PyPhi-Spectrum

PyPhi-Spectrum is a wrapper for PyPhi that can be used to calculate all possible $\Phi$ values for a given system. Its core functionality is based on elementary function calls to PyPhi, with the main difference from PyPhi being that whenever there is a minimization or maximization procedure, it looks for all minimizers or maximizers, forks the state of the computation accordingly, and carries on computations according to the mathematical definition for all forks. The primary wrapper is phi_spectrum.py and may be found in the pyphi directory.

The figure below shows the rank-ordered spectrum of possible $\Phi$ values for a simple two-gate AND+OR logic system, with the single output from PyPhi shown as a black X. For more details, see https://www.biorxiv.org/content/10.1101/2021.04.07.438793v1.full.

Installation

To install, download or clone this repository.

Sample Usage

import pyphi
import numpy as np
from pyphi import phi_spectrum

# Transition probability matrix. Saying where each state goes (little-end notation)
tpm = np.array([
    [0.,0.,0.],
    [0.,0.,0.],
    [1.,0.,0.],
    [1.,0.,1.],
    [0.,1.,0.],
    [0.,1.,0.],
    [1.,1.,0.],
    [1.,1.,1.]
])

# Set up network object
network = pyphi.Network(tpm, node_labels=['A','B','C'])
print("Network = ",network.node_labels)

# Put the system into a given state
state = (0,0,0)
nodes = ['A','B','C']

## Get the requisite Subsystem
subsystem = pyphi.Subsystem(network, state, nodes)

## Calculate all Phi values
display_CES = False  # if True, output will display all constellations
solution = None # how to handle degenerate purview elements (None,'Smallest','Largest', or 'Moon')
Phi_Spectrum = phi_spectrum.get_phi_spectrum(subsystem,display_CES,solution)

## Print the spectrum of Phi values for each cut
print("\nCuts = ",Phi_Spectrum[0])
print("\nPhi Spectrum = ",Phi_Spectrum[1])

## Print all valid Phi_MIP values
Phi_MIP = phi_spectrum.get_Phi_MIP(Phi_Spectrum)
print("Phi MIP = ",Phi_MIP)

Implementing Alternate Solutions

The problem of degenerate core causes has several unofficial solutions, which can be implemented using the solution keyword passed to the get_phi_spectrum function. Keyword values include "Moon", "Smallest", "Largest", and None. The "Moon" solution throws away degenerate core causes/effects if multiple cause/effect repertoires have the same phi value (https://doi.org/10.3390/e21040405), the "Smallest" solution is to keep the smallest of the degenerate core cause/effect repertoires, and the "Largest" solution is to keep the largest of the degenerate core cause/effect repertoires. Since the smallest and largest repertoires are not guaranteed to be unique, these solutions retain all possible degenerate core causes/effects of a given size (i.e. biggest or smallest). Using keyword argument None keeps all degenerate core causes/effects regardless of their size.

An additional solution is suggested by Krohn and Ostwald, 2017 (https://doi.org/10.1093/nc/nix017). Here, the authors propose a new definition of Phi ("big Phi") based on the sum of phi values ("little phi") rather than a distance between constellations. This solution can be implemented via the USE_SMALL_PHI_DIFFERENCE_FOR_CES_DISTANCE keyword in the standard PyPhi configuration file (pyphi_config.yml). This solution can be used in combination with any of the previous solutions since it implements a completely different definition of Phi.

References

More information about core PyPhi can be found at:

• Documentation for the latest stable release
• Documentation for the latest (potentially unstable) development version.
• Documentation is also available within the Python interpreter with the help function.

Please cite these papers if you use this code:

Mayner WGP, Marshall W, Albantakis L, Findlay G, Marchman R, Tononi G. (2018) PyPhi: A toolbox for integrated information theory. PLOS Computational Biology 14(7): e1006343. https://doi.org/10.1371/journal.pcbi.1006343

@article{mayner2018pyphi,
  title={PyPhi: A toolbox for integrated information theory},
  author={Mayner, William GP and Marshall, William and Albantakis, Larissa and Findlay, Graham and Marchman, Robert and Tononi, Giulio},
  journal={PLoS Computational Biology},
  volume={14},
  number={7},
  pages={e1006343},
  year={2018},
  publisher={Public Library of Science},
  doi={10.1371/journal.pcbi.1006343},
  url={https://doi.org/10.1371/journal.pcbi.1006343}
}

Albantakis L, Oizumi M, Tononi G (2014). From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0. PLoS Comput Biol 10(5): e1003588. doi: 10.1371/journal.pcbi.1003588.

@article{iit3,
    title={From the Phenomenology to the Mechanisms of Consciousness:
    author={Albantakis, Larissa AND Oizumi, Masafumi AND Tononi, Giulio},
    Integrated Information Theory 3.0},
    journal={PLoS Comput Biol},
    publisher={Public Library of Science},
    year={2014},
    month={05},
    volume={10},
    pages={e1003588},
    number={5},
    doi={10.1371/journal.pcbi.1003588},
    url={http://dx.doi.org/10.1371%2Fjournal.pcbi.1003588}
}

Correspondence

Correspondence regarding the modified PyPhi code (PyPhi-Spectrum) should be directed to Jake Hanson, at jake.hanson@asu.edu. Correspondence regarding core PyPhi functionality should be directed to the original authors.