  Storing memory for molecular recognition is an efficient strategy for
responding to external stimuli. Biological processes use different strategies
to store memory. In the olfactory cortex, synaptic connections form when
stimulated by an odor, and establish distributed memory that can be retrieved
upon re-exposure. In contrast, the immune system encodes specialized memory by
diverse receptors that recognize a multitude of evolving pathogens. Despite the
mechanistic differences between the olfactory and the immune memory, these
systems can still be viewed as different information encoding strategies. Here,
we present a theoretical framework with artificial neural networks to
characterize optimal memory strategies for both static and dynamic (evolving)
patterns. Our approach is a generalization of the energy-based Hopfield model
in which memory is stored as a network's energy minima. We find that while
classical Hopfield networks with distributed memory can efficiently encode a
memory of static patterns, they are inadequate against evolving patterns. To
follow an evolving pattern, we show that a distributed network should use a
higher learning rate, which in turn, can distort the energy landscape
associated with the stored memory attractors. Specifically, narrow connecting
paths emerge between memory attractors, leading to misclassification of
evolving patterns. We demonstrate that compartmentalized networks with
specialized subnetworks are the optimal solutions to memory storage for
evolving patterns. We postulate that evolution of pathogens may be the reason
for the immune system to encoded a focused memory, in contrast to the
distributed memory used in the olfactory cortex that interacts with mixtures of
static odors.
