Exact solution of transient dynamics for sequential associative memory
model is discussed. The path-integral method and the statistical
neurodynamics can analyze the transient dynamics. The path-integral
method can provide exact solutions of models. However only stationary
states have been discussed for sequential associative memory. In order
to analyze the transient dynamics, we analyze the correlation of
crosstalk noise and derive the exact solution of the transient dynamics.
Surprisingly the exact solution is equivalent to result derived through
the statistical neurodynamics, which assumes that the crosstalk noise is
normally distributed. In order to examine the theoretical finding, we
numerically obtained cumulants of the crosstalk noise. We verify that
the 3rd and 4th-order cumulants are equal to zero, and the crosstalk
noise is normally distributed even in the non-retrieval case. We show
that results obtained by the theory agree with those obtained by the
simulations. Moreover, we found that the macroscopic unstable state
completely coincides with the separatrix.