Third, weintroduce acomplexitymeasure (seeDefinition 5)thatcharacterizes theoptimal sample complexity of learning in settings (ii) and (iii) above, and we give optimal algorithms for these settings. Finally,wealso provide adaptivelearning algorithms that interpolate between settings (i) and (ii), i.e., whenh is partiallyinvariant.

Learning object-centric representations of complex scenes is a promising step towards enabling efficient abstract reasoning from low-levelperceptual features. Yet, most deep learning approaches learn distributed representations that do not capture the compositional properties of natural scenes.

The recent large-scale text-to-image generative models have attained unprecedented performance, while people establishedadaptor modules like LoRA and DreamBooth to extend this performance to even more unseen concept tokens. However, we empirically find that this workflow often fails to accurately depict the out-of-distributionconcepts. This failure is highly related to the low quality of training data.