  We study the specific star formation rate (SSFR) and its evolution at
$z\gtsim 4$, in models of galaxy formation, where the star formation is driven
by cold accretion flows. We show that constant star formation and feedback
efficiencies cannot reproduce the observed trend of SSFR with stellar mass and
its observed lack of evolution at $z>4$. Model galaxies with $\log(M_*) \ltsim
9.5$ M$_{\odot}$ show systematically lower specific star formation rates by
orders of magnitudes, while massive galaxies with M$_* \gtsim 5 \times 10^{10}$
M$_{\odot}$ have up to an order of magnitude larger SSFRs, compared to recent
observations by Stark et al.. To recover these observations we apply an
empirical star formation efficiency in galaxies that scales with the host halo
velocity dispersion as $\propto 1/\sigma^3$ during galaxy mergers. We find that
this modification needs to be of stochastic nature to reproduce the
observations, i.e. only applied during mergers and not during accretion driven
star formation phases. Our choice of star formation efficiency during mergers
allows us to capture both, the boost in star formation at low masses and the
quenching at high masses, and at the same time produce a constant SSFR-stellar
mass relation at $z\gtsim 4$ under the assumption that most of the observed
galaxies are in a merger triggered star formation phase. Our results suggest
that observed high-z low mass galaxies with high SSFRs are likely to be
frequently interacting systems, which experienced bursts in their star
formation rate and efficiency (mode 1), in contrast to low redshift $z \ltsim
3$ galaxies which are cold accretion-regulated star forming systems with lower
star formation efficiencies (mode 2).
