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REVIEW 2 major objections 5 minor 66 references

Hierarchical Compact Clustering Attention (COCA) for Unsupervised Object-Centric Learning

T0 review · 2 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Compactness, not preset slots, drives this unsupervised object segmenter.

desk verdict COCA-Net is a genuinely new compactness-guided hierarchical clustering architecture for object-centric learning with strong synthetic results, but the abstract overclaims dynamic slots and the sequential clustering concealment is not what it says it is. read the letter →

arxiv 2505.02071 v1 pith:TGO6ADEH submitted 2025-05-04 cs.CV cs.LG

Can Küçüksözen , Yücel Yemez This is my paper · ORCID
classification cs.CVcs.LG
keywords object-centriclearningunsupervisedsegmentationcompactnesspriormomentofinertiahierarchicalclusteringslotattentionsequentialscenedecomposition
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes COCA-Net, an unsupervised architecture that discovers objects in an image by clustering pixels hierarchically and, at every step, asking which candidate region is most compact. Its central claim is that a physical notion of compactness, the ratio of a shape's moment of inertia to that of a circle of equal area, identifies the centroid of a distinct object, so that repeatedly selecting the most compact remaining region and concealing it yields one object mask per iteration. The authors argue this spatial inductive bias fixes the main weaknesses of Slot-Attention models: sensitivity to initialization, a hard requirement to preset the number of slots, and poor background segmentation. Across six synthetic datasets and nine metrics, they report that COCA-Net outperforms or matches state-of-the-art baselines, with notably lower variance across training runs and strong masks coming directly from the encoder. If true, this means object-centric learning can rest on an explicit, interpretable notion of objectness rather than on learned slot routing.

What carries the argument

The load-bearing object is the compactness functional $C_i(\Lambda^l_i)$ of Eq. 3, which measures a candidate affinity mask's moment of inertia around node $i$ against that of a disk of equal area; because inertia is minimized at the true centroid, the node at an object's centroid receives the highest compactness score within that object. This single score drives anchor selection in the sequential stick-breaking clustering loop (Eqs. 5a-5d), which in turn determines all cluster assignments in the hierarchy.

What would settle it

Run COCA-Net unsupervised on a synthetic dataset of hollow rings, elongated rods, or U-shaped objects: if the highest-scoring anchor consistently lands away from the object's perceptual center, or on the background, the central premise fails and segmentation accuracy should drop sharply relative to the convex-blob datasets. The check can be made directly by comparing the argmax of Eq. 3 to the true object centroids on such shapes.

Watch

Extended reading notes

Core claim

COCA-Net claims that unsupervised object discovery reduces to a greedy search over compactness. A COCA layer refines pixel features with self-attention, computes an affinity mask for every node in a window, scores each mask with a mass-normalized moment-of-inertia compactness functional (Eq. 3), and then runs a stick-breaking concealing loop (Eqs. 5a-5d): take the highest-scoring remaining mask as the next cluster, mask out its nodes, and repeat until the scope is exhausted. Stacked in a bottom-up hierarchy over non-overlapping windows, this produces a dendrogram of object masks with a variable number of clusters, trained end-to-end with only a pixel-reconstruction loss. The paper reports state-of-the-art or competitive results on Tetrominoes, Multi-dSprites, ObjectsRoom, ShapeStacks, CLEVR6, and CLEVRTex across ARI and mean Segmentation Covering, on both the decoder side and, unusually, the encoder side, with background regions segmented more coherently than by the baselines.

Load-bearing premise

The method assumes that, within any window, the node whose affinity mask is most compact by the moment-of-inertia score is the centroid of a distinct foreground object, and that compactness separates objects from background; this premise is only validated on synthetic scenes of convex, blob-like objects.

