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Measuring information integration
Open accessAbstract
BACKGROUND: To understand the functioning of distributed networks such as the brain, it is important to characterize their ability to integrate information. The paper considers a measure based on effective information, a quantity capturing all causal interactions that can occur between two parts of a system. RESULTS: The capacity to integrate information, or Phi, is given by the minimum amount of effective information that can be exchanged between two complementary parts of a subset. It is shown that this measure can be used to identify the subsets of a system that can integrate information, or complexes. The analysis is applied to idealized neural systems that differ in the organization of their connections. The results indicate that Phi is maximized by having each element develop a different connection pattern with the rest of the complex (functional specialization) while ensuring that a large amount of information can be exchanged across any bipartition of the network (functional integration). CONCLUSION: Based on this analysis, the connectional organization of certain neural architectures, such as the thalamocortical system, are well suited to information integration, while that of others, such as the cerebellum, are not, with significant functional consequences. The proposed analysis of information integration should be applicable to other systems and networks.
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“IIT defines a property of a system called integrated information (Φ) and postulates that this is an exact measure of the quantity of consciousness of any system.”
From The Problem with Phi: A Critique of Integrated Information Theory (2015) · cites this paper as [1]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“In either case, IIT appears to be identifying consciousness with a specific measure of information.”
From The Problem with Phi: A Critique of Integrated Information Theory (2015) · cites this paper as [1]
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“Further simulations show that it is possible to construct a large complex of high Φ by joining smaller complexes through reciprocal connections [8].”
From An information integration theory of consciousness (2004) · cites this paper as [8]
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“This notion of brain complexity-defined as the coexistence of integration and differentiation-was at the core of IIT's original notion of F 89,90 and remains central to the empirical predictions of IIT in its mature form.95”
From An integrative, multiscale view on neural theories of consciousness (2024) · cites this paper as [90]
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In the citing paper
“A graph-theoretical analysis indicates that connection matrices yielding the highest values of information integration (Φ = 74 bits) share two key characteristics [8]. First, connection patterns are different for different elements, ensuring functional specialization. Second, all elements can be reached from all other elements of the network, ensuring functional integration.”
From An information integration theory of consciousness (2004) · cites this paper as [8]
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In the citing paper
“Tononi’s response is not surprising given that IIT implies a form of panpsychism [1–8].”
From The Problem with Phi: A Critique of Integrated Information Theory (2015) · cites this paper as [1]
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Citations
Cites
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Cited by
Sorted by citations
The economy of brain network organization
Bullmore, E., & Sporns, O. (2012) · Nature Reviews Neuroscience · doi:10.1038/nrn3214 · Cited by 3,284
Self-citationOrganization, development and function of complex brain networks
SPORNS, O., CHIALVO, D., KAISER, M., & HILGETAG, C. (2004) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2004.07.008 · Cited by 2,055
Self-citationAn information integration theory of consciousness
Tononi, G. (2004) · BMC Neuroscience · doi:10.1186/1471-2202-5-42 · Cited by 1,958
“Further simulations show that it is possible to construct a large complex of high Φ by joining smaller complexes through reciprocal connections [8].”
BackgroundInfluentialSelf-citationConsciousness as integrated information: a provisional manifesto
Tononi, G. (2008) · The Biological Bulletin · doi:10.2307/25470707 · Cited by 1,529
Self-citationConscious Processing and the Global Neuronal Workspace Hypothesis
Mashour, G. A., Roelfsema, P., Changeux, J.-P., & Dehaene, S. (2020) · Neuron · doi:10.1016/j.neuron.2020.01.026 · Cited by 1,164
“IIT is primarily a mathematical theory: it introduces a quantity called F, which quantifies the degree of consciousness of any system, biological or artificial, and suggests that at any given moment, the neural correlate of consciousness is a complex yielding a maximum of irreducible, intrinsic cause–effect power (Oiz…”
Background
Metadata
- Authors
- Tononi, G., & Sporns, O.
- Affiliations
- University of Wisconsin–Madison (US)
- Indiana University Bloomington (US)
- Corresponding author
- Tononi, Giulio
- Venue
- BMC Neuroscience
- Published
- 2003-12-02
- Volume
- 4
- Issue
- 1
- Pages
- 31-31
- ISSN
- 1471-2202 (ISSN-L)
- PMC
- PMC331407
- OpenAlex
- W1832461346
- Cited by
- 294
- References
- 51
- Citations by year
- 2026: 7 · 2025: 13 · 2024: 12 · 2023: 10 · 2022: 14 · 2021: 15 · 2020: 20 · 2019: 19 · 2018: 31 · 2017: 18 · 2016: 11 · 2015: 12 · 2014: 9 · 2013: 12 · 2012: 11
- FWCI
- 2.77
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- BMC Neuroscience (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion, other-oa)
- PubMed Central (publishedVersion, other-oa)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Keywords
- information integration, effective information, phi, distributed networks, brain connectivity, functional specialization, functional integration, thalamocortical system, cerebellum, network organization, causal interaction
- MeSH terms
- Brain, Information Theory, Models, Neurological, Nerve Net, Synaptic Transmission, Stochastic Processes, Normal Distribution, Neural Networks, Computer
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