# Provable Compositional Generalization for Object-Centric Learning

arXiv: https://arxiv.org/abs/2310.05327 · HTML: https://mlsanity.com/paper/2310.05327/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 65 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 30 of 47)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [MONet: Unsupervised Scene Decomposition and Representation](https://mlsanity.com/paper/1901.11390/) (2019)
- [Multi-Object Representation Learning with Iterative Variational Inference](https://mlsanity.com/paper/1903.00450/) (2019)
- [Understanding disentangling in β-VAE](https://mlsanity.com/paper/1804.03599/) (2018)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Weakly-Supervised Disentanglement Without Compromises](https://mlsanity.com/paper/2002.02886/) (2020)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [Bridging the Gap to Real-World Object-Centric Learning](https://mlsanity.com/paper/2209.14860/) (2022)
- [Contrastive Learning of Structured World Models](https://mlsanity.com/paper/1911.12247/) (2019)
- [SPACE: Unsupervised Object-Oriented Scene Representation via Spatial Attention and Decomposition](https://mlsanity.com/paper/2001.02407/) (2020)
- [SAVi++: Towards End-to-End Object-Centric Learning from Real-World Videos](https://mlsanity.com/paper/2206.07764/) (2022)
- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA](https://mlsanity.com/paper/2107.10098/) (2021)
- [Illiterate DALL-E Learns to Compose](https://mlsanity.com/paper/2110.11405/) (2021)
- [Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding](https://mlsanity.com/paper/2007.10930/) (2020)
- [ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA](https://mlsanity.com/paper/2002.11537/) (2020)
- [Independent mechanism analysis, a new concept?](https://mlsanity.com/paper/2106.05200/) (2021)
- [The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA](https://mlsanity.com/paper/1905.06642/) (2019)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [On the Identifiability of Nonlinear ICA: Sparsity and Beyond](https://mlsanity.com/paper/2206.07751/) (2022)
- [Weakly Supervised Disentanglement with Guarantees](https://mlsanity.com/paper/1910.09772/) (2019)
- [Generalization and Robustness Implications in Object-Centric Learning](https://mlsanity.com/paper/2107.00637/) (2021)
- [Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICA](https://mlsanity.com/paper/2106.09620/) (2021)

## Built on by (most cited first, 30 of 41)

- [On Provable Length and Compositional Generalization](https://mlsanity.com/paper/2402.04875/) (2024)
- [Position: Understanding LLMs Requires More Than Statistical Generalization](https://mlsanity.com/paper/2405.01964/) (2024)
- [When does compositional structure yield compositional generalization? A kernel theory](https://mlsanity.com/paper/2405.16391/) (2024)
- [Interaction Asymmetry: A General Principle for Learning Composable Abstractions](https://mlsanity.com/paper/2411.07784/) (2024)
- [Zero-Shot Object-Centric Representation Learning](https://mlsanity.com/paper/2408.09162/) (2024)
- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)
- [Deciphering the Role of Representation Disentanglement: Investigating Compositional Generalization in CLIP Models](https://mlsanity.com/paper/2407.05897/) (2024)
- [Compositional Risk Minimization](https://mlsanity.com/paper/2410.06303/) (2024)
- [A Complexity-Based Theory of Compositionality](https://mlsanity.com/paper/2410.14817/) (2024)
- [Does Data Scaling Lead to Visual Compositional Generalization?](https://mlsanity.com/paper/2507.07102/) (2025)
- [Are We Done with Object-Centric Learning?](https://mlsanity.com/paper/2504.07092/) (2025)
- [When and How Does CLIP Enable Domain and Compositional Generalization?](https://mlsanity.com/paper/2502.09507/) (2025)
- [Position: An Empirically Grounded Identifiability Theory Will Accelerate Self-Supervised Learning Research](https://mlsanity.com/paper/2504.13101/) (2025)
- [Scaling can lead to compositional generalization](https://mlsanity.com/paper/2507.07207/) (2025)
- [Object-Centric Pretraining via Target Encoder Bootstrapping](https://mlsanity.com/paper/2503.15141/) (2025)
- [A General Theory for Compositional Generalization](https://mlsanity.com/paper/2405.11743/) (2024)
- [Towards Understanding Extrapolation: a Causal Lens](https://mlsanity.com/paper/2501.09163/) (2025)
- [unMORE: Unsupervised Multi-Object Segmentation via Center-Boundary Reasoning](https://mlsanity.com/paper/2506.01778/) (2025)
- [AXIOM: Learning to Play Games in Minutes with Expanding Object-Centric Models](https://mlsanity.com/paper/2505.24784/) (2025)
- [Nonparametric Identification of Latent Concepts](https://mlsanity.com/paper/2510.00136/) (2025)
- [What Drives Compositional Generalization in Visual Generative Models? The Importance of Continuous Training Objectives](https://mlsanity.com/paper/2510.03075/) (2025)
- [Rule Extrapolation in Language Models: A Study of Compositional Generalization on OOD Prompts](https://mlsanity.com/paper/2409.13728/) (2024)
- [Aligning Generalisation Between Humans and Machines](https://mlsanity.com/paper/2411.15626/) (2024)
- [Neurosymbolic Object-Centric Learning with Distant Supervision](https://mlsanity.com/paper/2506.16129/) (2025)
- [Disentangled Representation Learning via Modular Compositional Bias](https://mlsanity.com/paper/2510.21402/) (2025)
- [Is Generation Required for Data-Efficient Perception?](https://mlsanity.com/paper/2512.08854/) (2025)
- [Learning by Analogy: A Causal Framework for Composition Generalization](https://mlsanity.com/paper/2512.10669/) (2025)
- [Mitigating Simplicity Bias in OOD Detection through Object Co-occurrence Analysis](https://mlsanity.com/paper/2605.07821/) (2026)
- [Next state prediction gives rise to entangled, yet compositional representations of objects](https://mlsanity.com/paper/2410.04940/) (2024)
- [Extrapolation Guarantees for Perturbation Modeling Under the Additive Latent Shift Assumption](https://mlsanity.com/paper/2504.18522/) (2025)

## Abstract (arXiv)

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.