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Solar flares are explosions in the solar atmosphere that release intense bursts of short-wavelength radiation and are capable of producing severe space-weather consequences. Flares release free energy built up in coronal fields, which are rooted in active regions (ARs) on the photosphere, via magnetic reconnection. The exact processes that lead to reconnection are not fully known and therefore reliable forecasting of flares is challenging. Recently, photospheric magnetic-field data has been extensively analysed using machine learning (ML) and these studies suggest that flare-forecasting accuracy does not strongly depend on how long in advance flares are predicted (Bobra & Couvidat 2015; Raboonik et al. 2017; Huang et al. 2018). Here, we use ML to understand the evolution of AR magnetic fields before and after flares. We explicitly train convolutional neural networks (CNNs) to classify SDO/HMI line-of-sight magnetograms into ARs producing at least one M- or X-class flare or as nonflaring. We find that flaring ARs remain in flare-productive states -- marked by recall >60% with a peak of ~ 80% -- days before and after flares. We use occlusion maps and statistical analysis to show that the CNN pays attention to regions between the opposite polarities from ARs and the CNN output is dominantly decided by the total unsigned line-of-sight flux of ARs. Using synthetic bipole magnetograms, we find spurious dependencies of the CNN output on magnetogram dimensions for a given bipole size. Our results suggest that it is important to use CNN designs that eliminate such artifacts in CNN applications for processing magnetograms and, in general, solar image data.