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Recurrent Complex-Weighted Autoencoders for Unsupervised Object Discovery
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Proposes SynCx, a fully convolutional recurrent autoencoder with complex-valued weights and activations that binds objects via iterative phase updates, achieving unsupervised object discovery on Tetrominoes, dSprites and CLEVR without gating or contrastive losses.
Problem
Unsupervised object discovery via synchrony-based binding is limited by real-valued weights, extra binding mechanisms (gating, cosine binding, contrastive training, depth masks), and reliance on color shortcuts.
Approach
A recurrent fully convolutional autoencoder with complex-valued weights processes complex-valued activations; phases are fed back across iterations (magnitudes clamped to the input image) so binding emerges from complex matrix-vector products and iterative constraint propagation, trained only with reconstruction loss averaged over iterations.
Key results
- SynCx achieves ARI 0.89 on Tetrominoes, outperforming the best synchrony baseline RF (0.42) and CtCAE (0.84), averaged over 5 seeds.
- On dSprites SynCx reaches ARI 0.82 vs RF 0.84; on CLEVR6 SynCx reaches 0.59 vs RF 0.65.
- On grayscale CLEVR6, SynCx achieves ARI 0.45 vs RF 0.22, showing less reliance on color cues; SynCx uses 6-23x fewer parameters than other synchrony baselines (~0.97M).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SynCx instead of CtCAE | unsupervised object discovery models · Tetrominoes | ARI: 0.84 { $\pm$ 0.09} -> 0.89 { $\pm$ 0.01} | Helped |
| use SynCx instead of RF | unsupervised object discovery models · dSprites | ARI: 0.84 { $\pm$ 0.03} -> 0.82 { $\pm$ 0.01} | No clear effect |
| use SynCx instead of RF | unsupervised object discovery models · CLEVR | ARI: 0.65 { $\pm$ 0.01} -> 0.59 { $\pm$ 0.03} | Hurt |
| remove spatial-resolution bottlenecks (ablation) | SynCx · Tetrominoes | ARI: 0.89 { $\pm$ 0.01} -> 0.10 { $\pm$ 0.06} | Hurt |
| increase training iterations from 1 to 2 (ablation) | SynCx · dSprites | ARI: 0.57 { $\pm$ 0.01} -> 0.81 { $\pm$ 0.03} | Helped |
| increase training iterations from 2 to 3 (ablation) | SynCx · dSprites | ARI: 0.81 { $\pm$ 0.03} -> 0.82 { $\pm$ 0.01} | No clear effect |
| increase training iterations from 3 to 4 (ablation) | SynCx · dSprites | ARI: 0.82 { $\pm$ 0.01} -> 0.79 { $\pm$ 0.03} | Hurt |
| increase test-time iterations from 4 to 6 (ablation) | SynCx trained with 3 iterations · dSprites | ARI: 0.81 { $\pm$ 0.01} -> 0.82 { $\pm$ 0.01} | No clear effect |
| use von-Mises rather than zero phase initialization (ablation) | SynCx · Tetrominoes | ARI: 0.74 -> 0.89 { $\pm$ 0.01} | Helped |
| use von-Mises rather than uniform phase initialization (ablation) | SynCx · Tetrominoes | ARI: 0.75 { $\pm$ 0.05} -> 0.89 { $\pm$ 0.01} | Helped |
| use SynCx instead of RF | unsupervised object discovery models · Grayscale CLEVR | ARI: 0.22 { $\pm$ 0.04} -> 0.45 { $\pm$ 0.01} | Helped |
Surprising findings
- Removing the representational bottleneck (stride 1 encoder) gives much lower MSE (6.29e-5) but collapses ARI from 0.89 to 0.10 on Tetrominoes.
- SynCx trails SlotAttention substantially on CLEVR (0.59 vs 0.99), indicating a remaining gap for synchrony-based models.
Limitations
- Performance gap to slot-based SlotAttention remains large, especially on CLEVR.
- Object assignment relies on k-Means with ground-truth cluster count and equal angular variance assumption, causing failures.
- Not yet scaled to more challenging multi-object benchmarks such as MOVi.
Experimental setup
Datasets: Tetrominoes dSprites CLEVR6 (filtered CLEVR) grayscale CLEVR6 (derived)
Benchmarks: Tetrominoes dSprites CLEVR6 grayscale CLEVR6
Metrics: ARI (foreground) MSE
Baselines: CAE CAE++ CtCAE RF SlotAttention
Builds on: Rotating Features (RF) CtCAE modReLU Complex AutoEncoder (CAE)
Closest papers by meaning
- Contrastive Training of Complex-Valued Autoencoders for Object Discovery (NeurIPS 2023 · similarity 0.90)
- Rotating Features for Object Discovery (NeurIPS 2023 · similarity 0.85)
- Finding Distributed Object-Centric Properties in Self-Supervised Transformers (CVPR 2026 · similarity 0.84)
- Universal Sparse Autoencoders: Interpretable Cross-Model Concept Alignment (ICML 2025 · similarity 0.83)
- Continuity-Preserving Convolutional Autoencoders for Learning Continuous Latent Dynamical Models from Images (ICLR 2025 · similarity 0.83)
- Improving Prototypical Visual Explanations with Reward Reweighing, Reselection, and Retraining (ICML 2024 · similarity 0.82)
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