The infrared-radio correlation ( IRRC ) offers a way to assess star formation from radio emission . Multiple studies found the IRRC to decrease with increasing redshift . This may in part be due to the lack of knowledge about the possible radio spectral energy distributions ( SEDs ) of star-forming galaxies . We constrain the radio SED of a complete sample of highly star-forming galaxies ( SFR > 100 \mathrm { M _ { \odot } } / \mathrm { yr } ) based on the VLA-COSMOS 1.4 \mathrm { GHz } Joint and 3 \mathrm { GHz } Large Project catalogs . We reduce archival GMRT 325 \mathrm { MHz } and 610 \mathrm { MHz } observations , broadening the rest-frame frequency range to 0.3 - 15 \mathrm { GHz } . Employing survival analysis and fitting a double power law SED , we find that the slope steepens from a spectral index of \alpha _ { 1 } = 0.51 \pm 0.04 below 4.5 \mathrm { GHz } to \alpha _ { 2 } = 0.98 \pm 0.07 above 4.5 \mathrm { GHz } . Our results suggest that the use of a K-correction assuming a single power-law radio SED for star forming galaxies is likely not the root cause of the IRRC trend .