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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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References (63)
  1. How to grow a mind: Statistics, structure, and abstraction. Science, 331:1279 – 1285, 2011.
  2. What is a cognitive map? organizing knowledge for flexible behavior. Neuron, 100(2):490–509, 2018. ISSN 0896-6273. doi: https://doi.org/10.1016/j.neuron.2018.10.002.
  3. Toward causal representation learning. Proceedings of the IEEE, 109(5):612–634, 2021.
  4. Connectionism and cognitive architecture: A critical analysis. Cognition, 28:3–71, 1988.
  5. Building machines that learn and think like people. Behavioral and Brain Sciences, 40:e253, 2017. doi: 10.1017/S0140525X16001837.
  6. Relational inductive biases, deep learning, and graph networks. ArXiv, abs/1806.01261, 2018.
  7. Inductive biases for deep learning of higher-level cognition. Proceedings of the Royal Society A, 478(2266):20210068, 2022.
  8. On the binding problem in artificial neural networks. arXiv preprint arXiv:2012.05208, 2020.
  9. MONet: Unsupervised Scene Decomposition and Representation, January 2019.
  10. Multi-object representation learning with iterative variational inference. In ICML, volume 97 of Proceedings of Machine Learning Research, pages 2424–2433, 2019.
  11. Object-Centric Learning with Slot Attention. In Advances in Neural Information Processing Systems, volume 33, pages 11525–11538. Curran Associates, Inc., 2020a.
  12. Space: Unsupervised object-oriented scene representation via spatial attention and decomposition. In International Conference on Learning Representations, 2020.
  13. Illiterate DALL-e learns to compose. In International Conference on Learning Representations, 2022.
  14. Savi++: Towards end-to-end object-centric learning from real-world videos. Advances in Neural Information Processing Systems, 35:28940–28954, 2022.
  15. Bridging the gap to real-world object-centric learning. In The Eleventh International Conference on Learning Representations, 2023.
  16. Contrastive learning of structured world models. In International Conference on Learning Representations, 2020.
  17. Nonlinear independent component analysis for principled disentanglement in unsupervised deep learning. ArXiv, abs/2303.16535, 2023.
  18. Provably learning object-centric representations. In Proceedings of the 40th International Conference on Machine Learning, volume 202 of Proceedings of Machine Learning Research, pages 3038–3062. PMLR, 23–29 Jul 2023.
  19. Toward compositional generalization in object-oriented world modeling. In International Conference on Machine Learning, pages 26841–26864. PMLR, 2022.
  20. Learning and generalization of compositional representations of visual scenes. arXiv preprint arXiv:2303.13691, 2023.
  21. Compositional generalization from first principles. arXiv preprint arXiv:2307.05596, 2023.
  22. Compositional scene representation learning via reconstruction: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023.
  23. Nonlinear independent component analysis: Existence and uniqueness results. Neural Networks, 12(3):429–439, 1999. ISSN 0893-6080.
  24. Challenging common assumptions in the unsupervised learning of disentangled representations. In ICML, volume 97 of Proceedings of Machine Learning Research, pages 4114–4124, 2019.
  25. The role of disentanglement in generalisation. In International Conference on Learning Representations, 2021.
  26. Lost in latent space: Examining failures of disentangled models at combinatorial generalisation. In Advances in Neural Information Processing Systems, volume 35, pages 10136–10149. Curran Associates, Inc., 2022.
  27. Visual representation learning does not generalize strongly within the same domain. In International Conference on Learning Representations, 2022.
  28. H. W. Kuhn. The Hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2(1-2):83–97, March 1955. ISSN 00281441, 19319193. doi: 10.1002/nav.3800020109.
  29. Unsupervised feature extraction by time-contrastive learning and nonlinear ICA. In NIPS, pages 3765–3773, 2016.
  30. Nonlinear ICA of temporally dependent stationary sources. In AISTATS, volume 54 of Proceedings of Machine Learning Research, pages 460–469, 2017.
  31. Nonlinear ICA using auxiliary variables and generalized contrastive learning. In AISTATS, volume 89 of Proceedings of Machine Learning Research, pages 859–868, 2019.
  32. Variational autoencoders and nonlinear ICA: A unifying framework. In AISTATS, volume 108 of Proceedings of Machine Learning Research, pages 2207–2217, 2020a.
