A Control-Theoretic Formulation of Global Workspace Theory
Ryota Kanai
q-bio.NC, cs.NE
2026-08-17
A boundary Hankel operator finds workspace-like mediators. Synthetic tests recover the planted set; macaque anesthesia raises mediation gain and cuts input-output alignment.
Global workspace theory says conscious access is a broadcast: selected content becomes available to the rest of a specialist network. The idea shaped cognitive science and a line of AI architectures that insert a workspace module. It still lacks an operational test for which subnetwork is doing the job.
A dense hub can touch many regions and still carry one redundant mode. A receiver can encode activity from elsewhere without sending anything back. A broadcaster can push widely while taking little in. Worse, a set can contain good receivers and good broadcasters with no internal route from what is read to what is written. Separate input and output scores will treat that split aggregate as a workspace.
Kanai treats a candidate set S as an open system sitting inside the remainder R. Finite-horizon reachability asks how R can drive S. Observability asks how S's states show up in R. Their product is a boundary Hankel operator whose singular modes are the internal directions that are jointly reachable from the remainder and observable through it.
The GMW signature has four parts. Potential capacity Cspec is the mediation envelope you would get if receive and send spectra were optimally paired. Alignment Aspec is the fraction of that envelope the actual modes realize. Effective dimensionality Deff tracks how flat the mediation spectrum is. Routed breadth Gpair tracks how evenly mediation energy is spread across specialist source-target pairs. Realized strength Q equals Cspec times Aspec, so large capacity with poor alignment is a system that can absorb one set of variations and emit another. Workspace Mediation Index is a product of the four components used only for fixed-size search. It is not a consciousness score.
The nonlinear extension evaluates the same operator along a trajectory and at finite perturbation amplitude. The coalition that currently instantiates the workspace can switch with context even if the anatomy is fixed. Ignition, in this language, is a rise in alignment that turns latent two-sided capacity into usable global mediation.
The synthetic graph has 64 nodes: four specialist modules, a four-node planted mediator, actuator-only nodes, observer-only nodes, a dense low-rank hub, and a split read/write decoy that glues two actuators to two observers. Among all 635,376 four-node sets, the planted GMW ranks first with WMI 3.242. The split decoy scores 4.107 on an external-access baseline, above the planted set's 3.074, but its WMI falls to 0.245 because Aspec is 0.145: the receive and send directions are nearly orthogonal. The dense hub has Aspec near 1.000 and effective rank 1.002, an aligned one-dimensional bottleneck. Across 50 independently generated networks, width-50 beam search recovered all four planted nodes in 45 runs, with mean Jaccard overlap 0.955.
The macaque ECoG analysis is a proof of application, not a confirmatory test of the theory. Four animals, 11 ketamine-medetomidine days. Median held-out R² for short-lag prediction rose from 0.253 awake to 0.890 under deep anesthesia. At candidate size k=4, the animal-balanced deep/awake ratio was 2.13 for realized mediation Q and 2.36 for Cspec, while Aspec fell to 0.91. Drops in dimensionality, routed breadth, and gain-free organization were clearer at k=5. Raw WMI stayed above 1 at every size because the gain increase outweighed the organizational drop. Recurrently selected awake sites sat across frontal, parietal, temporal, and other association cortex, with no single focus.
Anyone building workspace-style architectures, or scoring "hubs" in neural or artificial graphs, gets an operator that can tell a mediator from a hub and from a one-sided relay. A scalar will read high-gain anesthesia as a stronger workspace. The four-component signature will not. Ignition is also restated as a change in the boundary operator, not as a late potential or a frequency band.
The framework does not model winner-take-most competition among contents, nor endogenous attention as an explicit control policy. The ECoG study is small, four animals, and the fitted operator is 25 ms predictive dynamics, not synaptic causality. Montage, candidate selection, temporal grain, and incomplete coverage all move the numbers. Higher gain and lower alignment under anesthesia is not a consciousness marker. Which signature components are necessary for conscious access remains an empirical question the paper does not answer.