A Control-Theoretic Formulation of Global Workspace Theory
Organizations: Araya Inc., Tokyo, Japan
Abstract
Global workspace theory explains conscious access as the broadcasting of selected information to the rest of the network, but it lacks a formal criterion for identifying the mechanism that enables this access. We propose that a global workspace is a mediator, namely, a subnetwork that receives activity from distributed systems, transforms it through internal modes, and returns differentiated effects to the broader network. We formalize this claim as the Global Mediation Workspace (GMW), a control-theoretic formulation in which a candidate subnetwork is treated as an open system embedded in the remainder of the network. In this framework, reachability characterizes how the remainder can drive the candidate, observability characterizes how candidate states affect the remainder, and a boundary Hankel operator identifies the internal modes linking the two directions. The resulting signature quantifies mediation capacity, input-output alignment, effective dimensionality, and routed source-target breadth, each of which characterizes different components of global workspace. In synthetic benchmarks, we tested whether the signature can distinguish a planted differentiated mediator from dense hubs, one-sided receivers or broadcasters, and a split read/write aggregate with no common internal route. A nonlinear extension characterizes mediation through trajectory-conditioned differential operators, finite-amplitude response profiles, and state-dependent coalitions. As a preliminary application, we estimated the signature from ECoG recordings in four macaques under ketamine anesthesia. We found that input-output alignment was reduced during unconsciousness whereas potential capacity was increased. The GMW thus provides a formal and testable criterion for locating candidate global workspaces in neural recordings and for asking which aspects of mediation is crucial for conscious access.
Figures & tables
| Method family | Dynamics / walk gain | Bidirectional access | Common internal route | Mode rank / alignment | Primary target |
|---|---|---|---|---|---|
| Degree, rich club, participation | Structural hub or connector role | ||||
| Betweenness | shortest paths | Geodesic brokerage | |||
| Communicability / Katz | all walks | Aggregate walk-based access | |||
| Average/modal controllability | input modes only | One-sided actuation capacity | |||
| Sensor/actuator placement | usually | External measurement/control design | |||
| Granger / transfer entropy | data-dependent | directed pairs | usually | Predictive or information transfer |
| Candidate | WMI | |||||
|---|---|---|---|---|---|---|
| GMW | 3.699 | 0.978 | 3.616 | 3.839 | 0.934 | 3.242 |
| Actuator-only | 0.146 | 0.899 | 0.131 | 3.399 | 0.701 | 0.078 |
| Observer-only | 0.112 | 0.965 | 0.108 | 3.477 | 0.860 | 0.080 |
| Degree hub | 2.882 | 1.000 | 2.881 | 1.002 | 0.926 | 0.668 |
| Split I/O decoy | 2.775 | 0.145 | 0.401 | 2.961 | 0.825 | 0.245 |
| Random peripheral | 0.771 | 0.869 | 0.670 | 3.731 | 0.182 | 0.114 |
| Metric | GMW rank | Best disjoint set | Its raw score | Its WMI |
|---|---|---|---|---|
| Weighted strength | 36 | 60,61,62,63 | 33.218 | 0.668 |
| Betweenness | 1 | 0,18,24,63 | 0.268 | 1.204 |
| Participation | 76 | 52,57,61,63 | 2.986 | 0.555 |
| Communicability | 44 | 60,61,62,63 | 21.176 | 0.668 |
| Average controllability | 137 | 60,61,62,63 | 6.060 | 0.668 |
| Modal controllability | 635,365 | 2,3,4,44 | 3.952 | 0.071 |
| Global-workspace requirement | GMW object | Operational interpretation |
|---|---|---|
| Specialists can write to the workspace | , reachability spectrum | Boundary activity can drive distinct internal directions of the candidate |
| Workspace content can be broadcast to specialists | , observability spectrum | Candidate-state differences produce distinguishable effects in the remainder |
| What is admitted is what becomes available | Reachable and observable directions are aligned through the same internal modes | |
| The workspace has usable two-sided capacity | and | Potential receive/send capacity is converted into realized mediation |
| Arbitrary specialist pairs can be linked through a common blackboard | Mediation is distributed across source–target module pairs, not only across incident edges | |
| The workspace is limited but not undifferentiated | and | A compact bottleneck retains several distinguishable mediation modes |
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
| Metric | |||
|---|---|---|---|
| 2.467 [1.659, 3.797] | 2.134 [1.458, 3.571] | 2.346 [1.657, 3.639] | |
| 2.670 [1.735, 4.480] | 2.355 [1.585, 4.253] | 2.642 [1.851, 4.635] | |
| 0.924 [0.848, 0.991] | 0.906 [0.838, 0.980] | 0.888 [0.799, 0.988] | |
| 0.941 [0.818, 1.068] | 0.952 [0.893, 1.025] | 0.906 [0.805, 0.992] | |
| 0.986 [0.668, 1.585] | 0.976 [0.821, 1.160] | 0.831 [0.691, 1.061] | |
| 0.927 [0.547, 1.641] | 0.930 [0.789, 1.095] | 0.753 [0.557, 1.055] |
| Symbol | Meaning |
| Candidate node set and its remainder | |
| Candidate internal, boundary-input, and boundary-output operators | |
| Number of past/future samples and required minimum internal shift | |
| Finite-horizon boundary-reachability and observability matrices | |
| Linear shifted boundary-Hankel operator | |
| Mediation singular values and their sum |
Cognitive Modeling
Cognitive modeling uses computational theories to explain and predict how people perceive, learn, remember, reason, and decide.
See all 120 papers