  33. Ice-beem: Identifiable conditional energy-based deep models based on nonlinear ICA. In Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020b.
  34. Weakly supervised disentanglement with guarantees. In ICLR, 2020.
  35. Weakly-supervised disentanglement without compromises. In ICML, volume 119 of Proceedings of Machine Learning Research, pages 6348–6359, 2020b.
  36. The incomplete rosetta stone problem: Identifiability results for multi-view nonlinear ICA. In Proceedings of the Thirty-Fifth Conference on Uncertainty in Artificial Intelligence, UAI 2019, Tel Aviv, Israel, July 22-25, 2019, volume 115 of Proceedings of Machine Learning Research, pages 217–227, 2019.
  37. Disentanglement via mechanism sparsity regularization: A new principle for nonlinear ica. In First Conference on Causal Learning and Reasoning, 2021.
  38. Towards nonlinear disentanglement in natural data with temporal sparse coding. In ICLR, 2021.
  39. Disentangling identifiable features from noisy data with structured nonlinear ICA. In NeurIPS, pages 1624–1633, 2021.
  40. Self-supervised learning with data augmentations provably isolates content from style. In Advances in Neural Information Processing Systems, volume 34, pages 16451–16467, 2021.
  41. Causal component analysis. ArXiv, abs/2305.17225, 2023.
  42. Independent mechanism analysis, a new concept? Advances in Neural Information Processing Systems, 34:28233–28248, 2021.
  43. When is unsupervised disentanglement possible? In Advances in Neural Information Processing Systems, 2021.
  44. Identifiable deep generative models via sparse decoding. Transactions on Machine Learning Research, 2022. ISSN 2835-8856.
  45. Function classes for identifiable nonlinear independent component analysis. In NeurIPS, 2022.
  46. On the identifiability of nonlinear ICA: sparsity and beyond. In NeurIPS, 2022.
  47. Learning to Extrapolate: A Transductive Approach. In The Eleventh International Conference on Learning Representations, February 2023.
  48. First Steps Toward Understanding the Extrapolation of Nonlinear Models to Unseen Domains. In The Eleventh International Conference on Learning Representations, September 2022.
  49. Additive decoders for latent variables identification and cartesian-product extrapolation. arXiv preprint arXiv:2307.02598, 2023.
  50. Generative replay for compositional visual understanding in the prefrontal-hippocampal circuit. bioRxiv, 2021. doi: 10.1101/2021.06.06.447249.
  51. Replay and compositional computation. Neuron, 111:454–469, 2022.
  52. Constructing future behaviour in the hippocampal formation through composition and replay. bioRxiv, 2023. doi: 10.1101/2023.04.07.536053.
  53. Taming vaes. arXiv preprint arXiv:1810.00597, 2018.
  54. The autoencoding variational autoencoder. Advances in Neural Information Processing Systems, 33:15077–15087, 2020.
  55. Consistency regularization for variational auto-encoders. Advances in Neural Information Processing Systems, 34:12943–12954, 2021.
  56. Exploring the latent space of autoencoders with interventional assays. In Advances in Neural Information Processing Systems, 2022.
  57. Dreamcoder: growing generalizable, interpretable knowledge with wake–sleep bayesian program learning. Philosophical Transactions of the Royal Society A, 381(2251):20220050, 2023.
  58. Object-centric compositional imagination for visual abstract reasoning. In ICLR2022 Workshop on the Elements of Reasoning: Objects, Structure and Causality, 2022.
  59. Spriteworld: A flexible, configurable reinforcement learning environment. https://github.com/deepmind/spriteworld/, 2019.
  60. Generalization and robustness implications in object-centric learning. In International Conference on Machine Learning, 2021.
  61. Understanding disentangling in β𝛽\betaitalic_β-vae, 2018.
  62. Decoupled weight decay regularization. In International Conference on Learning Representations, 2019.
  63. Pytorch: An imperative style, high-performance deep learning library. In NeurIPS, pages 8024–8035, 2019.
Citations (12)
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Summary

  • The paper demonstrates that enforcing additivity in decoders and compositional consistency in encoders yields provable compositional generalization.
  • It establishes a theoretical framework based on identifiability to guarantee slot-level encoding and accurate out-of-distribution reconstructions.
  • Empirical validation on synthetic Spriteworld images shows that models with these structured regularizations outperform traditional methods.

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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