Editorial extensions

If this is right

  • Dynamic slot allocation: because clustering stops when the scope is exhausted or drops below a threshold, the number of output masks is not fixed in advance; the COCA-Net-Dyna variant trained on CLEVR6 transfers to CLEVR10 with only a small drop (ARI 0.978 vs 0.985).
  • The encoder alone produces segmentation masks that match or beat decoder masks on most datasets, so the trained hierarchy could be reused as a standalone unsupervised object-centric feature extractor.
  • Background elements are segmented as coherent clusters: with background included in the evaluation, COCA-Net gains roughly thirty ARI points over INV-SA and BOQ-SA on ObjectsRoom, where those baselines collapse to background ARI around 0.6 or lower.
  • Training is more stable: over three seeds COCA-Net shows markedly smaller standard deviation than GEN-v2, INV-SA, and BOQ-SA on nearly every dataset and metric.
  • The windowed hierarchy operates on $U\times U$ windows in parallel with per-layer complexity reducible to $O(N^2\log N)$, making the architecture amenable to parallel implementation and scaling to higher resolutions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A sharp empirical boundary follows from the compactness prior: the method should transfer to real-world images only insofar as objects are convex and blob-like; on elongated, hollow, or heavily concave objects the Eq. 3 anchor selection would likely drift from the perceptual center, a regime the six synthetic benchmarks do not probe.
  • Because the dendrogram is produced deterministically from compactness scores, encoder-side masks could be emitted without a decoder forward pass, suggesting a cheap inference mode for downstream tasks that the paper hints at but does not test.
  • The explicit geometric prior yields a falsifiable prediction that slot-attention models lack: deforming an object (stretching it, adding holes, making it concave) should degrade COCA-Net's anchor selection in a monotone, predictable way, and this degradation could be measured directly on synthetic shape morphs.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper proposes the Compact Clustering Attention (COCA) layer, an attention-based clustering module for unsupervised object-centric learning. COCA scores candidate affinity masks by a moment-of-inertia compactness measure and sequentially selects the most compact mask as an object cluster using a stick-breaking concealment strategy. Stacking these layers forms COCA-Net, which is trained end-to-end with a spatial broadcast decoder. The authors evaluate on six synthetic datasets (Tetrominoes, Multi-dSprites, ObjectsRoom, ShapeStacks, CLEVR6, CLEVRTex) against GEN-v2, INVSA, and BOQSA, reporting decoder and encoder segmentation masks, with and without background, and include ablations for compactness-based versus random anchor selection and for dynamic slot allocation.

Significance. If the results hold, COCA-Net offers a credible alternative to slot-attention models, with particular strengths in encoder-side segmentation, background handling, and lower variance across training runs. The compactness functional is an external geometric measure from the cited literature, not fitted to the data, and evaluation is on held-out test images, so circularity concerns are limited. The ablations in Table 3 and supplementary Tables 9-10 provide machine-checked support for the central design choice of compactness-guided anchor selection. However, the conceptual novelty rests on the claimed stick-breaking concealment mechanism and on the compactness prior; both need closer scrutiny, as detailed below.

major comments (2)
  1. [3.1.5, Eqs. (5a)-(5d) and Algorithm 1] The compactness scores C^l are computed once per layer from the full affinity masks Λ^l (Eq. 3), before sequential clustering begins. Eq. (5a) only multiplies C_{m-1} by the scope Z_{m-1}; it does not recompute Λ^l or C^l on the residual set of unassigned nodes. Consequently, the sentence in Sec. 3.1.5 that this "ensuring that only unassigned nodes (with non-zero scope values) contribute to subsequent calculations" is inaccurate for the anchor-selection signal. A remaining node's compactness score still includes contributions from pixels already assigned to earlier clusters, so the selected anchor may not be the most compact residual shape. This issue is load-bearing because compactness is the only inductive bias for choosing object centroids. The authors should either modify the algorithm to recompute compactness after masking the affinity masks by the scope, or revise the text to state that scores are computed once per layer and provide an experiment or argument demonstrating that stale scores do not degrade anchor selection.
  2. [3.1.5, compactness assumption] The paper assumes, in Sec. 3.1.5, that nodes corresponding to the centroids of distinct objects yield the highest compactness scores within their objects, and that foreground objects are more compact than background regions. This assumption is validated only on synthetic datasets composed of convex, blob-like objects. For elongated, concave, or hollow objects, or when background regions are more compact than foreground, the anchor-selection mechanism would likely fail. Because this compactness prior is the central spatial inductive bias of the method, the authors should either restrict their claims to the considered benchmark, or include a stress test with non-convex shapes (e.g., synthetic objects with holes or elongated structures) to characterize the limits of the approach.
minor comments (5)
  1. [Abstract and Sec. 4.3] The abstract and the concluding paragraph of Sec. 4.3 claim that COCA-Net is "not bound by a predetermined number of object masks," but all main experiments fix the number of output slots to the dataset maximum, and only the COCA-Net-Dyna ablation supports the dynamic-slot claim. Please qualify this claim in the abstract and conclusion.
  2. [Supplementary, Algorithm 1, line 6] In Algorithm 1, line 6 of the supplementary material, the scope update is written as "Zl = Zl ⊙ (1− Πl−1)"; this appears to use an undefined Πl−1. It should be the current cluster mask Πm (or Π appended in the previous line). Please correct the notation.
  3. [Tables 3, 9, 10] Table 3 and the supplementary Tables 9-10 report single-seed results, whereas Tables 1 and 2 report mean ± standard deviation over three seeds. To avoid confusion when comparing these results, the captions should state explicitly that these are single-seed numbers.
  4. [Eq. (3)] Equation (3) includes a summation over j < v without defining the index v in the main text. Please define all summation indices and the range of v.
  5. [Sec. 3.1.4] The text states that "A perfect circle achieves the maximum compactness value of 1," but Eq. (3) evaluates compactness around an arbitrary node i; the maximum may be less than 1 when i is not the centroid of the shape. Please rephrase to clarify that the bound applies when the reference point is the centroid.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the compactness measure is an external geometric prior, and the segmentation claims are benchmarked against held-out ground truth.

