Intrinsic units: identifying a system's causal grain.

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[1] § Examples › Example 2: coarse-graining ↔ marshall_intrinsic_units/marshall_intrinsic_units.py, lines 418–433 · score 0.50 · horizontal neighbor, vertical neighbor

Paper

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The authors' code

Python · 513 lines · 17 KB · GPL-3.0 · 1 match

import pathlib
import pickle
import matplotlib.pyplot as plt
import numpy as np
import pyphi
import pyphi.utils
import pyphi.visualize
from tqdm.auto import tqdm
_BU_MICRO_SAVEDIR = "results/bu_micro" # "Binary units micro"
_BBX_MACRO_SAVEDIR = "results/bbx_macro" # "Blackbox macro"
_BBX_MICRO_SAVEDIR = "results/bbx_micro" # "Blackbox micro"
_CG_MICRO_SAVEDIR = "results/cg_micro" # "Coarsegrain micro"
_CG_MACRO_SAVEDIR = "results/cg_macro" # "Coarsegrain macro"
_MIN_MICRO_SAVEDIR = "results/min_micro" # "Minimal micro"
_MIN_MACRO_SAVEDIR = "results/min_macro" # "Minimal macro"
_SFN_MICRO_SAVEDIR = "results/sfn_micro" # "Something from nothing"
_SFNN_MICRO_SAVEDIR = "results/sfnn_micro" # "Something from nearly nothing"
_SFS_MICRO_SAVEDIR = "results/sfs_micro" # "Something from something"
def get_subsets_by_size(network):
return {
size: list(
pyphi.utils.powerset(network.node_indices, min_size=size, max_size=size)
)
for size in range(1, len(network.node_indices) + 1)
}
def get_subsystem_string(network, subset):
return "".join(sorted(np.array(network.node_labels)[list(subset)].tolist()))
def run_example(
network,
network_state,
subsystem_size=None,
subsystem_index=None,
verbose=1,
savedir=None,
):
# Create savedir if it does not already exist
if savedir is not None:
savedir = pathlib.Path(savedir)
savedir.mkdir(parents=True, exist_ok=True)
# Get specific subsystems to check
if subsystem_size is not None:
subsets = get_subsets_by_size(network)[subsystem_size]
if subsystem_index is not None:
subsets = [subsets[subsystem_index]]
else: # Check all subsystems
subsets = list(
pyphi.utils.powerset(network.node_indices, nonempty=True, reverse=True)
)
sias = {}
for subset in tqdm(subsets):
# Print progress for user
subsystem_string = get_subsystem_string(network, subset)
if verbose:
print(f"Doing {subsystem_string}...")
# Do actual work
subsystem = pyphi.Subsystem(network, network_state, subset)
sias[subset] = subsystem.sia()
# Print output and save
if verbose == 1:
print(f" φ_s: {[sias[subset].phi]}")
elif verbose >= 2:
print(sias[subset])
if savedir is not None:
with open(savedir / f"{subsystem_string}.pickle", "wb") as f:
pickle.dump(sias[subset], f, protocol=pickle.HIGHEST_PROTOCOL)
def summarize_example(network, savedir):
savedir = pathlib.Path(savedir)
subsets = get_subsets_by_size(network)
with open(savedir / "summary.txt", "w") as f:
for subsystem_size in range(1, len(network.node_indices) + 1):
f.write(f"====={subsystem_size}-node subsystems=====\n")
for subset in subsets[subsystem_size]:
subsystem_string = get_subsystem_string(network, subset)
subsystem_file = savedir / f"{subsystem_string}.pickle"
if subsystem_file.exists():
with open(subsystem_file, "rb") as pf:
sia = pickle.load(pf)
f.write(f"φ_s({subsystem_string}) = {sia.phi}\n")
def run_binary_units_micro_example(savedir=_BU_MICRO_SAVEDIR, **kwargs):
network, network_state = get_binary_units_micro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_binary_units_micro_example(savedir=_BU_MICRO_SAVEDIR):
network, _ = get_binary_units_micro_example()
summarize_example(network, savedir)
def run_blackbox_micro_example(savedir=_BBX_MICRO_SAVEDIR, **kwargs):
network, network_state = get_blackbox_micro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_blackbox_micro_example(savedir=_BBX_MICRO_SAVEDIR):
