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https://ceur-ws.org/Vol-2287/short8.pdf
Towards Information-Theoretic Limits of the
Global Neuronal Workspace Architecture
Lav R. Varshney
University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
varshney@illinois.edu
Abstract. The global neuronal workspace architecture has been pro-
posed as a biologically plausible computational model for the opera-
tion of human consciousness, essentially arguing that signals flow from
several perceptual, memory, and attentional regions to a central broad-
cast medium where certain signals cause a cascade that enters conscious
awareness. Separately, the integrated information theory of conscious-
ness has proposed that multivariate information measures Φ that gen-
eralize Shannon’s mutual information capture the level of interaction
among brain regions and therefore measure consciousness. Here, we ask
whether these two theories are in fact two sides of the same coin, by sug-
gesting a mathematical theorem on the operational limits of the global
neuronal workspace, similar to Shannon’s noisy channel coding theorem,
that would naturally be in terms of one particular multivariate informa-
tion measure Φ.
Keywords: global neuronal workspace theory · integrated information
theory · coding theorem.
Over the last several years, a few different kinds of mathematically-oriented
theories of consciousness have emerged. One style of theory takes an operational
view of consciousness, in terms of the flow of signals and the allocation of atten-
tion in the brain. The global neuronal workspace (GNW) model [2] argues that
signals from perception, long-term memory, and evaluative systems are modu-
lated by attention (conscious access) mechanisms and combined in order to pro-
duce actions through the motor system. As part of conscious processing, signals
are also multicast back to the various input systems. The GNW model could
be implemented through the massive connectivity arising from long-distance
cortico-cortical axons, e.g. in prefrontal cortex. Another style of emerging the-
ory is the integrated information theory (IIT) [8] for measuring consciousness.
The basic idea is that measuring a multivariate information-theoretic quantity
called integration (Φ) would allow assessment of the extent to which informa-
tion is interconnected into a unified whole rather than split into disconnected
parts. Numerous specific multivariate information measures have been proposed
as integration, but there is no consensus on which one makes the most sense; a
recent paper by Tegmark suggested 420 different possibilities, of which at least
2 L. R. Varshney
Table 1. Coding Theorems Link the Operational and the Informational.
Operational Informational
Channel Maximum rate we can send C(B) = maxpX :E[b(X)]≤B I(X; Y )
capacity messages over noisy channel
(Shannon, and recover with arbitrarily
1948) low error probability
Consciousness The optimal information flow A multivariate information measure Φ
possible in the global neu-
ronal workspace architecture
under suitable reliability ob-
jectives
20 are efficiently computable [7]. The lack of consensus is perhaps since argu-
ments in favor of various Φ measres are axiomatic, rather than based on a specific
connection to an operational interpretation of the information measures.
Dehaene et al. [3] have recently stated: “A more modest proposal is that
Φ and related quantities provide one of many possible signatures of the state
of consciousness, simply because they reflect the brain’s capacity to broadcast
information in the global neuronal workspace, and therefore to entertain a cease-
less stream of episodes of conscious access and conscious processing.” Here we
formally take up this modest proposal to show that GNW (an operational defi-
nition) and IIT (an informational definition) are very much intertwined through
an understanding of the fundamental limits of information flow in the global
neuronal workspace. The approach is analogous to how Shannon’s noisy channel
coding theorem established equivalence between operational notions of reliable
communication and mutual information quantities [6], see Table 1 for a depiction
of how coding theorems link the operational and the informational.
Interestingly, the multiinformation among random variables X1 , . . . , Xn :
n
X
I(X1 , . . . , Xn ) = DKL (pX1 ,...,Xn kpX1 · · · pXn ) = H(Xi ) − H(X1 , . . . , Xn )
i=1
and its extension to partitioning, the minimum partition information
|P |
1 X
IM P (X1 , . . . , Xn ) = min H({Xi : i ∈ Pj }) − H(X1 , . . . , Xn )
P ∈P |P | − 1
j=1
defined using KL divergence or entropy emerge naturally in coding theorems
for the capacity of multiple-access channels [4], secret key distribution in cryp-
tography [1], and optimal algorithms for unsupervised learning (clustering) [5].
We are in process of a similar mathematization of the GNW architecture and
information flow, and believe IM P will emerge as the fundamental limit and the
correct measure for Φ.
Information-theoretic limits have driven technological development of com-
munication systems for decades; we similarly believe a characterization of con-
scious processing will prove inspirational for the design of future AI systems.
Towards Information-Theoretic Limits 3
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