Bayesian reconstruction of memories stored in neural networks from their connectivity

Comprehensive synaptic wiring diagrams or "connectomes" provide a detailed map of all the neurons and their interconnections in a brain region or even an entire organism. Since the connectome of the nematode C. elegans was obtained using electron microscopy methods in 1986 [1], methods for data acquisition and analysis have both been scaled up and improved significantly. Today, it has become possible to provide connectomes of much more complex systems such as various Drosophila melanogaster circuits [2, 3], or even a large part of its brain [4, 5]; the olfactory bulb of zebrafish [6]; and various pieces of the rodent retina [7-9], hippocampus [10], and cortex [11-14]. While there still remain a number of formidable challenges on the way to the complete connectome of a mammal or even human brain [15], the data sets available today already give rise to a number of intriguing questions. At the same time, it is becoming increasingly clear that new quantitative methods must be developed to fully exploit the new troves of data that connectomics provides [16]. Here, we focus on local neural networks that store information in their synaptic connectivity. It has been hypothesised that cortical networks with their extensive recurrent synaptic connectivity are optimised for this task [17]. A popular model for these networks are attractor neural networks such as the Hopfield's model [18] and various generalisations [19-22], where memories are stored as