  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 adjustments 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.
