Bayesian reconstruction of memories stored in neural networks from their connectivity

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in a recurrent network of neurons, given its synaptic connectivity matrix. Here, we address this question by determining when solving such an inference problem is theoretically possible in specific attractor network models and by providing a practical algorithm to do so. The algorithm builds on ideas from statistical physics to perform approximate Bayesian inference and is amenable to exact analysis. We study its performance on three different models, compare the algorithm to standard algorithms such as PCA, and explore the limitations of reconstructing stored patterns from synaptic connectivity.Author summary: One of the central hypothesis of neuroscience is that memories are stored in synaptic connectivity. Theoretical models show how large numbers of memories can be stored in recurrent neural circuits thanks to synaptic plasticity mechanisms. Recent advances in serial block-face electron microscopy, and machine learning methods, are making it possible to fully reconstruct the synaptic connectivity of neuronal circuits of increasingly large volumes. Here, we ask the question to what extent it is possible to reconstruct memories stored in a neural circuit from the knowledge of its synaptic connectivity. We present an approximate Bayesian inference algorithm, and study its properties on specific attractor network models.