Towards Information-Theoretic Limits of the Global Neuronal Workspace Architecture

Abstract

The global neuronal workspace architecture has been proposed as a biologically plausible computational model for the operation of human consciousness, essentially arguing that signals ow from several perceptual, memory, and attentional regions to a central broadcast medium where certain signals cause a cascade that enters conscious awareness. Separately, the integrated information theory of consciousness has proposed that multivariate information measures that generalize 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 suggesting 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 information measure .

Keywords

• global neuronal workspace theory integrated information theory coding theorem

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Over the last several years, a few di erent kinds of mathematically-oriented theories of consciousness have emerged. One style of theory takes an operational view of consciousness, in terms of the ow of signals and the allocation of attention in the brain. The global neuronal workspace (GNW) model [ 2 ] argues that signals from perception, long-term memory, and evaluative systems are modulated by attention (conscious access) mechanisms and combined in order to produce 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 theory is the integrated information theory (IIT) [ 8 ] for measuring consciousness. The basic idea is that measuring a multivariate information-theoretic quantity called integration ( ) would allow assessment of the extent to which information is interconnected into a uni ed whole rather than split into disconnected parts. Numerous speci c 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 di erent possibilities, of which at least

L. R. Varshney

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 ow A multivariate information measure possible in the global neuronal workspace architecture under suitable reliability objectives 20 are e ciently computable [ 7 ]. The lack of consensus is perhaps since arguments in favor of various measres are axiomatic, rather than based on a speci c connection to an operational interpretation of the information measures.

Dehaene et al. [ 3 ] have recently stated: \A more modest proposal is that and related quantities provide one of many possible signatures of the state of consciousness, simply because they re ect the brain's capacity to broadcast information in the global neuronal workspace, and therefore to entertain a ceaseless stream of episodes of conscious access and conscious processing." Here we formally take up this modest proposal to show that GNW (an operational de nition) and IIT (an informational de nition) are very much intertwined through an understanding of the fundamental limits of information ow 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 pXn ) = X H(Xi) i=1 I(X1; : : : ; Xn) = DKL(pX1;:::;Xn kpX1 H(X1; : : : ; Xn) and its extension to partitioning, the minimum partition information IMP (X1; : : : ; Xn) = min

P 2P jP j 1 1 jP j X H(fXi : i 2 Pj g) j=1

H(X1; : : : ; Xn) de ned using KL divergence or entropy emerge naturally in coding theorems for the capacity of multiple-access channels [ 4 ], secret key distribution in cryptography [ 1 ], and optimal algorithms for unsupervised learning (clustering) [ 5 ]. We are in process of a similar mathematization of the GNW architecture and information ow, and believe IMP will emerge as the fundamental limit and the correct measure for .

Information-theoretic limits have driven technological development of communication systems for decades; we similarly believe a characterization of conscious processing will prove inspirational for the design of future AI systems.

References

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