PyPhi is a Python platform for research in Integrated Information Theory (IIT). Its core task is computing Φ (integrated information) and the cause–effect structure a system specifies; around that it provides a broad toolkit for the analyses IIT research needs (see Beyond Φ).

Given a substrate — a network of interacting units defined by its transition probabilities — and a state, PyPhi computes:

• φ_s, the system integrated information — whether a set of units exists as one integrated whole — by finding the partition that makes the least difference;
• the cause–effect structure (Φ-structure): the distinctions (irreducible mechanisms) a system specifies and the relations that bind them, whose total is Φ, the structure integrated information.

It implements the current formalism, IIT 4.0 (Albantakis et al., 2023), and retains the earlier IIT 3.0 formalism, selectable by configuration.

Example

import pyphi

# The example system from the IIT 4.0 paper (Fig. 1A).
substrate = pyphi.examples.iit4_2023_fig1a_substrate()
state = (0, 1, 1)

# Analyze the candidate system {A, B} in that state under IIT 4.0.
analysis = pyphi.analyze(substrate, state, subset=(0, 1))

print(analysis.phi)      # system integrated information, φ_s ≈ 0.04
print(analysis.big_phi)  # structure integrated information, Φ ≈ 1.56

The result carries the full Φ-structure — its distinctions, relations, and the minimum-information partition. See the documentation and the IIT 4.0 demo notebook for a complete walkthrough.

Beyond Φ

Around the core Φ and cause–effect-structure computations, PyPhi is a toolkit for IIT research:

• Actual causation — which specific past events actually caused a given present event, and which effects it will actually cause (Albantakis et al., 2019).
• Matching and perception — quantify how well a system's cause–effect structure matches the causal structure of its environment, the basis of perception and intrinsic meaning in IIT (Mayner et al., 2024).
• Macro and micro scales — coarse-grain or black-box a substrate to analyze integrated information at different spatial and temporal scales.
• Analytical bounds — bound Φ and its components from above without the full combinatorial computation (Zaeemzadeh & Tononi, 2024).
• Parameter sweeps — evaluate many substrates, states, or configurations in one call, with optional parallelism.
• Estimating substrates from data — infer a substrate, with epistemic uncertainty, from observed state transitions.
• Simulating dynamics — settle a substrate to its most probable next states or sample stochastic trajectories.
• Substrate generation — build substrates from a library of unit mechanisms, weight matrices, or Ising models.
• Visualization — plot connectivity, repertoires, and Φ-structures (requires the visualize extra).
• Export and interop — export results to pandas DataFrames or xarray, and substrates to networkx, GraphML, or a two-timeslice dynamic Bayesian network.
• Saving and loading — persist any result to disk (JSON, transparently gzipped) and reload it later.

Release status. The current release on PyPI is the 2.0 line, which implements IIT 4.0. Upgrading from 1.x involves breaking changes; see What's new in 2.0. The 1.x line (IIT 3.0) remains available: install "pyphi<2".

Documentation

• Getting started: install and a first computation in ten minutes
• Documentation for the latest stable release
• Documentation for the latest development version
• Documentation for any object is also available in the interpreter with the help function.

For AI assistants

PyPhi ships an MCP server (pip install "pyphi[mcp]", then pyphi-mcp install) that gives an assistant tools for building substrates, estimating cost, and running analyses, along with the theory reference it needs to interpret results. The documentation site is also readable without it:

• https://pyphi.readthedocs.io/en/stable/llms.txt lists every page with a one-line summary; llms-full.txt at the same location is the whole site as one markdown file.
• Every page's MyST source is served under _sources/, for example https://pyphi.readthedocs.io/en/stable/_sources/theory/conditional-independence.md.txt.
• https://pyphi.readthedocs.io/en/stable/objects.inv is the intersphinx inventory that maps API names to their pages.

Installation

PyPhi requires Python 3.13+.

Using uv (recommended)

uv is a fast Python package manager:

# macOS/Linux
curl -LsSf https://astral.sh/uv/install.sh | sh
# Windows
powershell -c "irm https://astral.sh/uv/install.ps1 | iex"

Install the current release:

uv pip install pyphi

To install the latest development version from GitHub instead:

uv pip install "git+https://github.com/wmayner/pyphi@main"

Optional features are available as extras: visualize (plotting), caching (Redis-backed caches), emd (earth-mover's-distance measures), xarray (labeled array export), cluster (Dask-based cluster execution), and mcp (the MCP server for AI assistants). Install one or more with, e.g.:

uv pip install "pyphi[visualize,emd]"

Using pip

python -m pip install pyphi                                       # current release
python -m pip install "git+https://github.com/wmayner/pyphi@main" # development version

Contributing

To help develop PyPhi, fork the project on GitHub, clone your fork, and install the runtime extras plus the development tooling with uv:

git clone https://github.com/YOUR_USERNAME/pyphi.git
cd pyphi
uv sync --all-extras --group dev

Common development tasks are defined in the justfile (install just):

just test    # run the test suite
just bench   # run the performance benchmarks
just docs    # build the HTML documentation

The contributing page covers the test suite, changelog fragments, and the documentation build.

User group

For discussion about the software or integrated information theory in general, join the pyphi-users group.

For bug reports and feature requests, use the issues page.

Citation

If you use this software in your research, please cite the papers:

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.

@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}
}

For the theory PyPhi 2.0 implements, cite the IIT 4.0 paper:

Albantakis L, Barbosa L, Findlay G, Grasso M, Haun AM, Marshall W, Mayner WGP, Zaeemzadeh A, Boly M, Juel BE, Sasai S, Fujii K, David I, Hendren J, Lang JP, Tononi G. (2023). Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms. PLOS Computational Biology 19(10): e1011465.

@article{albantakis2023iit4,
  title={Integrated information theory (IIT) 4.0: Formulating the properties of phenomenal existence in physical terms},
  author={Albantakis, Larissa and Barbosa, Leonardo and Findlay, Graham and Grasso, Matteo and Haun, Andrew M and Marshall, William and Mayner, William GP and Zaeemzadeh, Alireza and Boly, Melanie and Juel, Bj{\o}rn E and Sasai, Shuntaro and Fujii, Keiko and David, Isaac and Hendren, Jeremiah and Lang, Jonathan P and Tononi, Giulio},
  journal={PLoS Computational Biology},
  volume={19},
  number={10},
  pages={e1011465},
  year={2023},
  publisher={Public Library of Science},
  doi={10.1371/journal.pcbi.1011465},
  url={https://doi.org/10.1371/journal.pcbi.1011465}
}

For the IIT 3.0 formalism, cite:

Oizumi M, Albantakis L, Tononi G. (2014). From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0. PLOS Computational Biology 10(5): e1003588.

@article{oizumi2014iit3,
  title={From the phenomenology to the mechanisms of consciousness: Integrated Information Theory 3.0},
  author={Oizumi, Masafumi and Albantakis, Larissa and Tononi, Giulio},
  journal={PLoS Computational Biology},
  volume={10},
  number={5},
  pages={e1003588},
  year={2014},
  publisher={Public Library of Science},
  doi={10.1371/journal.pcbi.1003588},
  url={https://doi.org/10.1371/journal.pcbi.1003588}
}

Acknowledgements

The initial version of this project was inspired by a previous project written in MATLAB by L. Albantakis, M. Oizumi, A. Hashmi, A. Nere, U. Olcese, P. Rana, and B. Shababo.

Correspondence

Correspondence regarding the PyPhi software should be directed to Will Mayner, at mayner@wisc.edu.