correlation between stellar mass and SFR, we are thus probing the population responsible for a large fraction the star formation (40-65% depending on the redshift according to the @Bethermin2012b model, see also @Karim2011). Our approach is thus different from @Santini2014 who explore in detail how the SEDs evolve at z$<$2.5 in the SFR-M$_\star$ plane using a combination of UV-derived and 24$\mu$m-derived SFRs. We aim to push our analysis to higher redshifts and we thus use this more simple and redshift-invariant selection to allow an easier interpretation and to limit potential selection biases. In addition to this mass selection, we divide our sample by intervals of redshift. The choice of their size is a compromise between large intervals to have a good signal-to-noise ratio at each wavelength and small intervals to limit the broadening of the SEDs because of redshift evolution within the broad redshift bin.\
We also removed strong starbursts from our sample (sSFR$>$10 sSFR$_{\rm MS}$) and studied them separately. These objects are selected using the photometric catalogs described in Sect.\[data\]. For the sources which are detected at 5$\sigma$ at least in two *Herschel* bands, we fitted the SEDs with the template library of @Magdis2012b allowing the mean intensity of 