full rationale

The paper's derivation chain is self-contained and non-circular. The compactness functional in Eq. 2 and Eq. 3 is an external geometric measure taken from references [39,54,55], not a fitted parameter and not defined in terms of the segmentation targets. The sequential clustering in Eqs. 5a-5d uses that external score to select anchors, and the output masks are evaluated against held-out ground truth on six synthetic datasets, so the central quantitative claims are external comparisons rather than re-statements of the method's inputs. No parameter is fitted to the reported ARI/mSC targets, and the ablation variants (COCA-Net-RAS and COCA-Net-Dyna) alter the algorithm rather than redefining the evaluation metric. The paper's compactness-as-objectness premise is an explicit inductive bias and a possible domain limitation for non-convex objects, but an inductive bias is not circularity: the predicted masks are not equal by construction to the compactness scores or to any fitted training target. The reviewer concern that masking does not recompute compactness on the residual set is a correctness or robustness question about the algorithm, not a circularity, because the output segmentation is still judged against external ground truth. There are no self-citations used as load-bearing evidence, and no uniqueness theorem or prior result by the same authors is invoked to force the method's choices.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim depends mainly on the compactness-as-objectness prior (domain assumption 2) and the learnability of informative feature affinities. There are no invented physical entities. The per-dataset hyperparameters are numerous but conventional for deep learning architectures. No code is shipped, which shifts some of the burden onto the detailed tables in the supplementary.

free parameters (6)
  • Per-layer temperature tau_l = 0.75 to 2.00 across layers/datasets (Table 6)
    Scales Euclidean distances in Eq. 1 before soft-argmin affinity computation; set separately for each layer and dataset.
  • Number of COCA layers L = 2 or 3 depending on dataset (Table 6)
    Depth of the hierarchy; chosen per dataset, affects window counts and cluster counts.
  • Window sizes and per-layer output cluster counts (h_l,w_l,k_l) = See Table 6, e.g., Tetrominoes [[4,4],[8,8]], k=[3,4]
    Determines the non-overlapping partitioning and the maximum number of clusters per window at each level; follows dataset resolution and object counts.
  • ViT-22B refinement stack depth and attention kernel sizes = Table 6, e.g., 2 or 3 ViT layers per COCA layer depending on L
    Controls how much feature refinement happens before clustering; hand-set per dataset.
  • Dyna stopping threshold = 2.5% of initial scope
    Hand-set stopping criterion for the dynamic slot variant COCA-Net-Dyna in Section 4.4 and Supplementary Algorithm 1.
  • Pad and random crop augmentation amount = three pixels
    Section 8.1 states images are padded with a small number of repeated pixels, e.g., three, before random cropping; hand-chosen augmentation.
assumptions (4)
  • standard math A node located at the centroid of its affinity mask's shape yields the maximum compactness score
    Section 3.1.5 invokes this property of moment-of-inertia compactness, citing [39,54,55]; it is a result from the compactness literature, not derived in this paper.
  • domain assumption Foreground objects in the evaluated scenes are more compact and convex than background regions
    Section 3.1.4 motivates compactness scoring by asserting that prominent foreground objects have compact and convex spatial form while background is scattered; this is used to select object anchors via Eq. 3.
  • domain assumption Objects can be recovered by clustering within non-overlapping windows at each hierarchy level and merging across levels
    The COCA-Net partitioning scheme in Section 3.2 assumes pixels of one object that fall in different windows at lower layers are merged correctly at higher layers through mask merging in Section 7.3.
  • domain assumption Soft-argmin with min-max scaling converts Euclidean feature distances into affinity masks whose compactness ranking is informative for objectness
    Section 3.1.3 and Supplementary Eq. 8a-8b define this conversion; the subsequent sequential clustering relies on these affinities producing meaningful candidate object masks.

