Same Behavior, Different Mechanism: What Finite Experiments Can Certify About Integrated Information
Abstract
Interpretability, AI auditing and assessments of machine consciousness increasingly rest on mechanism-level quantities: functionals of a system's causal transition law that describe how it computes, not what it outputs. Experiments see that law only through finite, partial and noisy interventions. We ask when such a quantity is identifiable from an experiment's access, continuous in the mechanism and certifiable from finite data, and answer exactly for a deliberately demanding case - the integrated information φ of integrated information theory - in stochastic networks of four and five units with known ground truth. Behavior can be silent: a recurrent and a feed-forward network with identical input-output laws at their response delay carry 0.28 and 0 bits, yet internal recordings separate them within 4-53 trials. Partial access can be just as blind: in our examples, units left out of a one-step recording impose precision floors of 0.30-1.02 bits that no sample size lowers, and in all-but-self parity networks, recordings of any length see several hidden units only through the product of their fidelities - a symmetry that one intervention broke in exact checks. The measure has sharp edges: because φ selects a partition, and the cause and effect it specifies, by one criterion and reports another, infinitesimal changes of mechanism that cross an edge change it by 25-100% at 99% of the edges we found in random networks, and about 1% of surrogate models that fit interventional data almost perfectly misreport it by more than 20%. One-sided claims survive: the same data certify a lower bound on both sides of an edge, and we prove φ>1.004 bits throughout a 64-dimensional region of mechanisms and certify it from about 107 controlled transitions with false-certificate probability at most α. Measurability is thus a design question with computable answers.
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BibTeX
@misc{wu2026same,
title = {{Same Behavior, Different Mechanism: What Finite Experiments Can Certify About Integrated Information}},
author = {Linqian Wu and Diaoxuan He},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08469},
eprint = {2611.08469},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08469},
}
RIS
TY - UNPB
TI - Same Behavior, Different Mechanism: What Finite Experiments Can Certify About Integrated Information
AU - Linqian Wu
AU - Diaoxuan He
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08469
UR - https://arxiv.org/abs/2611.08469
AB - Interpretability, AI auditing and assessments of machine consciousness increasingly rest on mechanism-level quantities: functionals of a system's causal transition law that describe how it computes, not what it outputs. Experiments see that law only through finite, partial and noisy interventions. We ask when such a quantity is identifiable from an experiment's access, continuous in the mechanism and certifiable from finite data, and answer exactly for a deliberately demanding case - the integrated information φ of integrated information theory - in stochastic networks of four and five units with known ground truth. Behavior can be silent: a recurrent and a feed-forward network with identical input-output laws at their response delay carry 0.28 and 0 bits, yet internal recordings separate them within 4-53 trials. Partial access can be just as blind: in our examples, units left out of a one-step recording impose precision floors of 0.30-1.02 bits that no sample size lowers, and in all-but-self parity networks, recordings of any length see several hidden units only through the product of their fidelities - a symmetry that one intervention broke in exact checks. The measure has sharp edges: because φ selects a partition, and the cause and effect it specifies, by one criterion and reports another, infinitesimal changes of mechanism that cross an edge change it by 25-100% at 99% of the edges we found in random networks, and about 1% of surrogate models that fit interventional data almost perfectly misreport it by more than 20%. One-sided claims survive: the same data certify a lower bound on both sides of an edge, and we prove φ>1.004 bits throughout a 64-dimensional region of mechanisms and certify it from about 10^7 controlled transitions with false-certificate probability at most α. Measurability is thus a design question with computable answers.
ER -