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

TL;DR

This paper rigorously analyzes the fundamental limits of stable memory allocation in the hippocampus, providing mathematical bounds and a neural circuit implementation that aligns with Valiant's neuroidal model.

Contribution

It introduces a formal mathematical framework for hippocampal memory allocation, deriving capacity bounds and demonstrating a feasible neural circuit realization.

Findings

Established fundamental limits for capacity and error probability of SMA

Proved the effectiveness of the neural SMA through simulations

Provided a concrete neuroidal circuit model for stable memory allocation

Abstract

It is believed that hippocampus functions as a memory allocator in brain, the mechanism of which remains unrevealed. In Valiant's neuroidal model, the hippocampus was described as a randomly connected graph, the computation on which maps input to a set of activated neuroids with stable size. Valiant proposed three requirements for the hippocampal circuit to become a stable memory allocator (SMA): stability, continuity and orthogonality. The functionality of SMA in hippocampus is essential in further computation within cortex, according to Valiant's model. In this paper, we put these requirements for memorization functions into rigorous mathematical formulation and introduce the concept of capacity, based on the probability of erroneous allocation. We prove fundamental limits for the capacity and error probability of SMA, in both data-independent and data-dependent settings. We also establish an example of stable memory allocator that can be implemented via neuroidal circuits. Both theoretical bounds and simulation results show that the neural SMA functions well.