ALMA measurements for 93 \(Herschel\)-selected galaxies at \(1.1 \leqslant z \leqslant 1.7\) in COSMOS reveal a sizable (\(>29\)\%) population with compact star formation (SF) sizes, lying on average \(> \times 3.6\) below the optical stellar mass (\(M_{\star}\))-size relation of disks. This sample widely spans the star-forming Main Sequence (MS), having \(10^{8} \leqslant M_{\star} \leqslant 10^{11.5} \ M_{\odot}\) and \(20 \leqslant SFR \leqslant 680 \ M_{\odot} \rm yr^{-1}\). The 32 size measurements and 61 upper limits are measured on ALMA images that combine observations of CO(5-4), CO(4-3), CO(2-1) and \(\lambda_{\rm obs} \sim 1.1-1.3 \ \rm mm\) continuum, all tracing the star-forming molecular gas. These compact galaxies have instead normally extended \(K_{band}\) sizes, suggesting strong specific \(SFR\) gradients. Compact galaxies comprise the \(50\pm18 \%\) of MS galaxies at \(M_{\star} > 10^{11} M_{\odot}\). This is not expected in standard bi-modal scenarios where MS galaxies are mostly steadily-growing extended disks. We suggest that compact MS objects are early post-starburst galaxies in which the merger-driven boost of SF has subsided. They retain their compact SF size until either further gas accretion restores pre-merger galaxy-wide SF, or until becoming quenched. The fraction of merger-affected SF inside the MS seems thus larger than anticipated and might reach \(\sim 50\)\% at the highest \(M_{\star}\). The presence of large galaxies above the MS demonstrates an overall poor correlation between galaxy SF size and specific \(SFR\).