Atacama Large Millimeter/submillimeter Array (ALMA) measurements for 93 Herschel-selected galaxies at 1.1 ≤ z ≤ 1.7 in COSMOS reveal a sizable (>29%) population with compact star formation (SF) sizes, lying on average > × 3.6 below the optical stellar mass (M ∗)-size relation of disks. This sample widely spans the star-forming main sequence (MS), having 108 ≤ M ∗ ≤ 1011.5 M o and 20 ≤ star formation rate (SFR) ≤ 680 M o 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 λ obs ∼ 1.1-1.3 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 ± 18% of MS galaxies at M ∗ > 1011 M o. This is not expected in standard bimodal 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 premerger galaxy-wide SF, or until becoming quenched. The fraction of merger-affected SF inside the MS seems thus larger than anticipated and might reach ∼50% at the highest M ∗. The presence of large galaxies above the MS demonstrates an overall poor correlation between galaxy SF size and specific SFR.