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It is believed that hippocampus functions as a memory allocator in brain, themechanism of which remains unrevealed. In Valiant's neuroidal model, thehippocampus was described as a randomly connected graph, the computation onwhich maps input to a set of activated neuroids with stable size. Valiantproposed three requirements for the hippocampal circuit to become a stablememory allocator (SMA): stability, continuity and orthogonality. Thefunctionality of SMA in hippocampus is essential in further computation withincortex, according to Valiant's model.  In this paper, we put these requirements for memorization functions intorigorous mathematical formulation and introduce the concept of capacity, basedon the probability of erroneous allocation. We prove fundamental limits for thecapacity and error probability of SMA, in both data-independent anddata-dependent settings. We also establish an example of stable memoryallocator that can be implemented via neuroidal circuits. Both theoreticalbounds and simulation results show that the neural SMA functions well.

Stable Memory Allocation in the Hippocampus: Fundamental Limits and Neural Realization