Provably Learning Object-Centric Representations
This work addresses the lack of theoretical understanding in object-centric learning, which is crucial for improving generalization in machine learning models, though it is incremental as it builds on prior empirical efforts.
The paper tackles the problem of unsupervised object-centric representation learning by introducing theoretical assumptions (compositionality and irreducibility) and proving that ground-truth object representations can be identified under these conditions, with empirical validation on synthetic data and evidence linking theory to existing models.
Learning structured representations of the visual world in terms of objects promises to significantly improve the generalization abilities of current machine learning models. While recent efforts to this end have shown promising empirical progress, a theoretical account of when unsupervised object-centric representation learning is possible is still lacking. Consequently, understanding the reasons for the success of existing object-centric methods as well as designing new theoretically grounded methods remains challenging. In the present work, we analyze when object-centric representations can provably be learned without supervision. To this end, we first introduce two assumptions on the generative process for scenes comprised of several objects, which we call compositionality and irreducibility. Under this generative process, we prove that the ground-truth object representations can be identified by an invertible and compositional inference model, even in the presence of dependencies between objects. We empirically validate our results through experiments on synthetic data. Finally, we provide evidence that our theory holds predictive power for existing object-centric models by showing a close correspondence between models' compositionality and invertibility and their empirical identifiability.