AUTHOR=Xie Kun , Fox Grace E. , Liu Jun , Lyu Cheng , Lee Jason C. , Kuang Hui , Jacobs Stephanie , Li Meng , Liu Tianming , Song Sen , Tsien Joe Z. 

TITLE=Brain Computation Is Organized via Power-of-Two-Based Permutation Logic

JOURNAL=Frontiers in Systems Neuroscience

VOLUME=Volume 10 - 2016

YEAR=2016

URL=https://www.frontiersin.org/journals/systems-neuroscience/articles/10.3389/fnsys.2016.00095

DOI=10.3389/fnsys.2016.00095

ISSN=1662-5137

ABSTRACT=There is considerable scientific interest in understanding how cell assemblies - the long-presumed computational motif - are organized so that the brain can generate cognitive behavior.  The Theory of Connectivity proposes that the origin of intelligence is rooted in a power-of-two-based permutation logic (N=2i–1), giving rise to the specific-to-general cell-assembly organization capable of generating specific perceptions and memories, as well as generalized knowledge and flexible actions.  We show that this power-of-two-based computational logic is widely used in cortical and subcortical circuits across animal species and is conserved for the processing of a variety of cognitive modalities including appetitive, emotional and social cognitions.  However, modulatory neurons, such as dopaminergic neurons, use a simpler logic despite their distinct subtypes.   Interestingly, this specific-to-general permutation logic remained largely intact despite the NMDA receptors – the synaptic switch for learning and memory – were deleted throughout adulthood, suggesting that it is likely developmentally pre-configured.  Moreover, this logic is implemented in the cortex vertically via combining a random-connectivity strategy in superficial layers 2/3 with nonrandom organizations in deep layers 5/6.  This randomness of layers 2/3 cliques – which preferentially encode specific and low-combinatorial features and project inter-cortically – is ideal for maximizing cross-modality novel pattern-extraction, pattern-discrimination, and pattern-categorization using sparse code, consequently explaining why it requires hippocampal offline-consolidation.  In contrast, the non-randomness in layers 5/6 - which consists of few specific cliques but a higher portion of more general cliques projecting mostly to subcortical systems – is ideal for robust feedback-control of motivation, emotion, consciousness, and behaviors.  These observations suggest that the brain’s basic computational algorithm is indeed organized by the power-of-two-based permutation logic.  This simple mathematical logic can account for brain computation across the entire evolutionary spectrum, ranging from the simplest neural networks to the most complex.