  In traditional recognition tasks of neural networks, a potential landscape or
cost function guides the system toward patterns using gradient dynamics. That
is not how the brain works as its dynamics is far from equilibrium. We present
an alternative and proof of principle for pattern recovery in a nonequilibrium
model whereby only time-symmetric kinetics are altered. As a mathematical
model, a random walker on a randomly-oriented complete graph is subject to
finite driving in the direction of the arcs. Some vertices of the graph
represent patterns. A first algorithm constructs basins of attraction for these
patterns. A second algorithm updates the time-symmetric factors in the
transition rates, in order for the walker to quickly reach a pattern and remain
there for a sufficiently long time, whenever starting from a vertex in its
basin of attraction.
