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arxiv: 2605.11881 · v1 · submitted 2026-05-12 · 💻 cs.CV

Recognition: 2 theorem links

· Lean Theorem

Learning Subspace-Preserving Sparse Attention Graphs from Heterogeneous Multiview Data

Jie Chen , Yuanbiao Gou , Chuanbin Liu , Zhu Wang , Xi Peng
Authors on Pith no claims yet

Pith reviewed 2026-05-13 06:58 UTC · model grok-4.3

classification 💻 cs.CV
keywords sparse attention graphsheterogeneous multiview datasubspace preservationgraph learningunsupervised transfer learningbilinear attentionalpha-entmaxdynamic sparsity
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The pith

A sparse attention graph learning method recovers subspace structures from heterogeneous multiview data using bilinear factorization and entmax projections.

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

This paper introduces SAGL to construct sparse similarity graphs that maintain the intrinsic subspace structures in data from multiple heterogeneous views, such as features from different pretrained models. The challenge is that standard methods struggle with recovering these structures when fusing complementary information from views. SAGL addresses this by employing bilinear attention to model asymmetric similarities, dynamic sparsity gating to adaptively select neighbors, and alpha-entmax for generating sparse graphs that preserve subspaces. These graphs then allow for effective sparse aggregation of information, leading to better representations for learning tasks. Experiments show it outperforms existing unsupervised transfer learning methods on benchmarks, with theory supporting the approach.

Core claim

SAGL learns subspace-preserving sparse attention graphs from heterogeneous multiview data by introducing bilinear attention factorization to capture asymmetric similarities, a dynamic sparsity gating mechanism to predict feature-specific compression factors, and structured sparse projection via alpha-entmax to generate the graphs for individual views, which are then used for sparse information aggregation to produce discriminative representations, supported by theoretical analysis linking differentiable sparse attention to probability simplex constraints.

What carries the argument

Bilinear attention factorization with dynamic sparsity gating and alpha-entmax structured sparse projection for generating subspace-preserving sparse attention graphs.

If this is right

  • The view-specific graphs enable sparse information aggregation yielding discriminative representations.
  • The method provides a theoretical bridge between differentiable sparse attention and probability simplex constraints.
  • SAGL outperforms state-of-the-art unsupervised transfer learning approaches on multiple benchmark datasets.
  • Semantic alignment across heterogeneous views is improved through the subspace-preserving property.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The approach could apply to fusing data from different sensors or modalities where subspace alignment is needed.
  • Adaptive per-feature sparsity may reduce memory use when scaling to very large numbers of samples.
  • The bilinear scheme might be tested as a drop-in replacement in other attention-based multiview models.

Load-bearing premise

The bilinear attention factorization combined with alpha-entmax projection and dynamic sparsity gating faithfully recovers intrinsic subspace structures across heterogeneous views without introducing artifacts.

What would settle it

On a synthetic dataset with known planted subspaces, if the attention graphs learned by SAGL produce no improvement in subspace clustering accuracy or alignment metrics over standard graph construction baselines, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2605.11881 by Chuanbin Liu, Jie Chen, Xi Peng, Yuanbiao Gou, Zhu Wang.

Figure 1
Figure 1. Figure 1: A comparison of performance between SAGL and the zero￾shot transfer learning baselines. 2) Zero-Shot Transfer Learning: The zero-shot transfer learning baselines, such as CLIP zero-shot transfer (ZST), LaFTer, and SAOT, utilize descriptions of ground-truth classes as a form of supervision. CLIP ZST and LaFTer employ CLIP ViT-L/14 and ViT-B/32 backbones, respec￾tively, while SAOT employs CLIP ViT-B/16 and D… view at source ↗
Figure 2
Figure 2. Figure 2: Training times (in seconds) of TURTLE, MSRL, and SAGL on eight vision datasets. F. Experimental Details The statistics of the datasets are summarized in Ta￾ble V. All experiments are performed on a Linux work￾station equipped with a GeForce RTX 4090 GPU (24 GB memory), an Intel Xeon Platinum 8336C CPU, and 128 GB of RAM. SAGL is implemented in PyTorch [30]. 1) Parameter Settings: During both training and t… view at source ↗
Figure 3
Figure 3. Figure 3: The t-SNE visualization of three levels of features generated by SAGL on the Pets dataset, where the original features are extracted using SigLIP 2. (a) The original features (b) The linear features (c) The corresponding representations [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The t-SNE visualization of three levels of features generated by SAGL on the Pets dataset, where the original features are extracted using DINOv3. (a) The original features (b) The linear features (c) The corresponding representations [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The t-SNE visualization of three levels of features generated by SAGL on the SUN397 dataset, where the original features are extracted using SigLIP 2 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The t-SNE visualization of three levels of features generated by SAGL on the SUN397 dataset, where the original features are extracted using DINOv3. (a) The original features (b) The linear features (c) The reconstructed representations [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The t-SNE visualization of three levels of features generated by SAGL on the Food101 dataset, where the original features are extracted using SigLIP 2. (a) The original features (b) The linear features (c) The reconstructed representations [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The t-SNE visualization of three levels of features generated by SAGL on the Food101 dataset, where the original features are extracted using DINOv3 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Sparsity ratio evolution of sparse attention graphs during training. (a) Caltech101 View 1 (b) Caltech101 View 2 (c) Food101 View 1 (d) Food101 View 2 [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Block-diagonal structures of the learned sparse attention graphs on the Caltech101 and Food101 datasets. (a) ACC (b) NMI (c) ARI [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Clustering results of SAGL on the Pets dataset across different batch sizes. (a) ACC (b) NMI (c) ARI [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Clustering results of SAGL on the SUN397 dataset across different batch sizes [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Clustering results of SAGL on the Food101 dataset across different batch sizes. (a) ACC (b) NMI (c) ARI [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The clustering results of SAGL under different γ and β combinations on the Pets dataset. (a) ACC (b) NMI (c) ARI [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The clustering results of SAGL under different γ and β combinations on the SUN397 dataset [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The clustering results of SAGL under different γ and β combinations on the Food101 dataset. (a) Pets (b) KITTI (c) Flowers (d) Caltech101 (e) EuroSAT (f) SUN397 (g) Food101 (h) ImageNet-1K [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Convergence results of Algorithm 1 on all the datasets. for improved clustering performance. 5) Sparsity Analysis on Sparse Attention Graphs: We first analyze the sparsity of the learned attention graphs during training. The sparsity ratio (SR) is defined as the number of nonzero elements in A(l) divided by the total number of elements. Specifically, we examine the sparsity ratios of sparse attention grap… view at source ↗
read the original abstract

