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Provable Compositional Generalization for Object-Centric Learning (2310.05327v2)

Published 9 Oct 2023 in cs.LG

Abstract: Learning representations that generalize to novel compositions of known concepts is crucial for bridging the gap between human and machine perception. One prominent effort is learning object-centric representations, which are widely conjectured to enable compositional generalization. Yet, it remains unclear when this conjecture will be true, as a principled theoretical or empirical understanding of compositional generalization is lacking. In this work, we investigate when compositional generalization is guaranteed for object-centric representations through the lens of identifiability theory. We show that autoencoders that satisfy structural assumptions on the decoder and enforce encoder-decoder consistency will learn object-centric representations that provably generalize compositionally. We validate our theoretical result and highlight the practical relevance of our assumptions through experiments on synthetic image data.

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Authors (6)
  1. Thaddäus Wiedemer (6 papers)
  2. Jack Brady (5 papers)
  3. Alexander Panfilov (8 papers)
  4. Attila Juhos (6 papers)
  5. Matthias Bethge (103 papers)
  6. Wieland Brendel (55 papers)
Citations (12)
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Summary

Insights into Provable Compositional Generalization for Object-Centric Learning

The paper "Provable Compositional Generalization for Object-Centric Learning" endeavors to bridge the gap in compositional generalization between human and machine perception. Object-centric representations are hypothesized to support compositional generalization, yet a precise understanding of when this holds true has been limited. This work presents a theoretical approach to determine the conditions under which compositionally generalizable representations can be learned, alongside an empirical evaluation on synthetic data.

Core Contributions

The paper's primary contribution is establishing conditions in which object-centric representations can be provably generalized compositionally. Leveraging the framework of identifiability, the authors show that autoencoders with particular structural properties enable this form of generalization. Specifically, they define two critical features for success:

  • Additivity of the Decoder: The decoder must exhibit additivity, where each slot is decoded independently and combined via summation.
  • Compositional Consistency: Ensuring that the encoder inverts the decoder both for in-distribution (ID) and out-of-distribution (OOD) inputs through a consistency regularization term.

Methodology and Theoretical Insights

The authors formalize compositional generalization within a latent variable framework. They consider scenarios where the model only encounters combinations of object configurations during training. A set of constraints rooted in identifiability theory is applied, requiring both compositionality and irreducibility in the model's structure.

The authors prove that models meeting these constraints achieve slot identifiability on a defined subset of the latent space. Through this identifiability, the decoder's additivity leads to correct OOD reconstructions. The paper provides theoretical results indicating that the enforcement of compositional consistency is essential for achieving encoder generalization.

Empirical Validation

The empirical section validates the theoretical results using synthetic images generated by the Spriteworld renderer. These experiments show that, without explicit enforcement of additivity and compositional consistency, existing object-centric methods like Slot Attention struggle with OOD generalization. Models trained with these properties demonstrate notable improvements in identifying and reconstructing novel object compositions.

Implications and Future Directions

The implications of this work are profound for the future development of AI systems that can robustly generalize beyond observed data. The results offer a framework for engineers and researchers to design object-representing AI models with strong generalization capabilities by focusing on model architecture and training regularization. The paper advances theoretical understanding, hinting that real-world object-centric learning tools may benefit substantially from employing such structured regularization techniques.

However, the assumptions and modeling choices, such as the exclusion of object occlusion, highlight limitations. Future extensions could explore more sophisticated compositions and interactions within the latent space, potentially accommodating complex real-world scenarios.

Overall, this work lays a foundation for exploring deeper intersections between object-centric representation learning and compositional generalization, charting a path toward more human-like generalization in AI systems.

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