A feasible probability and graph model for memory engrams

The capacity of long-term memory seems to be extremely large, capable of storing information spanning almost a lifetime. Why does it have such a vast capacity? Why are some memories so enduring? What is the actual physical form of long-term memory? In the movie Inside Out, it is depicted as individual orbs containing information. Is that really the case? Simply explaining this by saying that the cortex has many neurons, numerous neural connections, and complex electrochemical activity between them is not sufficient to answer these fundamental questions. We need to uncover the theory hidden behind these phenomena. In essence, a neural network is equivalent to a very large directed graph, with a massive number of nodes and directed connections. This paper posits that the physical form of long-term memory is a connected subgraph within this complex directed graph. This subgraph is capable of linking together the disparate fragments of the same event, spread across different sensory cortices, to form associations. This provides a physical realization of the engram theory. The robustness of the connected subgraph and the resources it consumes can explain various memory behaviors. Based on anatomical, brain imaging, and electrophysiological evidence, this paper constructs a probabilistic connectivity model and uses theorems from graph theory to prove the ease of constructing connected subgraphs. Finally, it explains why the potential capacity for memory is immense.