network, _ = get_blackbox_micro_example()
summarize_example(network, savedir)
def run_blackbox_macro_example(savedir=_BBX_MACRO_SAVEDIR, **kwargs):
network, network_state = get_blackbox_macro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_blackbox_macro_example(savedir=_BBX_MACRO_SAVEDIR):
network, _ = get_blackbox_macro_example()
summarize_example(network, savedir)
def run_coarsegrain_micro_example(savedir=_CG_MICRO_SAVEDIR, **kwargs):
network, network_state = get_coarsegrain_micro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_coarsegrain_micro_example(savedir=_CG_MICRO_SAVEDIR):
network, _ = get_coarsegrain_micro_example()
summarize_example(network, savedir)
def run_coarsegrain_macro_example(savedir=_CG_MACRO_SAVEDIR, **kwargs):
network, network_state = get_coarsegrain_macro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_coarsegrain_macro_example(savedir=_CG_MACRO_SAVEDIR):
network, _ = get_coarsegrain_macro_example()
summarize_example(network, savedir)
def run_minimal_micro_example(savedir=_MIN_MICRO_SAVEDIR, **kwargs):
network, network_state = get_minimal_micro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_minimal_micro_example(savedir=_MIN_MICRO_SAVEDIR):
network, _ = get_minimal_micro_example()
summarize_example(network, savedir)
def run_minimal_macro_example(savedir=_MIN_MACRO_SAVEDIR, **kwargs):
network, network_state = get_minimal_macro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_minimal_macro_example(savedir=_MIN_MACRO_SAVEDIR):
network, _ = get_minimal_macro_example()
summarize_example(network, savedir)
def run_something_from_nothing_micro_example(savedir=_SFN_MICRO_SAVEDIR, **kwargs):
network, network_state = get_something_from_nothing_micro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_something_from_nothing_micro_example(savedir=_SFN_MICRO_SAVEDIR):
network, _ = get_something_from_nothing_micro_example()
summarize_example(network, savedir)
def run_something_from_nearly_nothing_micro_example(
savedir=_SFNN_MICRO_SAVEDIR, **kwargs
):
network, network_state = get_something_from_nearly_nothing_micro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_something_from_nearly_nothing_micro_example(savedir=_SFNN_MICRO_SAVEDIR):
network, _ = get_something_from_nearly_nothing_micro_example()
summarize_example(network, savedir)
def run_something_from_something_micro_example(savedir=_SFS_MICRO_SAVEDIR, **kwargs):
network, network_state = get_something_from_something_micro_example()
run_example(network, network_state, savedir=savedir, **kwargs)
def summarize_something_from_something_micro_example(savedir=_SFS_MICRO_SAVEDIR):
network, _ = get_something_from_something_micro_example()
summarize_example(network, savedir)
def _get_iit4_fig6d_micro_tpm():
node_labels = ("A", "B", "C", "D", "E", "F")
network_size = len(node_labels)
current_states = np.array(list(pyphi.utils.all_states(network_size)))
tpm = np.zeros_like(current_states, dtype=float)
k = 4
for current_state, p in zip(current_states, tpm):
# Convert 0s to -1s for sigmoidal activation function
current_state = np.where(current_state == 0, -1, current_state)
total_input = np.sum(current_state)
prob = 1.0 / (1.0 + np.exp(-k * total_input))
p[:] = prob
return tpm, current_states, node_labels
def get_iit4_fig6d():
tpm, _, node_labels = _get_iit4_fig6d_micro_tpm()
network = pyphi.Network(tpm, node_labels=node_labels)
state = (1, 0, 0, 0, 0, 0)
return network, state
def get_binary_units_micro_example():
tpm = np.array(
[
[1, 1, 1],
[0, 1, 0],
[0, 0, 0],
[1, 1, 0],
[0, 0, 1],
[0, 1, 1],
[1, 0, 1],
[1, 0, 0],
]
)
node_labels = ("A", "B", "C")
