  We constrain the slope of the star formation rate ($\log\Psi$) to stellar
mass ($\log\mathrm{M_{\star}}$) relation down to
$\log(\mathrm{M_{\star}/M_{\odot}})=8.4$
($\log(\mathrm{M_{\star}/M_{\odot}})=9.2$) at $z=0.5$ ($z=2.5$) with a
mass-complete sample of 39,106 star-forming galaxies selected from the 3D-HST
photometric catalogs, using deep photometry in the CANDELS fields. For the
first time, we find that the slope is dependent on stellar mass, such that it
is steeper at low masses ($\log\mathrm{\Psi}\propto\log\mathrm{M_{\star}}$)
than at high masses
($\log\mathrm{\Psi}\propto(0.3-0.6)\log\mathrm{M_{\star}}$). These steeper low
mass slopes are found for three different star formation indicators: the
combination of the ultraviolet (UV) and infrared (IR), calibrated from a
stacking analysis of Spitzer/MIPS 24$\mu$m imaging; $\beta$-corrected UV SFRs;
and H$\alpha$ SFRs. The normalization of the sequence evolves differently in
distinct mass regimes as well: for galaxies less massive than
$\log(\mathrm{M_{\star}/M_{\odot}})<10$ the specific SFR
($\Psi/\mathrm{M_{\star}}$) is observed to be roughly self-similar with
$\Psi/\mathrm{M_{\star}}\propto(1+z)^{1.9}$, whereas more massive galaxies show
a stronger evolution with $\Psi/\mathrm{M_{\star}}\propto(1+z)^{2.2-3.5}$ for
$\log(\mathrm{M_{\star}/M_{\odot}})=10.2-11.2$. The fact that we find a steep
slope of the star formation sequence for the lower mass galaxies will help
reconcile theoretical galaxy formation models with the observations. The
results of this study support the analytical conclusions of Leja et al. (2014).
