Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements

Gómez, Juan David; Mayner, William G. P.; Beheler-Amass, M.; Tononi, Giulio; Albantakis, Larissa

doi:10.3390/e23010006

Cited by 13 publications

(13 citation statements)

References 44 publications

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“…While the skipping method is consistent with how empirical estimates of Φ from previous versions of IIT have been applied [10–12], simulation papers illustrating maximal Φ at macro temporal scales have utilised different methods [13–15]. Specifically, they utilise coarse-graining, whereby micro timesteps are collated together to form macro timesteps.…”

Section: Resultsmentioning

confidence: 94%

Emergence of integrated information at macro timescales in real neural recordings

Leung

Tsuchiya

2022

Preprint

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How a system generates conscious experience remains an elusive question. One approach towards answering this is to consider the information available in the system from the perspective of the system itself. Integrated information theory (IIT) proposes a measure to capture this, integrated information (Φ). While Φ can be computed at any spatiotemporal scale, IIT posits that it be applied at the scale at which the measure is maximised. Importantly, Φ should emerge to be maximal not at the smallest spatiotemporal scale, but at some macro scale where system elements or timesteps are grouped into larger elements or timesteps. Emergence in this sense has been demonstrated in artificial binary systems, but it remains unclear whether it occurs in real neural recordings which are generally continuous and noisy. Here we first utilise a computational model to confirm that Φ becomes maximal at the temporal scales underlying its generative mechanisms. Second, we search for emergence in local field potentials from the fly brain recorded during wakefulness and anaesthesia, finding that normalised Φ (wake/anaesthesia), but not raw Φ values, peaks at 5 ms. Lastly, we extend our model to investigate why raw Φ values themselves did not peak. This work extends the application of Φ to simple artificial systems consisting of logic gates towards searching for emergence of a macro spatiotemporal scale in real neural systems.

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Section: Resultsmentioning

confidence: 94%

Emergence of integrated information at macro timescales in real neural recordings

Leung

Tsuchiya

2022

Preprint

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“…The intrinsicality property is defined based on the behavior of the difference measure when distributions are extended by adding units to the purview or increasing the number of possible states of a unit [14]. A distribution P n 1 is extended by a distribution P n 2 to create a new distribution P n 1 b P n 2 , where b is the Kronecker product.…”

Section: Intrinsic Difference (Id)mentioning

confidence: 99%

Mechanism Integrated Information

Barbosa

Marshall

Albantakis

et al. 2021

Entropy

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The Integrated Information Theory (IIT) of consciousness starts from essential phenomenological properties, which are then translated into postulates that any physical system must satisfy in order to specify the physical substrate of consciousness. We recently introduced an information measure (Barbosa et al., 2020) that captures three postulates of IIT—existence, intrinsicality and information—and is unique. Here we show that the new measure also satisfies the remaining postulates of IIT—integration and exclusion— and create the framework that identifies maximally irreducible mechanisms. These mechanisms can then form maximally irreducible systems, which in turn will specify the physical substrate of conscious experience.

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“…, H n , which are each described by a finite dimensional Hilbert space such that H Q = n i=1 H i . Without lack of generality [16], we will focus on systems constituted of n qubits. The system's time evolution is defined by a completely positive (trace-preserving) linear map T = {T α } [35], as…”

Section: Quantum Systemsmentioning

confidence: 99%

“…IIT's causal framework has been formalized for discrete dynamical systems in the classical realm [1,4,[14][15][16]. Accordingly, in prior studies [8][9][10], micro-level systems corresponded to classical causal networks [17,18], constituted of individual, conditionally independent physical units, that can (in principle) be manipulated and whose states can be observed.…”

Section: Introductionmentioning

confidence: 99%