Neural noise limits the fidelity of representations in the brain. This limitation has been extensively analyzed for sensory coding. However, in short-term memory and integrator networks, where noise accumulates and can play an even more prominent role, much less is known about how neural noise interacts with neural and network parameters to determine the accuracy of the computation. Here we analytically derive how the stored memory in continuous attractor networks of probabilistically spiking neurons will degrade over time through diffusion. By combining statistical and dynamical approaches, we establish a fundamental limit on the network’s ability to maintain a persistent state: The noise-induced drift of the memory state over time within the network is strictly lower-bounded by the accuracy of estimation of the network’s instantaneous memory state by an ideal external observer. This result takes the form of an information-diffusion inequality. We derive some unexpected consequences: Despite the persistence time of short-term memory networks, it does not pay to accumulate spikes for longer than the cellular time-constant to read out their contents. For certain neural transfer functions, the conditions for optimal sensory coding coincide with those for optimal storage, implying that short-term memory may be co-localized with sensory representation.

A cognitive map is a suitably structured representation that enables an agent to perform novel computations using prior experience, for instance planning a new route in a familiar space[1,2]. Recent work in mammals has found direct evidence for such structured representations in the presence of exogenous sensory inputs in both spatial[3,4] and non-spatial domains[5-15]. Here, we test a foundational postulate of the original cognitive map theory[1,16] that cognitive maps are recruited endogenously during mental navigation without external input. We recorded from the entorhinal cortex of monkeys in a mental navigation task that required animals to use a joystick to produce one-dimensional vectors between pairs of visual landmarks without sensory feedback about the intermediate landmarks. Animals' ability to perform the task and generalize to new pairs indicated that they relied on a structured representation of the landmarks. Task-modulated neurons exhibited periodicity and ramping that matched the temporal structure of the landmarks. Neuron pairs with high periodicity scores had invariant cross-correlation structure, a signature of grid cell continuous attractor states[17-19]. A basic continuous attractor network model of path integration[20] augmented with a Hebbian learning mechanism provided an explanation of how the system endogenously recalls landmarks. The model also made an unexpected prediction that endogenous landmarks transiently slow down path integration, reset the dynamics, and thereby, reduce variability. Remarkably, this prediction was borne out of a reanalysis of behavior. Together, our findings connect the structured activity patterns in the entorhinal cortex to the endogenous recruitment of a cognitive map during mental navigation.

It is widely believed that persistent neural activity underlies short-term memory. Yet, as we show, the degradation of information stored directly in such networks behaves differently from human short-term memory performance. We build a more general framework where memory is viewed as a problem of passing information through noisy channels whose degradation characteristics resemble those of persistent activity networks. If the brain first encoded the information appropriately before passing the information into such networks, the information can be stored substantially more faithfully. Within this framework, we derive a fundamental lowerbound on recall precision, which declines with storage duration and number of stored items. We show that human performance, though inconsistent with models involving direct (uncoded) storage in persistent activity networks, can be well-fit by the theoretical bound. This finding is consistent with the view that if the brain stores information in patterns of persistent activity, it might use codes that minimize the effects of noise, motivating the search for such codes in the brain.