network = pyphi.Network(tpm, node_labels=node_labels)
state = (0, 0, 0)
return network, state
def _get_blackbox_example_micro_tpm():
node_labels = ("A", "B", "C", "D", "E", "F", "G", "H")
network_size = len(node_labels)
current_states = np.array(list(pyphi.utils.all_states(network_size)))
tpm = np.zeros_like(current_states, dtype=float)
for current_state, p in zip(current_states, tpm):
p[0] = (
0.01
+ 0.01 * current_state[0]
+ 0.1 * current_state[3]
+ 0.8 * current_state[6]
+ 0.05 * current_state[1]
) # A
p[1] = (
0.01
+ 0.01 * current_state[1]
+ 0.1 * current_state[3]
+ 0.8 * current_state[6]
+ 0.05 * current_state[0]
) # B
p[2] = (
0.01
+ 0.01 * current_state[2]
+ 0.85 * int(current_state[0] + current_state[1] > 0)
+ 0.1 * int(current_state[0] + current_state[1] == 2)
) # C
p[3] = (
0.01
+ 0.01 * current_state[3]
+ 0.85 * current_state[2]
+ 0.05 * (current_state[0] + current_state[1])
) # D
p[4] = (
0.01
+ 0.01 * current_state[4]
+ 0.1 * current_state[7]
+ 0.8 * current_state[2]
+ 0.05 * current_state[5]
) # E
p[5] = (
0.01
+ 0.01 * current_state[5]
+ 0.1 * current_state[7]
+ 0.8 * current_state[2]
+ 0.05 * current_state[4]
) # F
p[6] = (
0.01
+ 0.01 * current_state[6]
+ 0.85 * int(current_state[4] + current_state[5] > 0)
+ 0.1 * int(current_state[4] + current_state[5] == 2)
) # G
p[7] = (
0.01
+ 0.01 * current_state[7]
+ 0.85 * current_state[6]
+ 0.05 * (current_state[4] + current_state[5])
) # H
return tpm, current_states, node_labels
def get_blackbox_micro_example():
tpm, _, node_labels = _get_blackbox_example_micro_tpm()
network = pyphi.Network(tpm, node_labels=node_labels)
state = (1, 1, 1, 1, 1, 1, 1, 1)
return network, state
def _get_blackbox_example_macro_tpm():
micro_tpm, micro_states, _ = _get_blackbox_example_micro_tpm()
tpm = pyphi.convert.sbn2sbs(micro_tpm)
tpm2 = np.dot(tpm, tpm) # Take tau=2
D00 = np.where((micro_states[:, 2] == 0) & (micro_states[:, 6] == 0))[0]
D10 = np.where((micro_states[:, 2] == 1) & (micro_states[:, 6] == 0))[0]
D01 = np.where((micro_states[:, 2] == 0) & (micro_states[:, 6] == 1))[0]
D11 = np.where((micro_states[:, 2] == 1) & (micro_states[:, 6] == 1))[0]
Dalpha0 = np.where(micro_states[:, 2] == 0)[0]
Dalpha1 = np.where(micro_states[:, 2] == 1)[0]
Dbeta0 = np.where(micro_states[:, 6] == 0)[0]
Dbeta1 = np.where(micro_states[:, 6] == 1)[0]
assert micro_tpm.shape[0] == 2**8
assert micro_tpm.shape[1] == 8
macro_network_size = 2
macro_states = np.array(list(pyphi.utils.all_states(macro_network_size)))
macro_tpm = np.zeros_like(macro_states, dtype=float) # state-by-node
macro_node_labels = ("α", "β")
macro_tpm[0, 0] = np.mean(np.sum(tpm2[D00[:, np.newaxis], Dalpha1], axis=1))
macro_tpm[0, 1] = np.mean(np.sum(tpm2[D00[:, np.newaxis], Dbeta1], axis=1))
macro_tpm[1, 0] = np.mean(np.sum(tpm2[D10[:, np.newaxis], Dalpha1], axis=1))
macro_tpm[1, 1] = np.mean(np.sum(tpm2[D10[:, np.newaxis], Dbeta1], axis=1))
macro_tpm[2, 0] = np.mean(np.sum(tpm2[D01[:, np.newaxis], Dalpha1], axis=1))
macro_tpm[2, 1] = np.mean(np.sum(tpm2[D01[:, np.newaxis], Dbeta1], axis=1))
macro_tpm[3, 0] = np.mean(np.sum(tpm2[D11[:, np.newaxis], Dalpha1], axis=1))
macro_tpm[3, 1] = np.mean(np.sum(tpm2[D11[:, np.newaxis], Dbeta1], axis=1))
return macro_tpm, macro_states, macro_node_labels
def get_blackbox_macro_example():
tpm, _, node_labels = _get_blackbox_example_macro_tpm()
network = pyphi.Network(tpm, node_labels=node_labels)
state = (1, 1)
return network, state
def get_coarsegrain_micro_example():
tpm = np.array(
[
[0.05, 0.05, 0.05, 0.05],
[0.06, 0.15, 0.05, 0.05],
[0.15, 0.06, 0.05, 0.05],
[0.16, 0.16, 0.85, 0.85],
[0.05, 0.05, 0.06, 0.15],
[0.06, 0.15, 0.06, 0.15],
[0.15, 0.06, 0.06, 0.15],