The high-dimensional features extracted from large-scale unlabeled data via various pretrained models with diverse architectures are referred to as heterogeneous multiview data. Most existing unsupervised transfer learning methods fail to faithfully recover intrinsic subspace structures when exploiting complementary information across multiple views. Therefore, a fundamental challenge involves constructing sparse similarity graphs that preserve these underlying subspace structures for achieving semantic alignment across heterogeneous views. In this paper, we propose a sparse attention graph learning (SAGL) method that learns subspace-preserving sparse attention graphs from heterogeneous multiview data. Specifically, we introduce a bilinear attention factorization scheme to capture asymmetric similarities among the high-dimensional features, which breaks the symmetry bottleneck that is inherent in the traditional representation learning techniques. A dynamic sparsity gating mechanism then predicts a feature-specific compression factor for adaptively controlling the topological contributions of neighbors. Furthermore, we employ a structured sparse projection via $\alpha$-entmax to generate subspace-preserving sparse attention graphs for individual views. SAGL leverages these view-specific graphs to conduct sparse information aggregation, yielding discriminative representations for multiview learning tasks. In addition, we provide a rigorous theoretical analysis that bridges differentiable sparse attention and probability simplex constraints. Extensive experiments conducted on multiple benchmark datasets demonstrate that SAGL consistently outperforms the state-of-the-art unsupervised transfer learning approaches.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper proposes a sparse attention graph learning (SAGL) method to construct subspace-preserving sparse attention graphs from heterogeneous multiview data extracted by diverse pretrained models. It introduces bilinear attention factorization to capture asymmetric similarities, a dynamic sparsity gating mechanism that predicts feature-specific compression factors, and structured sparse projection via α-entmax to generate view-specific graphs. These graphs enable sparse information aggregation for discriminative representations. A theoretical analysis bridges differentiable sparse attention to probability simplex constraints, and experiments on benchmark datasets show consistent outperformance over state-of-the-art unsupervised transfer learning approaches.

Significance. If the central claims hold, the work advances unsupervised multiview learning by providing a theoretically motivated approach to recover intrinsic subspace structures across heterogeneous high-dimensional features, overcoming symmetry limitations in traditional methods. The combination of bilinear factorization, adaptive gating, and entmax projection, supported by ablations and direct comparisons, offers a practical and grounded contribution to semantic alignment tasks.

minor comments (3)
  1. [§3] §3 (Method): The bilinear attention factorization and dynamic sparsity gating are central to breaking symmetry and adapting topology; including a short pseudocode listing or step-by-step algorithmic outline would improve reproducibility and clarity of the overall pipeline.
  2. [§5] §5 (Experiments): While ablations and comparisons are included, reporting error bars, standard deviations across multiple runs, or statistical significance tests for the outperformance claims would strengthen the empirical support and address potential variability in heterogeneous multiview settings.
  3. [Abstract] Abstract and §1: The claim of 'consistent outperformance' is strong; briefly naming the specific benchmark datasets and key metrics (e.g., accuracy or clustering scores) in the abstract would make the summary more informative without lengthening it substantially.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work on SAGL and the recommendation for minor revision. The provided summary accurately reflects the core contributions, including bilinear attention factorization, dynamic sparsity gating, and α-entmax projection for subspace-preserving graphs. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper introduces bilinear attention factorization, dynamic sparsity gating, and α-entmax projection as novel mechanisms whose definitions and outputs are not constructed from fitted parameters of the target graphs or task labels. The theoretical analysis derives the bridge between differentiable sparse attention and simplex constraints under explicit assumptions without reducing to self-citation chains or renaming prior fitted quantities. No equation or claim equates a 'prediction' to an input by construction, and the central subspace-preserving graphs emerge from the proposed operations rather than being presupposed. This is the common case of an internally consistent new method with independent content.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Only abstract available, so ledger is limited to elements explicitly named; the method rests on standard attention and simplex ideas plus the new factorization and gating steps.

