Network dilution and asymmetry in an efficient brain

Abstract

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. ARTICLE HISTORY

TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State

“…On the other hand, asymmetric and diluted connectivity matrices exhibit optimal storage capacity, meaning that a significant fraction of elements in the connectivity matrix are zero. Such connectivity features are observed in biological cases, such as in the neocortex and hippocampus regions, and are implicated in memory storage and retrial [ 43 , 44 , 45 ].…”

Prediction of Time Series Gene Expression and Structural Analysis of Gene Regulatory Networks Using Recurrent Neural Networks

“…Since our goal is to predict the dynamic of all the genes that belong to the GRN, we built a scheme parallel to the DA-RNN. We use RNNs because we know that these neural networks can store several patterns and that the network structure affects the dynamics and the number of the stored patterns [ 42 , 43 , 44 ].…”

Satisfiability transition in asymmetric neural networks

“…As noted in some of the early physical literature on the subject [3][4][5][6][7], the motivation to do so is twofold. First of all, the symmetric interaction between neurons is not a realistic hypothesis to model biological neural networks [8][9][10][11]: in the brain, neurons are connected through both unidirectional and bidirectional synapses, which can be excitatory or inhibitory. Moreover, beside the interest strictly from the field of Neuroscience, the study of dynamical systems with non-reciprocal couplings is considered crucial in the much broader field of out-of-equilibrium statistical mechanics and its multidisciplinary applications, as pointed out in the context of nonequilibrium critical phenomena [12], dynamical systems [13], replicators models [14,15], multi-agents economy [16,17], ecology [18][19][20][21][22], reporting only a few examples.…”