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Provable Compositional Generalization for Object-Centric Learning
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Proves via identifiability theory that additive autoencoders with a compositional-consistency regularizer learn object-centric slots that generalize compositionally to unseen slot combinations, and validates on synthetic Spriteworld data and Slot Attention ablations.
Problem
When is compositional generalization to unseen combinations of known object slots guaranteed for object-centric representation learning, given training data that covers each slot's values but not all combinations?
Approach
Combines slot identifiability on a slot-supported training subset with an additive decoder (which propagates slot renders to OOD combinations) and a compositional consistency loss that trains the encoder to invert the decoder on synthetically recombined latent slots.
Key results
- Additive decoder plus compositional consistency loss raised Slot Attention OOD identifiability R^2 from 0.81 to 0.94 (with deterministic inference).
- OOD reconstruction R^2 for Slot Attention rose from 0.71 (standard) to 0.92 with additivity, consistency loss, and deterministic encoding.
- OOD slot identifiability is maximized exactly when reconstruction and consistency losses are minimized in the toy additive autoencoder experiments.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace softmax mask normalization with slot-wise sigmoid functions to make the decoder additive (ablation) | Slot Attention · Multi-object dataset, OOD | Identifiability R²: 0.81 -> 0.83 | Helped |
| Replace softmax mask normalization with slot-wise sigmoid functions to make the decoder additive (ablation) | Slot Attention · Multi-object dataset, OOD | Reconstruction R²: 0.71 -> 0.72 | Helped |
| Add compositional consistency loss to the additive decoder variant (ablation) | Slot Attention · Multi-object dataset, OOD | Identifiability R²: 0.83 -> 0.92 | Helped |
| Add compositional consistency loss to the additive decoder variant (ablation) | Slot Attention · Multi-object dataset, OOD | Reconstruction R²: 0.72 -> 0.79 | Helped |
| Use deterministic inference by replacing random slot initialization with fixed initialization (ablation) | Slot Attention with additive decoder and consistency loss · Multi-object dataset, OOD | Identifiability R²: 0.92 -> 0.94 | Helped |
| Use deterministic inference by replacing random slot initialization with fixed initialization (ablation) | Slot Attention with additive decoder and consistency loss · Multi-object dataset, OOD | Reconstruction R²: 0.79 -> 0.92 | Helped |
Surprising findings
- Standard Slot Attention with softmax-normalized masks does not generalize OOD on the synthetic data, even though it identifies slots ID almost perfectly.
- Compositional contrast decreases during training without explicit regularization, so the compositionality constraint need not be optimized explicitly.
Limitations
- Additivity and compositionality prohibit slot interactions during rendering, so general multi-object scenes with occlusion are not modeled.
- Uniform random sampling of OOD slot combinations may produce implausible images (e.g., two background slots).
- Experiments are limited to synthetic two-object Spriteworld data.
Experimental setup
Datasets: synthetic multi-object Spriteworld data
Benchmarks: synthetic multi-object Spriteworld dataset
Metrics: slot identifiability R^2 (ID and OOD) reconstruction R^2 (ID and OOD) compositional contrast
Baselines: Slot Attention (softmax masked decoder) Slot Attention with additive decoder Slot Attention without consistency loss
Builds on: Slot Attention identifiability of compositional generators (Brady et al.) Hungarian algorithm
Closest papers by meaning
- Learning to Compose: Improving Object Centric Learning by Injecting Compositionality (ICLR 2024 · similarity 0.92)
- Unlocking Compositional Generalization in Continual Few-Shot Learning (NeurIPS 2026 · similarity 0.90)
- Does Data Scaling Lead to Visual Compositional Generalization? (ICML 2025 · similarity 0.90)
- Scalable Evaluation and Neural Models for Compositional Generalization (NeurIPS 2025 · similarity 0.88)
- When does compositional structure yield compositional generalization? A kernel theory. (ICLR 2025 · similarity 0.88)
- Scaling can lead to compositional generalization (NeurIPS 2025 · similarity 0.87)
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