[0.16, 0.16, 0.86, 0.95],
[0.05, 0.05, 0.15, 0.06],
[0.06, 0.15, 0.15, 0.06],
[0.15, 0.06, 0.15, 0.06],
[0.16, 0.16, 0.95, 0.86],
[0.85, 0.85, 0.16, 0.16],
[0.86, 0.95, 0.16, 0.16],
[0.95, 0.86, 0.16, 0.16],
[0.96, 0.96, 0.96, 0.96],
]
)
node_labels = ("A", "B", "C", "D")
network = pyphi.Network(tpm, node_labels=node_labels)
state = (0, 0, 0, 0)
return network, state
def get_coarsegrain_macro_example():
tpm = np.array(
[[0.006833, 0.006833], [0.0256, 0.7855], [0.7855, 0.0256], [0.9212, 0.9212]]
)
node_labels = ("α", "β")
network = pyphi.Network(tpm, node_labels=node_labels)
state = (0, 0)
return network, state
def get_minimal_micro_example():
tpm = np.array(
[
[0.05, 0.05],
[0.05, 0.06],
[0.06, 0.05],
[0.95, 0.95],
]
)
node_labels = ("A", "B")
network = pyphi.Network(tpm, node_labels=node_labels)
state = (0, 0)
return network, state
def get_minimal_macro_example():
tpm = np.array([[0.05 * 0.05 + 2 * 0.01 * 0.05 / 3], [(1 - 0.05) * (1 - 0.05)]])
node_labels = ("α",)
network = pyphi.Network(tpm, node_labels=node_labels)
state = (0,)
return network, state
def get_dancing_couple_node(
current_state: np.ndarray,
self_index: int,
horizontal_neighbor: int,
vertical_neighbor: int,
w_vertical: float,
w_base: float = 0.05,
w_self: float = 0.05,
w_horizontal: float = 0.6,
) -> float:
return (
w_base
+ w_self * current_state[self_index]
+ w_horizontal * current_state[horizontal_neighbor]
+ w_vertical * current_state[vertical_neighbor]
)
def get_dancing_couples_network(w_vertical: float) -> np.ndarray:
node_labels = ("A", "B", "C", "D")
connectivity = {
0: {"horizontal_neighbor": 1, "vertical_neighbor": 2},
1: {"horizontal_neighbor": 0, "vertical_neighbor": 3},
2: {"horizontal_neighbor": 3, "vertical_neighbor": 0},
3: {"horizontal_neighbor": 2, "vertical_neighbor": 1},
}
network_size = len(node_labels)
current_states = np.array(list(pyphi.utils.all_states(network_size)))
tpm = np.zeros_like(current_states, dtype=float)
for current_state, p in zip(current_states, tpm):
for i in connectivity:
p[i] = get_dancing_couple_node(
current_state,
i,
connectivity[i]["horizontal_neighbor"],
connectivity[i]["vertical_neighbor"],
w_vertical=w_vertical,
)
return pyphi.Network(tpm, node_labels=node_labels)
def get_something_from_nothing_micro_example():
network = get_dancing_couples_network(w_vertical=0.00)
state = (0, 0, 0, 0)
return network, state
def get_something_from_nearly_nothing_micro_example():
network = get_dancing_couples_network(w_vertical=0.01)
state = (0, 0, 0, 0)
return network, state
def get_something_from_something_micro_example():
network = get_dancing_couples_network(w_vertical=0.25)
state = (0, 0, 0, 0)
return network, state
#### Plotting functions #####
def plot_sbs_tpm(network, use_node_labels=True, height=None):
def _italicize(text):
return "$\it{" + "".join(text) + "}$"
sbs = pyphi.convert.state_by_node2state_by_state(network.tpm)
states_labels = list(pyphi.utils.all_states(network.size))
if use_node_labels:
state_labels = [
pyphi.visualize.phi_structure.text.Labeler(
state, network.node_labels, postprocessor=_italicize
).nodes(network.node_indices)
for state in states_labels
]
figsize = None if height is None else (height, height)
fig, ax = plt.subplots(figsize=figsize)
ax.pcolormesh(sbs, edgecolors="k", linewidth=0.5, cmap="Greys", vmin=0, vmax=1)
ax.tick_params(
top=False,
labeltop=use_node_labels,
bottom=False,
labelbottom=False,
left=False,
labelleft=use_node_labels,
)
if use_node_labels:
ax.set_xticks(
np.arange(len(state_labels)) + 0.5, labels=state_labels, rotation=90
)
ax.set_yticks(np.arange(len(state_labels)) + 0.5, labels=state_labels)
ax.set_aspect("equal")
ax.invert_yaxis()
return fig, ax