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Cite this review

Pith. "Pith review of Hierarchical Compact Clustering Attention (COCA) for Unsupervised Object-Centric Learning." pith.science (2026). https://pith.science/paper/TGO6ADEH

@misc{pith2026250502071,
  author       = {Pith},
  title        = {Pith review of: Hierarchical Compact Clustering Attention (COCA) for Unsupervised Object-Centric Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TGO6ADEH}},
  note         = {Machine review of arXiv:2505.02071}
}
read the original abstract

We propose the Compact Clustering Attention (COCA) layer, an effective building block that introduces a hierarchical strategy for object-centric representation learning, while solving the unsupervised object discovery task on single images. COCA is an attention-based clustering module capable of extracting object-centric representations from multi-object scenes, when cascaded into a bottom-up hierarchical network architecture, referred to as COCA-Net. At its core, COCA utilizes a novel clustering algorithm that leverages the physical concept of compactness, to highlight distinct object centroids in a scene, providing a spatial inductive bias. Thanks to this strategy, COCA-Net generates high-quality segmentation masks on both the decoder side and, notably, the encoder side of its pipeline. Additionally, COCA-Net is not bound by a predetermined number of object masks that it generates and handles the segmentation of background elements better than its competitors. We demonstrate COCA-Net's segmentation performance on six widely adopted datasets, achieving superior or competitive results against the state-of-the-art models across nine different evaluation metrics.

Figures

Figures reproduced from arXiv: 2505.02071 by the authors.

Figure 1
Figure 1. Compactness scores obtained for each pixel in the scene, across four different datasets. The transition from bright yellow to [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overall summary of the COCA-Net hierarchy and a single COCA layer. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Qualitative results of the COCA-Net architecture across six datasets examined in this work. For each dataset, we present four [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Visualization of the Non-Overlapping partitioning strategy. [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: Qualitative results obtained for real-world datasets. Slot masks predicted by COCA-Net Encoder are shared for Birds (left) and [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: Qualitative results of COCA-Net on Tetrominoes dataset. Accompanying each input image, we visualize COCA-Net’s recon [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]
Figure 7
Figure 7. Figure 7: Qualitative results of COCA-Net on Multi-dSprites dataset. Accompanying each input image, COCA-Net’s reconstruction, [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]
Figure 8
Figure 8. Figure 8: Qualitative results of COCA-Net on Shapestacks dataset. With each input image, we visualize COCA-Net’s reconstruction, [PITH_FULL_IMAGE:figures/full_fig_p021_8.png]
Figure 9
Figure 9. Figure 9: Qualitative results of COCA-Net on ObjectRoom dataset. With each input image, we visualize COCA-Net’s reconstruction, [PITH_FULL_IMAGE:figures/full_fig_p022_9.png]
Figure 10
Figure 10. Figure 10: Qualitative results of COCA-Net on CLEVR6 dataset. With each input image, we visualize COCA-Net’s reconstruction, [PITH_FULL_IMAGE:figures/full_fig_p023_10.png]
Figure 11
Figure 11. Figure 11: Qualitative results of COCA-Net on CLEVRTex dataset. With each input image, we visualize COCA-Net’s reconstruction, [PITH_FULL_IMAGE:figures/full_fig_p024_11.png]

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Reference graph

Works this paper leans on

66 extracted references · 55 canonical work pages

  1. [1]

    Barron, Fer- ran Marques, and Jitendra Malik

    Pablo Arbelaez, Jordi Pont-Tuset, Jonathan T. Barron, Fer- ran Marques, and Jitendra Malik. Multiscale combinatorial grouping. In Proceedings of the IEEE Conference on Com- puter Vision and Pattern Recognition (CVPR), 2014. 3

    work page 2014

  2. [2]

    Contour detection and hierarchical image seg- mentation

    Pablo Arbel ´aez, Michael Maire, Charless Fowlkes, and Ji- tendra Malik. Contour detection and hierarchical image seg- mentation. IEEE Transactions on Pattern Analysis and Ma- chine Intelligence, 33(5):898–916, 2011. 3

    work page 2011

  3. [3]

    CuVLER: Enhanced Unsupervised Object Discov- eries through Exhaustive Self-Supervised Transformers

    Shahaf Arica, Or Rubin, Sapir Gershov, and Shlomi Laufer. CuVLER: Enhanced Unsupervised Object Discov- eries through Exhaustive Self-Supervised Transformers . In 2024 IEEE/CVF Conference on Computer Vision and Pat- tern Recognition (CVPR), pages 23105–23114, Los Alami- tos, CA, USA, 2024. IEEE Computer Society. 3

    work page 2024

  4. [4]

    Spectral clustering with graph neural networks for graph pooling

    Filippo Maria Bianchi, Daniele Grattarola, and Cesare Alippi. Spectral clustering with graph neural networks for graph pooling. In International Conference on Machine Learning, 2019. 3

    work page 2019

  5. [5]

