iitx

Integrated Information Theory, accelerated in JAX. ⚡

iitx computes integrated information — φ_s, big Φ, and the full cause-effect structure of IIT 3.0 and 4.0 — for any finite discrete dynamical system given as a transition probability matrix. It reproduces the reference implementation PyPhi's numbers on the canonical examples, and does three things PyPhi cannot:

• Parallelize within a system 🚀 — candidate systems, mechanisms, purviews, partitions, and cuts are batched tensor work on CPU, GPU, or TPU, not Python loops.
• Batch across systems 📦 — every analysis is a pure function of (system, state) that composes with jax.vmap: ten thousand systems are one call.
• Differentiate 🎯 — the IIT 4.0 pipeline is differentiable with respect to the system's dynamics, almost everywhere and with exact subgradients: gradient ascent on integrated information itself.

Overview

• General. Binary or multi-valued units, uniform or heterogeneous alphabets, deterministic or stochastic dynamics. Coarse-graining and black-boxing are pure System → System transforms, so macro-level systems feed the unchanged pipeline.
• Faithful. PyPhi (pinned) is the frozen test oracle: the regression suite compares values against generated golden fixtures for both theory versions, including non-binary systems, and every deliberate divergence is a documented finding (docs/notes/oracle-findings.md), never a silent patch.
• Honest about exactness. Everything is exact; the IIT 3.0 earth mover's distances are host linear programs (so 3.0 jits and vmaps but refuses grad loudly), while the IIT 4.0 intrinsic-difference pipeline is pure tensor algebra end to end.

Getting started

import jax
import jax.numpy as jnp

from iitx.measures import iit4
from iitx.system import System

# The standard 3-unit example (OR, COPY, XOR), as a state-by-node TPM.
tpm = jnp.asarray(
	[
		[0.0, 0.0, 0.0],
		[0.0, 0.0, 1.0],
		[1.0, 0.0, 1.0],
		[1.0, 0.0, 0.0],
		[1.0, 1.0, 0.0],
		[1.0, 1.0, 1.0],
		[1.0, 1.0, 1.0],
		[1.0, 1.0, 0.0],
	]
)
system = System.from_state_by_node(tpm)
state = jnp.asarray([1, 0, 0])

# System integrated information and the full Φ-structure.
analysis = iit4.system_phi(system, state)
structure = iit4.phi_structure(system, state)
print(analysis.phi, structure.big_phi)  # 0.415... and 1.0

# Batch over all 8 states of the system in one call.
states = jnp.stack([jnp.asarray([s >> i & 1 for i in range(3)]) for s in range(8)])
batched = jax.vmap(iit4.system_phi, in_axes=(None, 0))(system, states)

# Differentiate φ_s with respect to the dynamics.
gradient = jax.grad(
	lambda tpm: iit4.system_phi(System(tpm, system.shape, system.cm), state).signed_phi
)(system.tpm)

Installation

uv pip install git+https://github.com/maxencefaldor/iitx.git

Requires Python ≥ 3.14. Dependencies: jax, numpy, and POT (the exact earth-mover's-distance backend for IIT 3.0).

Examples

Design

The design documents are part of the repository: docs/design.md (the core abstractions and why), docs/generality.md (the PyPhi-vs-iitx capability table), and docs/glossary.md (one vocabulary, used identically in code and papers). Everything learned the hard way lives in docs/notes/.

Citing iitx

Citation information will accompany the first release.

Contributing

Contributions are welcome — see CONTRIBUTING. Start from the design documents; the tests define correctness.

License

MIT