When Can Intrinsic Causal Integration Be Inferred from Finite Interventions?
Linqian Wu, Diaoxuan He
Zenodo (CERN European Organization for Nuclear Research) November 4, 2026 preprint DOI: 10.5281/zenodo.23967612 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or computational modeling study |
|---|---|
| Population | Small stochastic networks with known ground truth |
| Key points | Argues that whether causal-structure theories of consciousness can be tested depends on experimental design, identifying three conditions: access (internal recordings distinguish networks carrying 0.28 versus 0 bits of integrated information within tens of trials, while input-output data cannot), stability (1.13 bits can collapse to 0.33 bits under arbitrarily small asymmetry), and robustness (integrated information exceeds 1.004 bits across a 64-dimensional region, certifiable from finite interventions). |
Abstract
Theories linking consciousness to the intrinsic causal organization of a system, most notably "Integrated Information Theory" (IIT), hold that how a computation is implemented is as significant as the what is computed. Whether such theories can be tested turns on a concrete question: when can intrinsic causal integration be inferred from finite interventions? Working exactly in small stochastic networks with known truth, we identify three conditions. The first is access. A recurrent and a feedforward network compute the same input-output function yet carry 0.28 and 0 bits of integrated information; input and output never separate them, whereas internal recordings do within tens of trials. Partial recordings can hide a 0.24-bit difference at any sample size, which sets a hard floor on precision. The second is stability. The selection rules that define integrated information create sharp edges, where 1.13 bits collapses to 0.33 bits under an arbitrarily small asymmetry, and finite data recover the high value only under a warranted structural assumption. The third is robustness. We prove that integrated information exceeds 1.004 bits throughout a 64-dimensional region of transition laws, and show that simultaneous confidence sets certify this from finite interventions. Calibration and model checks complete the picture: treating estimated sensor error as exact cut coverage to 35%, and a design with near-best precision was the weakest at detecting a wrong model. These results make the testability of causal-structure theories of consciousness a design question with computable answers, and chart a route from theoretical claims about intrinsic integration to certified experimental evidence.