    Ondrej Biza, Sjoerd Van Steenkiste, Mehdi S. M. Saj- jadi, Gamaleldin Fathy Elsayed, Aravindh Mahendran, and Thomas Kipf. Invariant slot attention: Object discovery with slot-centric reference frames. In Proceedings of the 40th In- ternational Conference on Machine Learning , pages 2507–

    work page

  6. [6]

    Burgess, Lo ¨ıc Matthey, Nicholas Watters, Rishabh Kabra, Irina Higgins, Matthew M

    Christopher P. Burgess, Lo ¨ıc Matthey, Nicholas Watters, Rishabh Kabra, Irina Higgins, Matthew M. Botvinick, and Alexander Lerchner. Monet: Unsupervised scene decompo- sition and representation. ArXiv, abs/1901.11390, 2019. 3, 5

    arXiv 1901

  7. [7]

    HASSOD: Hierarchical adaptive self-supervised ob- ject detection

    Shengcao Cao, Dhiraj Joshi, Liangyan Gui, and Yu-Xiong Wang. HASSOD: Hierarchical adaptive self-supervised ob- ject detection. In Thirty-seventh Conference on Neural In- formation Processing Systems, 2023. 3

    work page 2023

  8. [8]

    SOHES: Self-supervised open- world hierarchical entity segmentation

    Shengcao Cao, Jiuxiang Gu, Jason Kuen, Hao Tan, Ruiyi Zhang, Handong Zhao, Ani Nenkova, Liangyan Gui, Tong Sun, and Yu-Xiong Wang. SOHES: Self-supervised open- world hierarchical entity segmentation. In The Twelfth In- ternational Conference on Learning Representations , 2024. 3

    work page 2024

Show all 66 references
  1. [9]

    Emerg- ing properties in self-supervised vision transformers

    Mathilde Caron, Hugo Touvron, Ishan Misra, Herv’e J’egou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerg- ing properties in self-supervised vision transformers. 2021 IEEE/CVF International Conference on Computer Vision (ICCV), pages 9630–9640, 2021. 3

    2021

  2. [10]

    Spotlight atten- tion: Robust object-centric learning with a spatial locality prior

    Ayush K Chakravarthy, Trang Nguyen, Anirudh Goyal, Yoshua Bengio, and Michael Curtis Mozer. Spotlight atten- tion: Robust object-centric learning with a spatial locality prior. ArXiv, abs/2305.19550, 2023. 2

    2023 arXiv

  3. [11]

    Object representations as fixed points: Training iterative refinement algorithms with implicit differentiation

    Michael Chang, Tom Griffiths, and Sergey Levine. Object representations as fixed points: Training iterative refinement algorithms with implicit differentiation. In Advances in Neu- ral Information Processing Systems , pages 32694–32708. Curran Associates, Inc., 2022. 1, 2

    2022

  4. [12]

    Spatially invariant unsuper- vised object detection with convolutional neural networks

    Eric Crawford and Joelle Pineau. Spatially invariant unsuper- vised object detection with convolutional neural networks. In AAAI Conference on Artificial Intelligence, 2019. 3

    2019

  5. [13]

    Mostafa Dehghani, Josip Djolonga, Basil Mustafa, Piotr Padlewski, Jonathan Heek, Justin Gilmer, Andreas Peter Steiner, Mathilde Caron, Robert Geirhos, Ibrahim Alabdul- mohsin, Rodolphe Jenatton, Lucas Beyer, Michael Tschan- nen, Anurag Arnab, Xiao Wang, Carlos Riquelme Ruiz, M...

    2023

  6. [14]

    Perceptual group to- kenizer: Building perception with iterative grouping

    Zhiwei Deng, Ting Chen, and Yang Li. Perceptual group to- kenizer: Building perception with iterative grouping. In The Twelfth International Conference on Learning Representa- tions, 2024. 3

    2024

  7. [15]

    Dittadi, S

    A. Dittadi, S. S. Papa, M. De Vita, B. Sch¨olkopf, O. Winther, and F. Locatello. Generalization and robustness implications in object-centric learning. In Proceedings of the 39th In- ternational Conference on Machine Learning (ICML), pages 5221–5285. PMLR, 2022. 1, 2, 6, 16

    2022

  8. [16]

    An image is worth 16x16 words: Transformers for image recognition at scale

    Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Syl- vain Gelly, Jakob Uszkoreit, and Neil Houlsby. An image is worth 16x16 words: Transformers for image recognition ...

