  We investigate the spontaneous growth of noise that accompanies the nonlinear
evolution of seeded modulation instability into Fermi-Pasta-Ulam recurrence.
Results from the Floquet linear stability analysis of periodic solutions of the
three-wave truncation are compared with full numerical solutions of the
nonlinear Schr\"odinger equation. The predicted initial stage of noise growth
is in good agreement with simulations, and is expected to provide further
insight in the subsequent dynamics of the field evolution after recurrence
breakup.