marshall_intrinsic_units.py at commit 48471b5, under GPL-3.0 · at the source

Overview

Authors: William Marshall¹, Graham Findlay², Larissa Albantakis², Giulio Tononi²

ORCID iDs: Graham Findlay, Larissa Albantakis

Institutions: Brock University (Canada); University of Wisconsin–Madison (United States)

Journal: Neuroscience of consciousness, volume 2026, issue 1, article niag013

Dates: received 10 January 2025; accepted 13 February 2026; published online 15 April 2026

Type: Research article · Language: English

License: CC BY

Identifiers: DOI 10.1093/nc/niag013 · PMID 41993058 · PMCID PMC13082400 · OpenAlex W7154469130

Open access: gold, a free copy (OpenAlex)

Status: code verified

Categories: computational modeling (no new data) (modality), none (in silico) (organism)

Keywords: theories and models, philosophy, consciousness, computational modeling, integrated information, causal emergence

Topic: Embodied and Extended Cognition (Cognitive Neuroscience, Neuroscience), according to OpenAlex

Funding: Templeton World Charity Foundation (Templeton World Charity Foundation, Inc.) (TWCF 0216); David P White Chair in Sleep Medicine at the University of Wisconsin-Madison; Tiny Blue Dot Foundation (UW 133AAG3451); Natural Sciences and Engineering Research Council of Canada (RGPIN-2019-05418)

Citations: not cited yet (Europe PMC); 49 references in the paper

Abstract

Integrated information theory (IIT) aims to account for the quality and quantity of consciousness in physical terms. According to IIT, a substrate of consciousness must be a system of units (e.g. synapses, neurons, minicolumns, etc.) that is a maximum of intrinsic, specific, unitary cause-effect power, quantified by integrated information (). The grain of each unit must be the one—from micro (finer) to macro (coarser)—that maximizes the system’s integrated information. Here we provide a framework for computing the integrated information of systems whose constituents include macro units, and in doing so provide the means to identify a system’s intrinsic units—those that constitute the system from its intrinsic perspective, and directly account for its experience. First, we formalize what it means for these units, as part of a substrate of consciousness, to satisfy IIT’s postulates of physical existence. Next, we extend the mathematical framework of IIT 4.0 to assess cause-effect power across grains. Then, using simple, simulated systems, we show that the integrated information of systems containing macro units can be higher than that of corresponding systems of micro units. Three examples highlight specific kinds of macro units, and how each kind can increase cause-effect power. The implications of the framework are discussed in the broader context of IIT, including how it provides a foundation for tests and inferences about consciousness.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repositories

Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.

Zenodo 11211435

License: GPL-3.0

State: the link answers, verified on 29 September 2026

Evidence: files inventoried

Size: 1 file

Software Heritage: not checked

Found in: the references

Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation

Tools: Matplotlib (2 files), NumPy (2 files)

Availability: 1 check, the latest on 29 September 2026: the link answers (HTTP 200)

29 September 2026: the link answers (HTTP 200)

15 files

figures.ipynb, Jupyter, 177 lines
marshall_intrinsic_units/__init__.py, Python, 79 lines
marshall_intrinsic_units/marshall_intrinsic_units.py, Python, 513 lines
scripts/run_bbx_macro.py, Python, 4 lines
scripts/run_bbx_micro.py, Python, 12 lines
scripts/run_bu_micro.py, Python, 7 lines
scripts/run_cg_macro.py, Python, 4 lines
scripts/run_cg_micro.py, Python, 4 lines
scripts/run_min_macro.py, Python, 4 lines
scripts/run_min_micro.py, Python, 4 lines
scripts/run_sfn_micro.py, Python, 4 lines
scripts/run_sfnn_micro.py, Python, 4 lines
scripts/run_sfs_micro.py, Python, 4 lines
LICENSE, License, 674 lines
README.md, Text, 21 lines