    2021

  9. [17]

    Kosiorek, Oiwi Parker Jones, and Ingmar Posner

    Martin Engelcke, Adam R. Kosiorek, Oiwi Parker Jones, and Ingmar Posner. Genesis: Generative scene inference and sampling with object-centric latent representations. ArXiv, abs/1907.13052, 2019. 3, 6

    1907 arXiv

  10. [18]

    Genesis-v2: Inferring unordered object representations with- out iterative refinement

    Martin Engelcke, Oiwi Parker Jones, and Ingmar Posner. Genesis-v2: Inferring unordered object representations with- out iterative refinement. In Neural Information Processing Systems, 2021. 3, 5, 6, 7, 8, 16, 18

    2021

  11. [19]

    Everitt, S

    B. Everitt, S. Landau, M. Leese, D. Stahl, and an O’Reilly Media Company Safari. Cluster Analysis, 5th Edition. John Wiley & Sons, 2011. 2

    2011

  12. [20]

    Adap- tive slot attention: Object discovery with dynamic slot num- ber, 2024

    Ke Fan, Zechen Bai, Tianjun Xiao, Tong He, Max Horn, Yanwei Fu, Francesco Locatello, and Zheng Zhang. Adap- tive slot attention: Object discovery with dynamic slot num- ber, 2024. 2

    2024

  13. [21]

    Gonzalez and Richard E

    Rafael C. Gonzalez and Richard E. Woods. Digital Image Processing (3rd Edition). Prentice-Hall, Inc., USA, 2006. 2

    2006

  14. [22]

    On the binding problem in artificial neural networks

    Klaus Greff, Sjoerd van Steenkiste, and J¨urgen Schmidhuber. On the binding problem in artificial neural networks. ArXiv, abs/2012.05208, 2020. 1, 2, 3

    2012 arXiv

  15. [23]

    Fuchs, Ingmar Posner, and Andrea Vedaldi

    Oliver Groth, Fabian B. Fuchs, Ingmar Posner, and Andrea Vedaldi. Shapestacks: Learning vision-based physical intu- ition for generalised object stacking. In Computer Vision – ECCV 2018, pages 724–739, Cham, 2018. Springer Interna- tional Publishing. 6 9

    2018

  16. [24]

    Vision GNN: An image is worth graph of nodes

    Kai Han, Yunhe Wang, Jianyuan Guo, Yehui Tang, and En- hua Wu. Vision GNN: An image is worth graph of nodes. In Advances in Neural Information Processing Systems , 2022. 3

    2022

  17. [25]

    Hastie, R

    T. Hastie, R. Tibshirani, and J.H. Friedman. The Elements of Statistical Learning: Data Mining, Inference, and Predic- tion. Springer, 2009. 2

    2009

  18. [26]

    Comparing partitions

    Lawrence Hubert and Phipps Arabie. Comparing partitions. Journal of Classification, 2(1):193–218, 1985. 6

    1985

  19. [27]

    Jain and Richard C

    Anil K. Jain and Richard C. Dubes. Algorithms for clustering data. 1988. 2

    1988

  20. [28]

    Improving object- centric learning with query optimization

    Baoxiong Jia, Yu Liu, and Siyuan Huang. Improving object- centric learning with query optimization. InThe Eleventh In- ternational Conference on Learning Representations , 2023. 1, 2, 6, 7, 8, 16, 18

    2023

  21. [29]

    Scalor: Generative world models with scal- able object representations

    Jindong Jiang, Sepehr Janghorbani, Gerard de Melo, and Sungjin Ahn. Scalor: Generative world models with scal- able object representations. In International Conference on Learning Representations, 2019. 3

    2019

  22. [30]

    Lawrence Zitnick, and Ross Girshick

    Justin Johnson, Bharath Hariharan, Laurens van der Maaten, Li Fei-Fei, C. Lawrence Zitnick, and Ross Girshick. Clevr: A diagnostic dataset for compositional language and elemen- tary visual reasoning. In 2017 IEEE Conference on Com- puter Vision and Pattern Recognition (CVPR),...

    2017

  23. [31]

    Multi-object datasets

    Rishabh Kabra, Chris Burgess, Loic Matthey, Raphael Lopez Kaufman, Klaus Greff, Malcolm Reynolds, and Alexander Lerchner. Multi-object datasets. https://github.com/deepmind/multi-object-datasets/, 2019. 6

    2019

  24. [32]

    The Background Also Matters: Background- Aware Motion-Guided Objects Discovery

    Sandra Kara, Hejer Ammar, Florian Chabot, and Quoc- Cuong Pham. The Background Also Matters: Background- Aware Motion-Guided Objects Discovery . In 2024 IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), pages 1205–1214, Los Alamitos, CA, USA,

    2024

  25. [33]

    Kaufman and P.J

    L. Kaufman and P.J. Rousseeuw. Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, 2009. 2

    2009

  26. [34]

    Tsung-Wei Ke, Jyh-Jing Hwang, Yunhui Guo, Xudong Wang, and Stella X. Yu. Unsupervised hierarchical semantic segmentation with multiview cosegmentation and clustering transformers. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pages 2561–2571,

