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Measure

iitx.measures.measure

The measure interface: integrated information as a first-class, replaceable object.

A measure maps (system, state) to integrated-information results. Holding the definition of Φ behind one protocol is what lets alternative definitions — theory versions, distances, partition schemes — be expressed, compared, and swapped under one interface (docs/design.md §5).

Measure

Bases: Protocol

A measure of integrated information.

Implementations are frozen dataclasses whose fields are the measure's configuration; both methods are pure and compose with jax.jit and jax.vmap (and, where the measure's mathematics allows, jax.grad).

Source code in src/iitx/measures/measure.py 
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@runtime_checkable
class Measure(Protocol):
	"""A measure of integrated information.

	Implementations are frozen dataclasses whose fields are the measure's configuration;
	both methods are pure and compose with ``jax.jit`` and ``jax.vmap`` (and, where the
	measure's mathematics allows, ``jax.grad``).
	"""

	def phi(self, system: System, state: jax.Array) -> jax.Array:
		"""Compute the measure's headline scalar for a system in a state.

		Args:
			system: The system.
			state: Current state, shape ``(n,)``.

		Returns:
			The scalar value (which quantity it is — φ_s, Φ — is the measure's to
			document).

		"""
		...

	def analyze(self, system: System, state: jax.Array) -> Any:
		"""Compute the measure's full result for a system in a state.

		Args:
			system: The system.
			state: Current state, shape ``(n,)``.

		Returns:
			The measure's result pytree.

		"""
		...

phi(system, state)

Compute the measure's headline scalar for a system in a state.

Parameters:

Name Type Description Default
system System

The system.

 required
state Array

Current state, shape (n,).

 required

Returns:

Type Description
Array

The scalar value (which quantity it is — φ_s, Φ — is the measure's to
Array

document).
Source code in src/iitx/measures/measure.py 
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def phi(self, system: System, state: jax.Array) -> jax.Array:
	"""Compute the measure's headline scalar for a system in a state.

	Args:
		system: The system.
		state: Current state, shape ``(n,)``.

	Returns:
		The scalar value (which quantity it is — φ_s, Φ — is the measure's to
		document).

	"""
	...

analyze(system, state)

Compute the measure's full result for a system in a state.

Parameters:

Name Type Description Default
system System

The system.

 required
state Array

Current state, shape (n,).

 required

Returns:

Type Description
Any

The measure's result pytree.
Source code in src/iitx/measures/measure.py 
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def analyze(self, system: System, state: jax.Array) -> Any:
	"""Compute the measure's full result for a system in a state.

	Args:
		system: The system.
		state: Current state, shape ``(n,)``.

	Returns:
		The measure's result pytree.

	"""
	...

IIT4 dataclass

IIT 4.0 in its canonical configuration (Albantakis et al. 2023).

phi is the system integrated information φ_s (existence); analyze unfolds the full Φ-structure (distinctions, relations, and Φ). Differentiable almost everywhere with respect to the TPM.

Attributes:

Name Type Description
version str

Theory version — "2023" (canonical) or "2026" (the Mayner et al. 2026 intrinsic-information cap on φ_s).
Source code in src/iitx/measures/measure.py 
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@dataclasses.dataclass(frozen=True)
class IIT4:
	"""IIT 4.0 in its canonical configuration (Albantakis et al. 2023).

	``phi`` is the system integrated information φ_s (existence); ``analyze`` unfolds
	the full Φ-structure (distinctions, relations, and Φ). Differentiable almost
	everywhere with respect to the TPM.

	Attributes:
		version: Theory version — ``"2023"`` (canonical) or ``"2026"`` (the Mayner et
			al. 2026 intrinsic-information cap on φ_s).

	"""

	version: str = "2023"

	def phi(self, system: System, state: jax.Array) -> jax.Array:
		"""Compute φ_s.

		Args:
			system: The system.
			state: Current state, shape ``(n,)``.

		Returns:
			System integrated information φ_s, in ibits (clamped at zero; see
			:class:`iitx.measures.iit4.SystemPhi`).

		"""
		return iit4.system_phi(system, state, version=self.version).phi

	def analyze(self, system: System, state: jax.Array) -> iit4.PhiStructure:
		"""Unfold the Φ-structure.

