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We explore a large uniformly selected sample of H${\alpha}$ selectedstar-forming galaxies (SFGs) at z=0.40,0.84,1.47,2.23 to unveil the evolutionof the star formation rate (SFR) function and the stellar mass function. Wefind strong evolution in the SFR function, with the typical SFR of SFGsdeclining exponentially with time in the last 11Gyrs asSFR$^*$(T[Gyr])=10$^{4.23/T+0.37}$ M$_{\odot}$yr$^{-1}$, but with no evolutionin the faint-end slope, ${\alpha}\approx$-1.6. The stellar mass function ofSFGs, however, reveals little evolution: ${\alpha} \approx$-1.4,M$^*$$\approx$10$^{11.2\pm0.2}$ M$_{\odot}$ and just a slight increase of$\approx$2.3x in ${\Phi}^*$ from z=2.23 to z=0.4. The stellar mass densitywithin SFGs has been roughly constant since z=2.23 at$\approx$10$^{7.65\pm0.08}$ M$_{\odot}$Mpc$^{-3}$, comprising $\approx$100% ofthe stellar mass density in all galaxies at z=2.23, and declining to$\approx$20% by z=0.4, driven by the rise of the passive population. We findthat SFGs with M$\approx$10$^{10.0\pm0.2}$ M$_{\odot}$ contribute most to theSFR density (${\rho}_{\rm SFR}$) per dlog$_{10}$M, and that there is nosignificant evolution in the fractional contribution from SFGs of differentmasses to ${\rho}_{\rm SFR}$ or ${\rho}_{\rm SFR}$(dlog$_{10}$M)$^{-1}$ sincez=2.23. Instead, we show that the decline of SFR$^*$ and of ${\rho}_{\rm SFR}$are primarily driven by an exponential decline in SFRs at all masses. Ourresults have important implications not only on how SFGs need to be quenchedacross cosmic time, but also on the driver(s) of the exponential decline inSFR$^*$ from $\approx$66 M$_{\odot}$yr$^{-1}$ to $\approx$5M$_{\odot}$yr$^{-1}$ since z=2.23.

The stellar mass function of star-forming galaxies and the mass-dependent SFR function since z=2.23 from HiZELS