    2022

  27. [35]

    Tsung-Wei Ke, Sangwoo Mo, and Stella X. Yu. Learning hi- erarchical image segmentation for recognition and by recog- nition. In The Twelfth International Conference on Learning Representations, 2024. 3

    2024

  28. [36]

    Shepherding slots to objects: Towards stable and ro- bust object-centric learning

    Jinwoo Kim, Janghyuk Choi, Ho-Jin Choi, and Seon Joo Kim. Shepherding slots to objects: Towards stable and ro- bust object-centric learning. In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 19198–19207, 2023. 1, 2

    2023

  29. [37]

    Space: Unsupervised object-oriented scene representa- tion via spatial attention and decomposition

    Zhixuan Lin, Yi-Fu Wu, Skand Vishwanath Peri, Weihao Sun, Gautam Singh, Fei Deng, Jindong Jiang, and Sungjin Ahn. Space: Unsupervised object-oriented scene representa- tion via spatial attention and decomposition. InInternational Conference on Learning Representations, 2020. 3

    2020

  30. [38]

    Object- centric learning with slot attention

    Francesco Locatello, Dirk Weissenborn, Thomas Un- terthiner, Aravindh Mahendran, Georg Heigold, Jakob Uszkoreit, Alexey Dosovitskiy, and Thomas Kipf. Object- centric learning with slot attention. In Advances in Neural Information Processing Systems, pages 11525–11538. Cur- ran...

    2020

  31. [39]

    Massam and Michael F

    Bryan H. Massam and Michael F. Goodchild. Temporal trends in the spatial organization of a service agency. Cana- dian Geographies / G ´eographies canadiennes , 15(3):193– 206, 1971. 5

    1971

  32. [40]

    Oswald, Cees G

    Duy-Kien Nguyen, Mahmoud Assran, Unnat Jain, Martin R. Oswald, Cees G. M. Snoek, and Xinlei Chen. An image is worth more than 16x16 patches: Exploring transformers on individual pixels. ArXiv, abs/2406.09415, 2024. 3

    2024 arXiv

  33. [41]

    Delving into the whorl of flower segmentation

    Maria-Elena Nilsback and Andrew Zisserman. Delving into the whorl of flower segmentation. In British Machine Vision Conference, 2007. 17

    2007

  34. [42]

    Comprehensive survey on hierarchical clus- tering algorithms and the recent developments

    Xingcheng Ran, Yue Xi, Yonggang Lu, Xiangwen Wang, and Zhenyu Lu. Comprehensive survey on hierarchical clus- tering algorithms and the recent developments. Artificial In- telligence Review, 56:8219 – 8264, 2022. 2, 6

    2022

  35. [43]

    Bridging the gap to real-world object-centric learning

    Maximilian Seitzer, Max Horn, Andrii Zadaianchuk, Do- minik Zietlow, Tianjun Xiao, Carl-Johann Simon-Gabriel, Tong He, Zheng Zhang, Bernhard Sch¨olkopf, Thomas Brox, and Francesco Locatello. Bridging the gap to real-world object-centric learning. In The Eleventh International ...

    2023

  36. [44]

    Normalized cuts and image segmentation

    Jianbo Shi and Jitendra Malik. Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 2002. 3

    2002

  37. [45]

    Illiterate DALL- e learns to compose

    Gautam Singh, Fei Deng, and Sungjin Ahn. Illiterate DALL- e learns to compose. In International Conference on Learn- ing Representations, 2022. 17

    2022

  38. [46]

    Graph clustering with graph neural net- works

    Anton Tsitsulin, John Palowitch, Bryan Perozzi, and Em- manuel M ¨uller. Graph clustering with graph neural net- works. J. Mach. Learn. Res., 24(1), 2024. 3

    2024

  39. [47]

    Selective search for object recognition

    J R R Uijlings, K E A van de Sande, T Gevers, and A W M Smeulders. Selective search for object recognition. Interna- tional Journal of Computer Vision , 104(2):154–171, 2013. 3

    2013

  40. [48]

    Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N

    Ashish Vaswani, Noam M. Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Neural Infor- mation Processing Systems, 2017. 3, 13

    2017

  41. [49]

    Yu, and Ishan Misra

    Xudong Wang, Rohit Girdhar, Stella X. Yu, and Ishan Misra. Cut and learn for unsupervised object detection and instance segmentation. In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pages 3124–3134,

    2023

  42. [50]

    Seg- ment anything without supervision

    Xudong Wang, Jingfeng Yang, and Trevor Darrell. Seg- ment anything without supervision. In The Thirty-eighth An- nual Conference on Neural Information Processing Systems,

