Recent hydrodynamical simulations predict that stellar feedback in intermediate mass galaxies ( IMGs ) can drive strong fluctuations in structure ( e.g. , half-light radius , R _ { e } ) . This process operates on timescales of only a few hundred Myr and persists even at late cosmic times . One prediction of this quasi-periodic , galactic-scale “ breathing ” is an anti -correlation between star formation rate ( SFR ) and half-light radius as central gas overdensities lead to starbursts whose feedback drags stars to larger radii while star formation dwindles . We test this prediction with a sample of 322 isolated IMGs with stellar masses of 10 ^ { 9.0 } \leq M / M _ { \odot } \leq 10 ^ { 9.5 } at 0.3 < z < 0.4 in the HST I _ { 814 } COSMOS footprint . We find that IMGs with higher specific SFRs ( SSFR > 10 ^ { -10 } yr ^ { -1 } ) are the most extended with median sizes of R _ { e } \sim 3 - 3.4 kpc and are mostly disk-dominated systems . In contrast , IMGs with lower SSFRs ( < 10 ^ { -10 } yr ^ { -1 } ) are a factor of \sim 2 - 3 more compact with median sizes of R _ { e } \sim 0.9 - 1.6 kpc and have more significant bulge contributions to their light . These observed trends are opposite the predictions for stellar feedback that operate via the “ breathing ” process described above . We discuss various paths to reconcile the observations and simulations , all of which likely require a different implementation of stellar feedback in IMGs that drastically changes their predicted formation history .