectivity patterns that differentiate consciousness from unconsciousness remain unclear. Previous studies have demonstrated that effective connectivity, as assessed by transcranial magnetic stimulation combined with electroencephalography TMS—EEG , breaks down during the loss of consciousness.

 - Беккер не мог поверить, что это говорит он. Если бы Сьюзан слышала меня сейчас, - подумал.  - Я тоже толстый и одинокий. Я тоже хотел бы с ней покувыркаться. Заплачу кучу денег. Хотя спектакль и показался достаточно убедительным, но Беккер зашел слишком. Проституция в Испании запрещена, а сеньор Ролдан был человеком осторожным.

COMMENT 5

  • measures of conscious level​​ Here, we describe recent progress in the development of measures of dynamical complexity, in particular causal density and integrated information. These and similar measures capture in different ways the extent to which a system's dynamics are simultaneously differentiated and integrated. Hamilton L. - 06.05.2021 at 18:14
  • Introduction to psychology kalat 9th edition pdf download the best of mystery alfred hitchcock pdf Gogbaregett - 06.05.2021 at 20:37
  • We use simulations to demonstrate the in-practice applicability of our measures, and to explore their properties. Charlot B. - 08.05.2021 at 23:51
  • Such measures would most readily apply to conscious level (a position on a scale from total unconsciousness as in brain death or coma to full. Dylan C. - 10.05.2021 at 06:32
  • And yes, it will contain that quantitative calculation. Brittany W. - 12.05.2021 at 02:17

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