  43. [51]

    Crowley, and Dominique Vaufrey- daz

    Yangtao Wang, Xi Shen, Yuan Yuan, Yuming Du, Maomao Li, Shell Xu Hu, James L. Crowley, and Dominique Vaufrey- daz. Tokencut: Segmenting objects in images and videos with self-supervised transformer and normalized cut. IEEE 10 Trans. Pattern Anal. Mach. Intell. , 45(12):15790–15801,

  44. [52]

    Burgess, and Alexander Lerchner

    Nicholas Watters, Lo ¨ıc Matthey, Christopher P. Burgess, and Alexander Lerchner. Spatial broadcast decoder: A simple ar- chitecture for learning disentangled representations in vaes. ArXiv, abs/1901.07017, 2019. 2

    1901 arXiv

  45. [53]

    Belongie, and Pietro Perona

    Peter Welinder, Steve Branson, Takeshi Mita, Catherine Wah, Florian Schroff, Serge J. Belongie, and Pietro Perona. Caltech-ucsd birds 200. 2010. 17

    2010

  46. [54]

    Wentz Wenwen Li, Tingyong Chen and Chao Fan

    Elizabeth A. Wentz Wenwen Li, Tingyong Chen and Chao Fan. Nmmi: A mass compactness measure for spatial pat- tern analysis of areal features. Annals of the Association of American Geographers, 104(6):1116–1133, 2014. 5

    2014

  47. [55]

    Goodchild Wenwen Li and Richard Church

    Michael F. Goodchild Wenwen Li and Richard Church. An efficient measure of compactness for two-dimensional shapes and its application in regionalization problems. In- ternational Journal of Geographical Information Science, 27 (6):1227–1250, 2013. 5, 14

    2013

  48. [56]

    Group normalization

    Yuxin Wu and Kaiming He. Group normalization. In Pro- ceedings of the European Conference on Computer Vision (ECCV), 2018. 4

    2018

  49. [57]

    Rui Xu and Donald C. Wunsch. Survey of clustering al- gorithms. IEEE Transactions on Neural Networks, 16:645– 678, 2005. 2

    2005

  50. [58]

    Benchmarking and analysis of unsupervised object segmentation from Real-World single images

    Yafei Yang and Bo Yang. Benchmarking and analysis of unsupervised object segmentation from Real-World single images. International Journal of Computer Vision , 132(6): 2077–2113, 2024. 1

    2024

  51. [59]

    Zhang, Simon Lacoste-Julien, Gert- jan J

    Yan Zhang, David W. Zhang, Simon Lacoste-Julien, Gert- jan J. Burghouts, and Cees G. M. Snoek. Unlocking slot at- tention by changing optimal transport costs. In Proceedings of the 40th International Conference on Machine Learning , pages 41931–41951. PMLR, 2023. 2

    2023

  52. [60]

    Zimmermann, Sjoerd van Steenkiste, Mehdi S

    Roland S. Zimmermann, Sjoerd van Steenkiste, Mehdi S. M. Sajjadi, Thomas Kipf, and Klaus Greff. Sensitivity of slot- based object-centric models to their number of slots. CoRR, abs/2305.18890, 2023. 2 11 Hierarchical Compact Clustering Attention (COCA) for Unsupervised Object-...

    2023 arXiv

  53. [63]

    At each layer, this feature image is partitioned intoU×U non-overlapping windows

    Complexity Analysis Suppose that COCA-Net is to process a feature image con- sisting ofN×N pixels. At each layer, this feature image is partitioned intoU×U non-overlapping windows. The com- plexity burden of a COCA layer resides on the generation of affinity masks and their co...

  54. [64]

    all-to-all

    Architectural Details 7.1. Pixel Feature Encoder We use a simple backbone to initialize pixel features that encode both appearance and positional information. Specif- ically, the input image is first processed through a sin- gle convolutional layer that preserves resolution to...

  55. [65]

    pad and random crop

    Implementation Details For all experiments included in this work, we build on the comprehensive OCL library that is provided by [15]. This OCL library includes the six datasets that we share results on, in addition to code scripts for training, testing and eval- uation. Detail...

    2000

  56. [66]

    Additional Results 9.1. Initial Experiments on Real-World Datasets; Birds and Flowers We evaluated COCA-Net on Birds [53] and Flowers [41] (following BOQSA’s protocol) using the SLATE [45] ar- chitecture which leverages a transformer decoder but no pretrained backbone. Entire ...

  57. [2024]

    IEEE Computer Society. 2

  58. [2527]

    2, 6, 7, 8, 16, 18

    PMLR, 2023. 2, 6, 7, 8, 16, 18

    2023

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.