At the source:

csc-uw/marshall-intrinsic-units

License: GPL-3.0

State: the link answers, verified on 29 September 2026

Evidence: files inventoried

Commit: 48471b5d43e1453ac536cd4d3a5c48820cbe73cc, 22 September 2025

Languages: Python (12), Jupyter (1)

Size: 30 files, 13 scripts

Software Heritage: not archived

Found in: the Zenodo archive record

Holds: README, license file, CITATION.cff, environment (pyproject.toml, uv.lock), 1 notebook

Not found: tests, continuous integration, documentation

Tools: Matplotlib (2 files), NumPy (2 files)

Availability: 1 check, the latest on 29 September 2026: the link answers

29 September 2026: the link answers

15 files

figures.ipynb, Jupyter, 177 lines
marshall_intrinsic_units/__init__.py, Python, 79 lines
marshall_intrinsic_units/marshall_intrinsic_units.py, Python, 513 lines, 1 match
scripts/run_bbx_macro.py, Python, 4 lines
scripts/run_bbx_micro.py, Python, 12 lines
scripts/run_bu_micro.py, Python, 7 lines
scripts/run_cg_macro.py, Python, 4 lines
scripts/run_cg_micro.py, Python, 4 lines
scripts/run_min_macro.py, Python, 4 lines
scripts/run_min_micro.py, Python, 4 lines
scripts/run_sfn_micro.py, Python, 4 lines
scripts/run_sfnn_micro.py, Python, 4 lines
scripts/run_sfs_micro.py, Python, 4 lines
LICENSE, License, 674 lines
README.md, Text, 21 lines

At the source: github.com/CSC-UW/Marshall-Intrinsic-Units/tree/v0.1.2

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
26 scripts, each with its path and the digest of its content;
1 match between paragraphs of the paper and lines of the code (method lexical-v1);
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Data

No dataset and no data link were found in the paper.

Data availability

No new data were generated or analysed in support of this research. All code used to obtain figures and examples can be found at (Findlay and Marshall, 2025).

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 1, 29 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 6 keywords, 4 funders, 43 references.

Cite

This paper

Marshall, W., Findlay, G., Albantakis, L., & Tononi, G. (2026). Intrinsic units: identifying a system's causal grain. Neuroscience of consciousness, 2026(1), niag013. https://doi.org/10.1093/nc/niag013

BibTeX

@article{marshall2026intrinsic, author = {Marshall, William and Findlay, Graham and Albantakis, Larissa and Tononi, Giulio}, title = {{Intrinsic units: identifying a system's causal grain}}, journal = {Neuroscience of consciousness}, year = {2026}, month = apr, volume = {2026}, number = {1}, pages = {niag013}, publisher = {Oxford University Press}, issn = {2057-2107}, doi = {10.1093/nc/niag013}, url = {https://doi.org/10.1093/nc/niag013}, pmid = {41993058}, pmcid = {PMC13082400} }

RIS

TY - JOUR AU - Marshall, William AU - Findlay, Graham AU - Albantakis, Larissa AU - Tononi, Giulio TI - Intrinsic units: identifying a system's causal grain T2 - Neuroscience of consciousness J2 - Neurosci Conscious PY - 2026 DA - 2026/04/15 VL - 2026 IS - 1 SP - niag013 SN - 2057-2107 PB - Oxford University Press DO - 10.1093/nc/niag013 UR - https://doi.org/10.1093/nc/niag013 LA - en ER -

CSL-JSON

{ "id": "10.1093/nc/niag013", "type": "article-journal", "title": "Intrinsic units: identifying a system's causal grain", "container-title": "Neuroscience of consciousness", "author": [ { "family": "Marshall", "given": "William" }, { "family": "Findlay", "given": "Graham" }, { "family": "Albantakis", "given": "Larissa" }, { "family": "Tononi", "given": "Giulio" } ], "container-title-short": "Neurosci Conscious", "volume": "2026", "issue": "1", "page": "niag013", "DOI": "10.1093/nc/niag013", "PMID": "41993058", "PMCID": "PMC13082400", "ISSN": "2057-2107", "publisher": "Oxford University Press", "URL": "https://doi.org/10.1093/nc/niag013", "language": "en", "issued": { "date-parts": [ [ 2026, 4, 15 ] ] } }

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