Network dilution and asymmetry in an efficient brain

The ultimate goal of neuroscience is to ultimately understand how the brain functions. The advancement of brain imaging shows us how the brain continuously alternates complex activity patterns and experimentally reveals how these patterns are responsible for memory, association, reasoning, and countless other tasks. Two fundamental parameters, dilution (the number of connections per node), and symmetry (the number of bidirectional connections of the same weight) characterise two fundamental features underlying the networks that connect the single neurons in the brain and generate these patterns. Mammalian brains show large variations of dilution, and mostly asymmetric connectivity, unfortunately the advantages which drove evolution to these state of network dilution and asymmetry are still unknown. Here, we studied the effects of symmetry and dilution on a discrete-time recurrent neural network with McCulloch–Pitts neurons. We use an exhaustive approach, in which we probe all possible inputs for several randomly connected neuron networks with different degrees of dilution and symmetry. We find an optimum value for the synaptic dilution and symmetry, which turns out to be in striking quantitative agreement with what previous researchers have found in the brain cortex, neocortex and hippocampus. The diluted asymmetric brain shows high memory capacity and pattern recognition speed, but most of all it is the less energy-consumptive with respect to fully connected and symmetric network topologies.