		Args:
			system: The system.
			state: Current state, shape ``(n,)``.

		Returns:
			The Φ-structure.

		"""
		return iit4.phi_structure(system, state, version=self.version)

phi(system, state)

Compute φ_s.

Parameters:

Name Type Description Default
system System

The system.

 required
state Array

Current state, shape (n,).

 required

Returns:

Type Description
Array

System integrated information φ_s, in ibits (clamped at zero; see
Array

class:iitx.measures.iit4.SystemPhi).
Source code in src/iitx/measures/measure.py 
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def phi(self, system: System, state: jax.Array) -> jax.Array:
	"""Compute φ_s.

	Args:
		system: The system.
		state: Current state, shape ``(n,)``.

	Returns:
		System integrated information φ_s, in ibits (clamped at zero; see
		:class:`iitx.measures.iit4.SystemPhi`).

	"""
	return iit4.system_phi(system, state, version=self.version).phi

analyze(system, state)

Unfold the Φ-structure.

Parameters:

Name Type Description Default
system System

The system.

 required
state Array

Current state, shape (n,).

 required

Returns:

Type Description
PhiStructure

The Φ-structure.
Source code in src/iitx/measures/measure.py 
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def analyze(self, system: System, state: jax.Array) -> iit4.PhiStructure:
	"""Unfold the Φ-structure.

	Args:
		system: The system.
		state: Current state, shape ``(n,)``.

	Returns:
		The Φ-structure.

	"""
	return iit4.phi_structure(system, state, version=self.version)

IIT3 dataclass

IIT 3.0 in its canonical configuration (Oizumi et al. 2014).

phi is big Φ — the integrated conceptual information at the minimal unidirectional cut; analyze returns the Φ analysis with the cause-effect structure. Exact EMDs are host linear programs, so this measure does not differentiate (it says so loudly under jax.grad).

Source code in src/iitx/measures/measure.py 
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@dataclasses.dataclass(frozen=True)
class IIT3:
	"""IIT 3.0 in its canonical configuration (Oizumi et al. 2014).

	``phi`` is big Φ — the integrated conceptual information at the minimal
	unidirectional cut; ``analyze`` returns the Φ analysis with the cause-effect
	structure. Exact EMDs are host linear programs, so this measure does not
	differentiate (it says so loudly under ``jax.grad``).
	"""

	def phi(self, system: System, state: jax.Array) -> jax.Array:
		"""Compute big Φ.

		Args:
			system: The system.
			state: Current state, shape ``(n,)``.

		Returns:
			Integrated conceptual information Φ, in bits.

		"""
		return iit3.system_phi(system, state).phi

	def analyze(self, system: System, state: jax.Array) -> iit3.SystemPhi:
		"""Compute the Φ analysis with its cause-effect structure.

		Args:
			system: The system.
			state: Current state, shape ``(n,)``.

		Returns:
			The Φ analysis.

		"""
		return iit3.system_phi(system, state)

phi(system, state)

Compute big Φ.

Parameters:

Name Type Description Default
system System

The system.

 required
state Array

Current state, shape (n,).

 required

Returns:

Type Description
Array

Integrated conceptual information Φ, in bits.
Source code in src/iitx/measures/measure.py 
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def phi(self, system: System, state: jax.Array) -> jax.Array:
	"""Compute big Φ.

	Args:
		system: The system.
		state: Current state, shape ``(n,)``.

	Returns:
		Integrated conceptual information Φ, in bits.

	"""
	return iit3.system_phi(system, state).phi

analyze(system, state)

Compute the Φ analysis with its cause-effect structure.

Parameters:

Name Type Description Default
system System

The system.

 required
state Array

Current state, shape (n,).

 required

Returns:

Type Description
SystemPhi

The Φ analysis.
Source code in src/iitx/measures/measure.py 
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def analyze(self, system: System, state: jax.Array) -> iit3.SystemPhi:
	"""Compute the Φ analysis with its cause-effect structure.

	Args:
		system: The system.
		state: Current state, shape ``(n,)``.

	Returns:
		The Φ analysis.

	"""
	return iit3.system_phi(system, state)