The storage of continuous variables in working memory is hypothesized to be sustained in the brain by the dynamics of recurrent neural networks (RNNs) whose steady states form continuous manifolds. In some cases, it is thought that the synaptic connectivity supports multiple attractor manifolds, each mapped to a different context or task. For example, in hippocampal area CA3, positions in distinct environments are represented by distinct sets of population activity patterns, each forming a continuum. It has been argued that the embedding of multiple continuous attractors in a single RNN inevitably causes detrimental interference: quenched noise in the synaptic connectivity disrupts the continuity of each attractor, replacing it by a discrete set of steady states that can be conceptualized as lying on local minima of an abstract energy landscape. Consequently, population activity patterns exhibit systematic drifts towards one of these discrete minima, thereby degrading the stored memory over time. Here we show that it is possible to dramatically attenuate these detrimental interference effects by adjusting the synaptic weights. Synaptic weight adjustment are derived from a loss function that quantifies the roughness of the energy landscape along each of the embedded attractor manifolds. By minimizing this loss function, the stability of states can be dramatically improved, without compromising the capacity.

Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal's motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing.