  Many cognitive processes rely on the ability of the brain to hold sequences
of events in short-term memory. Recent studies have revealed that such memory
can be read out from the transient dynamics of a network of neurons. However,
the memory performance of such a network in buffering past information has only
been rigorously estimated in networks of linear neurons. When signal gain is
kept low, so that neurons operate primarily in the linear part of their
response nonlinearity, the memory lifetime is bounded by the square root of the
network size. In this work, I demonstrate that it is possible to achieve a
memory lifetime almost proportional to the network size, "an extensive memory
lifetime", when the nonlinearity of neurons is appropriately utilized. The
analysis of neural activity revealed that nonlinear dynamics prevented the
accumulation of noise by partially removing noise in each time step. With this
error-correcting mechanism, I demonstrate that a memory lifetime of order
$N/\log N$ can be achieved.
