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Identifiable Object-Centric Representation Learning via Probabilistic Slot Attention
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Proposes probabilistic slot attention that places an aggregate Gaussian mixture prior over slots, proving slot identifiability up to affine transformation and permutation without supervision and without additive decoders.
Problem
Object-centric slot representations lack theoretical identifiability guarantees; existing identifiability results rely on additive decoders and computationally expensive compositional contrast objectives.
Approach
Introduce per-datapoint local GMMs over slots via an EM-style probabilistic slot attention, then aggregate posteriors across the dataset into a global GMM prior over slots; combined with piecewise-affine (leaky-ReLU) weakly injective decoders, this yields slot identifiability up to affine transformation and slot permutation.
Key results
- On the 2D synthetic GMM-of-objects task, PSA achieves SMCC of 0.93 ± 0.04 and R2 of 0.50 ± 0.08, with aggregate posteriors recovered up to affine transformations across runs.
- On Pascal VOC2012 with DINO features, PSA MLP (w/ DINO) with attention masks reaches mBO_i 0.405 and mBO_c 0.436, versus DINOSAUR MLP at 0.395 and 0.409.
- PSA Transformer (w/ DINO) reports mBO_i 0.447 and mBO_c 0.521, competitive with the DINOSAUR Transformer baseline (0.44 and 0.512).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace slot attention with PSA in the DINO MLP setup | DINO MLP on Pascal VOC2012 · Pascal VOC2012 | mBO_c: 0.397 -> 0.422 | Helped |
| Replace slot attention with PSA in the DINO MLP setup | DINO MLP on Pascal VOC2012 · Pascal VOC2012 | mBO_i: 0.384 -> 0.389 | Helped |
| Evaluate using slot attention masks rather than decoder alpha masks (ablation) | PSA MLP (w/ DINO) on Pascal VOC2012 · Pascal VOC2012 | mBO_c: 0.422 -> 0.436 | Helped |
| Evaluate using slot attention masks rather than decoder alpha masks (ablation) | PSA MLP (w/ DINO) on Pascal VOC2012 · Pascal VOC2012 | mBO_i: 0.389 -> 0.405 | Helped |
| Use PSA rather than standard slot attention in the transformer-decoder setup | Transformer decoder on Pascal VOC2012 · Pascal VOC2012 | mBO_i: 0.44 -> 0.447 | Helped |
| Use PSA rather than standard slot attention in the transformer-decoder setup | Transformer decoder on Pascal VOC2012 · Pascal VOC2012 | mBO_c: 0.512 -> 0.521 | Helped |
| Use PSA with a transformer decoder | CLEVR slot representation learning · CLEVR | SMCC | Helped |
| Use PSA with a transformer decoder | CLEVR slot representation learning · CLEVR | R2 | Helped |
Surprising findings
- Compositional contrast was lowest for the framework without being explicitly trained toward it, despite non-additive decoders.
- Non-additive (piecewise affine) decoders with PSA retain higher SMCC and SIS even when compositional contrast does not drop drastically.
Limitations
- Weak injectivity of the mixing function may not hold for all architectures; slot permutation invariance makes the mixing function technically non-invertible.
- Occlusion and bordering objects are not studied.
- Piecewise-affine decoder assumption may be misspecified for real-world data.
Experimental setup
Datasets: SpriteWorld CLEVR ObjectsRoom Pascal VOC2012 synthetic 2D Gaussian mixture of objects
Benchmarks: SpriteWorld CLEVR ObjectsRoom Pascal VOC2012
Metrics: SMCC slot identifiability score (SIS) R2 score FG-ARI FID mBO_i mBO_c compositional contrast
Baselines: Slot Attention MONET SLATE DINOSAUR MLP DINOSAUR Transformer DINO k-means DINO CAE Block Masks Rotating Features
Builds on: Slot Attention Brady et al. compositional contrast identifiability Kivva et al. identifiability of piecewise affine maps DINOSAUR SLATE
Closest papers by meaning
- Grounded Object-Centric Learning (ICLR 2024 · similarity 0.91)
- Adaptive Slot Attention: Object Discovery with Dynamic Slot Number (CVPR 2024 · similarity 0.91)
- GLASS: Guided Latent Slot Diffusion for Object-Centric Learning (CVPR 2025 · similarity 0.89)
- MetaSlot: Break Through the Fixed Number of Slots in Object-Centric Learning (NeurIPS 2025 · similarity 0.88)
- Object-Centric Learning with Slot Mixture Module (ICLR 2024 · similarity 0.88)
- Cycle Consistency Driven Object Discovery (ICLR 2024 · similarity 0.88)
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