Star-forming galaxies have been found to follow a relatively tight relation between stellar mass ($M_{*}$) and star formation rate (SFR), dubbed the `star formation sequence. A turnover in the sequence has been observed, where galaxies with $M_{*} < 10^{10} {rm M}_{odot}$ follow a steeper relation than their higher mass counterparts, suggesting that the low-mass slope is (nearly) linear. In this paper, we characterise the properties of the low-mass end of the star formation sequence between $7 leq log M_{*}[{rm M}_{odot}] leq 10.5$ at redshift $0.11 < z < 0.91$. We use the deepest MUSE observations of the Hubble Ultra Deep Field and the Hubble Deep Field South to construct a sample of 179 star-forming galaxies with high signal-to-noise emission lines. Dust-corrected SFRs are determined from H$beta$ $lambda 4861$ and H$alpha$ $lambda 6563$. We model the star formation sequence with a Gaussian distribution around a hyperplane between $log M_{*}$, $log {rm SFR}$, and $log (1+z)$, to simultaneously constrain the slope, redshift evolution, and intrinsic scatter. We find a sub-linear slope for the low-mass regime where $log {rm SFR}[{rm M}_{odot}/{rm yr}] = 0.83^{+0.07}_{-0.06} log M_{*}[{rm M}_{odot}] + 1.74^{+0.66}_{-0.68} log (1+z)$, increasing with redshift. We recover an intrinsic scatter in the relation of $sigma_{rm intr} = 0.44^{+0.05}_{-0.04}$ dex, larger than typically found at higher masses. As both hydrodynamical simulations and (semi-)analytical models typically favour a steeper slope in the low-mass regime, our results provide new constraints on the feedback processes which operate preferentially in low-mass halos.
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