Integrated information theory provides a mathematical framework to fully characterize the cause-effect structure of a physical system. Here, we introduce PyPhi, a Python software package that implements this framework for causal analysis and unfolds the full cause-effect structure of discrete dynamical systems of binary elements. The software allows users to easily study these structures, serves as an up-to-date reference implementation of the formalisms of integrated information theory, and has been applied in research on complexity, emergence, and certain biological questions. We first provide an overview of the main algorithm and demonstrate PyPhi’s functionality in the course of analyzing an example system, and then describe details of the algorithm’s design and implementation. PyPhi can be installed with Python’s package manager via the command ‘’ on Linux and macOS systems equipped with Python 3.4 or higher. PyPhi is open-source and licensed under the GPLv3; the source code is hosted on GitHub at https://github.com/wmayner/pyphi. Comprehensive and continually-updated documentation is available at https://pyphi.readthedocs.io. The mailing list can be joined at https://groups.google.com/forum/#!forum/pyphi-users. A web-based graphical interface to the software is available at http://integratedinformationtheory.org/calculate.html.

Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements.

Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of consciousness (called a complex), which are then used to formulate a mathematical framework for assessing both the quality and quantity of experience. The explanatory identity proposed by IIT is that an experience is identical to the cause–effect structure unfolded from a maximally irreducible substrate (a Φ-structure). In this work we introduce a definition for the integrated information of a system (φs) that is based on the existence, intrinsicality, information, and integration postulates of IIT. We explore how notions of determinism, degeneracy, and fault lines in the connectivity impact system-integrated information. We then demonstrate how the proposed measure identifies complexes as systems, the φs of which is greater than the φs of any overlapping candidate systems.

Despite significant progress in understanding neural coding, it remains unclear how the coordinated activity of large populations of neurons relates to what an observer actually perceives. Since neurophysiological differences must underlie differences among percepts, differentiation analysis-quantifying distinct patterns of neurophysiological activity-has been proposed as an "inside-out" approach that addresses this question. This methodology contrasts with "outside-in" approaches such as feature tuning and decoding analyses, which are defined in terms of extrinsic experimental variables. Here we used two-photon calcium imaging in mice of both sexes to systematically survey stimulus-evoked neurophysiological differentiation in excitatory neuronal populations in layers 2/3, 4, and 5 across five visual cortical areas (primary, lateromedial, anterolateral, posteromedial, and anteromedial) in response to naturalistic and phase-scrambled movie stimuli. We find that unscrambled stimuli evoke greater neurophysiological differentiation than scrambled stimuli specifically in layers 2/3 of the anterolateral and anteromedial areas, and that this effect is modulated by arousal state and locomotion. By contrast, decoding performance was far above chance and did not vary substantially across areas and layers. Differentiation also differed within the unscrambled stimulus set, suggesting that differentiation analysis may be used to probe the ethological relevance of individual stimuli. Significance statementMuch is known about how neurons encode stimuli in the visual system, yet it remains unclear how their activity generates conscious percepts. Recent studies have linked differentiation of neural activity to subjective ratings of stimulus "meaningfulness" and the presence of consciousness itself. We systematically surveyed different neuronal populations in mouse visual cortex and showed that activity in layers 2/3 of the anterolateral and anteromedial areas is more 3 differentiated in response to naturalistic movie stimuli compared to meaningless phasescrambled stimuli. Contrariwise, decoding performance was high and did not vary substantially across populations. These findings advance our understanding of functional differences among layers and areas and highlight differentiation analysis as a theoretically-motivated approach that can complement analyses that focus on stimulus encoding.

The mechanisms leading to the alternation between active (UP) and silent (DOWN) states during sleep slow waves (SWs) remain poorly understood. Previous models have explained the transition to the DOWN state by a progressive failure of excitation because of the build‐up of adaptation currents or synaptic depression. However, these models are at odds with recent studies suggesting a role for presynaptic inhibition by Martinotti cells (MaCs) in generating SWs. Here, we update a classical large‐scale model of sleep SWs to include MaCs and propose a different mechanism for the generation of SWs. In the wake mode, the network exhibits irregular and selective activity with low firing rates (FRs). Following an increase in the strength of background inputs and a modulation of synaptic strength and potassium leak potential mimicking the reduced effect of acetylcholine during sleep, the network enters a sleep‐like regime in which local increases of network activity trigger bursts of MaC activity, resulting in strong disfacilitation of the local network via presynaptic GABAB1a‐type inhibition. This model replicates findings on slow wave activity (SWA) during sleep that challenge previous models, including low and skewed FRs that are comparable between the wake and sleep modes, higher synchrony of transitions to DOWN states than to UP states, the possibility of triggering SWs by optogenetic stimulation of MaCs, and the local dependence of SWA on synaptic strength. Overall, this work points to a role for presynaptic inhibition by MaCs in the generation of DOWN states during sleep.

The target article misrepresents the foundations of integrated information theory (IIT) and ignores many essential publications. It, thus, falls to this lead commentary to outline the axioms and postulates of IIT and correct major misconceptions. The commentary also explains why IIT starts from phenomenology and why it predicts that only select physical substrates can support consciousness. Finally, it highlights that IIT's account of experience – a cause–effect structure quantified by integrated information – has nothing to do with “information transfer.”

Neurophysiological differentiation (ND), a measure of the number of distinct activity states that a neural population visits over a time interval, has been used as a correlate of meaningfulness or subjective perception of visual stimuli. ND has largely been studied in non-invasive human whole-brain recordings where spatial resolution is limited. However, it is likely that perception is supported by discrete neuronal populations rather than the whole brain. Therefore, here we use Neuropixels recordings from the mouse brain to characterize the ND metric across a wide range of temporal scales, within neural populations recorded at single-cell resolution in localized regions. Using the spiking activity of thousands of simultaneously recorded neurons spanning 6 visual cortical areas and the visual thalamus, we show that the ND of stimulus-evoked activity of the entire visual cortex is higher for naturalistic stimuli relative to artificial ones. This finding holds in most individual areas throughout the visual hierarchy. Moreover, for animals performing an image change detection task, ND of the entire visual cortex (though not individual areas) is higher for successful detection compared to failed trials, consistent with the assumed perception of the stimulus. Together, these results suggest that ND computed on cellular-level neural recordings is a useful tool highlighting cell populations that may be involved in subjective perception.

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