  We examine the behaviour of the infrared-radio correlation (IRRC) over the
range $0<z<6$ using new, highly sensitive 3GHz observations with the Karl G.
Jansky Very Large Array (VLA) and infrared data from the Herschel Space
Observatory in the 2deg$^{2}$ COSMOS field. We distinguish between objects
where emission is believed to arise solely from star-formation, and those where
an active galactic nucleus (AGN) is thought to be present. We account for
non-detections in the radio or in the infrared using a doubly-censored survival
analysis. We find that the IRRC of star-forming galaxies, quantified by the
infrared-to-1.4GHz radio luminosity ratio ($q_{\rm TIR}$), decreases with
increasing redshift: $q_{\rm TIR}(z)=(2.88\pm0.03)(1+z)^{-0.19\pm0.01}$.
Moderate-to-high radiative luminosity AGN do not follow the same $q_{\rm
TIR}$$(z)$ trend, having a lower normalisation and steeper decrease with
redshift. We cannot rule out the possibility that unidentified AGN
contributions only to the radio regime may be steepening the observed $q_{\rm
TIR}(z)$ trend of the star-forming population. An increasing fractional
contribution to the observed 3GHz flux by free-free emission of star-forming
galaxies may also affect the derived evolution. However, we find that the
standard (M82-based) assumption of the typical radio spectral energy
distribution (SED) for star-forming galaxies is inconsistent with our results.
This suggests a more complex shape of the typical radio SED for star-forming
galaxies, and that imperfect $K$ corrections in the radio may govern the
derived redshift trend of $q_{\rm TIR}$. Lastly, we present a
redshift-dependent relation between rest-frame 1.4GHz radio luminosity and star
formation rate taking the derived redshift trend into account.
