Context-modular memory networks support high-capacity, flexible, and robust associative memories
Biological memory is known to be flexible -- memory formation and recall depend on factors such as the behavioral context of the organism. However, this property is often ignored in associative memory models. Here, we bring this dynamic nature of memory to the fore by introducing a novel model of associative memory, which we refer to as the context-modular memory network. In our model, stored memory patterns are associated to one of several background network states, or contexts. Memories are accessible when their corresponding context is active, and are otherwise inaccessible. Context modulates the effective network connectivity by imposing a specific configuration of neuronal and synaptic gating - gated neurons (respectively synapses) have their activity (respectively weights) momentarily silenced, thereby reducing interference from memories belonging to other contexts. Memory patterns are randomly and independently chosen, while neuronal and synaptic gates may be selected randomly or optimized through a process of contextual synaptic refinement. Through signal-to-noise and mean field analyses, we show that context-modular memory networks can exhibit substantially increased memory capacity with random neuronal gating, but not with random synaptic gating. For contextual synaptic refinement, we devise a method in which synapses are gated off for a given context if they destabilize the memory patterns in that context, drastically improving memory capacity. Notably, synaptic refinement allows for patterns to be accessible in multiple contexts, stabilizing memory patterns even for weight matrices that do not contain any information about the memory patterns such as Gaussian random matrices. Lastly, we show that context modulates the relative stability of accessible versus inaccessible memories, thereby confirming that contextual control acts as a mechanism to temporarily hide or reveal particular memories. Overall, our model integrates recent ideas about context-dependent memory organization with classic associative memory models, highlights an intriguing trade-off between memory capacity and accessibility, and carries important implications for the understanding of biological memory storage and recall in the brain.