Neuroscience of Consciousness
January 1, 2016
Erik Hoel, Larissa Albantakis, William Marshall et al.
153 citations
Causal interactions in complex systems like the brain can be examined at different spatiotemporal levels. While it is often assumed that the micro level is causally complete, this work shows that causal power can be stronger at macro levels. Using a measure called ΦMax, developed within integrated information theory, the authors systematically evaluated causal power at micro and macro levels in simplified neuronal-like systems. For systems with indeterminism or degeneracy, ΦMax peaked at a macro level when coarse-graining micro elements produced macro mechanisms with high irreducible causal selectivity.
Entropy
March 18, 2021
Leonardo S. Barbosa, William Marshall, Larissa Albantakis et al.
74 citations
Integrated Information Theory (IIT) begins with essential properties of consciousness and translates them into postulates that any physical system must satisfy to specify the physical substrate of consciousness. A recently introduced information measure captures three of these postulates—existence, intrinsicality, and information—and is unique. This work shows that the measure also satisfies the remaining postulates of integration and exclusion, creating a framework that identifies maximally irreducible mechanisms. These mechanisms can form maximally irreducible systems, which then specify the physical substrate of conscious experience.
Entropy
February 11, 2023
William Marshall, Matteo Grasso, William G. P. Mayner et al.
19 citations
Integrated information theory (IIT) proposes that consciousness is identical to the cause-effect structure generated by a maximally irreducible substrate (a Φ-structure). This work introduces a definition for system-integrated information (φs) grounded in IIT's postulates of existence, intrinsicality, information, and integration. It examines how determinism, degeneracy, and connectivity fault lines affect system-integrated information. The proposed measure identifies complexes as systems whose φs exceeds that of any overlapping candidate systems.
Entropy (Basel, Switzerland)
April 4, 2026
William G. P. Mayner, William Marshall, Giulio Tononi
Integrated information theory (IIT) begins with the fact of consciousness and identifies its essential features: every experience is intrinsic, specific, unitary, definite, and structured. The theory then translates these features into operational terms based on the cause-effect power of a substrate of units. To have cause-effect power intrinsically and specifically, substrate units in their current state must both (i) ensure the intrinsic availability of a repertoire of cause-effect states and (ii) increase the probability of a specific cause-effect state. A previous study showed that requirement (ii) can be measured by the intrinsic difference of a state's probability from maximal differentiation.
Neuroscience of Consciousness
January 1, 2026
William Marshall, Graham Findlay, Larissa Albantakis et al.
Integrated information theory (IIT) holds that consciousness corresponds to a system's maximum intrinsic, specific, and unitary cause-effect power, quantified as integrated information (Φ). The appropriate grain of analysis—from micro to macro—is the one that maximizes Φ. This paper presents a formal framework for computing Φ in systems that include macro units, thereby identifying a system's intrinsic units. It extends IIT 4.0's mathematics to assess cause-effect power across grains. Simulations of simple systems show that including macro units can yield higher integrated information than micro-only systems. Three examples illustrate how different macro units increase cause-effect power. The framework provides a foundation for testing and inferring consciousness.
arXiv Preprint Archive
October 4, 2025
William G. P. Mayner, William Marshall, Giulio Tononi
Integrated information theory (IIT) defines consciousness by its essential properties: intrinsic, specific, unitary, definite, and structured existence. The theory operationalizes existence as cause-effect power of a substrate of units. For substrate units to have cause-effect power intrinsically and specifically, they must both ensure the intrinsic availability of a repertoire of cause-effect states and increase the probability of a specific cause-effect state. Previous work addressed the second requirement via intrinsic difference from maximal differentiation; this paper shows the first requirement can be assessed by intrinsic difference from maximal specification. Using simple micro-unit systems, the authors illustrate that for macro systems like neural systems, a tradeoff between differentiation and specification is a necessary condition for intrinsic existence, i.e., consciousness.
arXiv Preprint Archive
December 5, 2024
Graham Findlay, William Marshall, Larissa Albantakis et al.
A digital computer could simulate human behavior without replicating subjective experience, according to Integrated Information Theory (IIT). Using simple Boolean units, the authors show that two systems can be functionally equivalent—one simulating the other—yet not phenomenally equivalent. This contradicts computational functionalism, which holds that performing the right computations is necessary and sufficient for consciousness. The analysis demonstrates that functional equivalence does not guarantee phenomenal equivalence, and this conclusion holds regardless of the simulated system's function. Even a computer that simulates neurons in the brain may not experience sights, sounds, or thoughts as humans do.
The Behavioral and brain sciences
March 23, 2022
Giulio Tononi, Melanie Boly, Matteo Grasso et al.
Integrated information theory (IIT) begins with phenomenology and predicts that only select physical substrates can support consciousness. The theory's account of experience—a cause-effect structure quantified by integrated information—has nothing to do with information transfer. This commentary outlines IIT's axioms and postulates, correcting major misconceptions from a target article that misrepresents the theory's foundations and ignores essential publications.
Entropy (Basel, Switzerland)
May 24, 2019
André Sevenius Nilsen, Bjørn Erik Juel, William Marshall
Integrated information theory (IIT) proposes a measure called Phi (Φ) to capture the level of consciousness in a physical system, but calculating Φ is only possible for very small systems. Researchers tested whether several heuristic measures and computational approximations could estimate Φ accurately in small binary networks of 3-6 nodes. They found that some approximations correlated strongly with Φ (r > 0.95) but did not reduce computational demands. Measures of signal complexity, decoder-based integrated information, and state differentiation correlated with the maximum Φ across states. These measures may help estimate a system's capacity for high Φ or identify low-Φ systems, but their applicability to larger or more complex systems remains uncertain.