The memory tesseract: Mathematical equivalence between composite and separate storage memory models

Computational memory models can explain the behaviour of human memory in diverse experimental paradigms. But research has produced a profusion of competing models, and, as different models focus on different phenomena, there is no best model. However, by examining commonalities among models, we can move towards theoretical unification. Computational memory models can be grouped into composite and separate storage models. We prove that MINERVA 2, a separate storage model of long-term memory, is mathematically equivalent to composite storage memory implemented as a fourth order tensor, and approximately equivalent to a fourth-order tensor compressed into a holographic vector. Building of these demonstrations, we show that MINERVA 2 and related separate storage models can be implemented in neurons. Our work clarifies the relationship between composite and separate storage models of memory, and thereby moves memory models a step closer to theoretical unification.