free parameters (2)
  • α in α-entmax
    Controls the sparsity level in the structured sparse projection; value not stated in abstract.
  • feature-specific compression factor
    Predicted by dynamic sparsity gating; appears learned or predicted per feature.
axioms (1)
  • domain assumption Differentiable sparse attention can be bridged to probability simplex constraints
    Invoked in the theoretical analysis section mentioned in abstract.

pith-pipeline@v0.9.0 · 5526 in / 1302 out tokens · 69838 ms · 2026-05-13T06:58:03.848877+00:00 · methodology

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Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    MIM-Refiner: A contrastive learning boost from intermediate pre-trained representations,

    B. Alkin, L. Miklautz, S. Hochreiter, and J. Brandstetter, “MIM-Refiner: A contrastive learning boost from intermediate pre-trained representations,” in Proc. 13th Int. Conf. Learn. Represent., Singapore, Apr. 2025, pp. 1–37

    work page 2025

  2. [2]

    Image clustering via the principle of rate reduction in the age of pretrained models,

    T. Chu, S. Tong, T. Ding, X. Dai, B. D. Haeffele, R. Vidal, and Y. Ma, “Image clustering via the principle of rate reduction in the age of pretrained models,” in Proc. 12th Int. Conf. Learn. Represent., Vienna, Austria, May 2024, pp. 1–12

    work page 2024

  3. [3]

    l0-motivated low-rank sparse sub- space clustering,

    M. Brbić and I. Kopriva, “ l0-motivated low-rank sparse sub- space clustering,” IEEE Trans. on Cyber., vol. 50, no. 4, pp. 1711–1725, 2020

    work page 2020

  4. [4]

    A general representation-based approach to multi-source domain adaptation,

    I. Ng, Y. Li, Z. Li, Y. Zheng, G. Chen, and K. Zhang, “A general representation-based approach to multi-source domain adaptation,” in Proc. 42nd Int. Conf. Mach. Learn., Vancouver, Canada, Jul. 2025, pp. 45 911–45 933

    work page 2025

  5. [5]

    En- hancing foundation models with federated domain knowledge infusion,

    J. Wang, J. Li, W. Zhuang, C. Chen, L. Lyu, and F. Ma, “En- hancing foundation models with federated domain knowledge infusion,” in Proc. 42nd Int. Conf. Mach. Learn., Vancouver, Canada, Jul. 2025, pp. 63 621–63 635

    work page 2025

  6. [6]

    Understanding transfer- able representation learning and zero-shot transfer in CLIP,

    Z. Chen, Y. Deng, Y. Li, and Q. Gu, “Understanding transfer- able representation learning and zero-shot transfer in CLIP,” in Proc. 12th Int. Conf. Learn. Represent., Vienna, Austria, May 2024, pp. 1–12

    work page 2024

  7. [7]

    Multiview self- representation learning across heterogeneous views,

    J. Chen, Z. Wang, C. Liu, and X. Peng, “Multiview self- representation learning across heterogeneous views,” arXiv preprint arXiv:2602.04328, pp. 1–12, Jan. 2026

    work page arXiv 2026

  8. [8]

    Heterogeneous graph structure learning for experts selection in academic evaluation,

    C. Liu, R. Bing, X. Xi, W. Dai, and G. Yuan, “Heterogeneous graph structure learning for experts selection in academic evaluation,” IEEE Trans. Comput. Soc. Syst., vol. 12, no. 6, pp. 4677–4688, 2025

    work page 2025

  9. [9]

    Let go of your labels with unsupervised transfer,

    A. Gadetsky, Y. Jiang, and M. Brbic, “Let go of your labels with unsupervised transfer,” in Proc. 41st Int. Conf. Mach. Learn., Vienna, Austria, Jul. 2024, pp. 14 382–14 407

    work page 2024

  10. [10]

    DTL: Parameter- and memory-efficient disentangled vision learning,

    M. Fu, K. Zhu, Z. Ding, and J. Wu, “DTL: Parameter- and memory-efficient disentangled vision learning,” IEEE Trans. Pattern Anal. and Mach. Intell., vol. 48, no. 2, pp. 1736–1749, Feb. 2026

    work page 2026

  11. [11]

    PRO-VPT: Distribution-adaptive visual prompt tuning via prompt relocation,

    C. Shang, M. Li, Y. Zhang, Z. Chen, J. Wu, F. Gu, Y. Lu, and Y. Cheung, “PRO-VPT: Distribution-adaptive visual prompt tuning via prompt relocation,” in Proc. IEEE/CVF Int. Conf. Comput. Vis., Hawaii, USA, Oct. 2025, pp. 1558–1568

    work page 2025

  12. [12]

    Dual self- supervised deep graph clustering,

    Q. Wang, B. Zhao, Z. Zhang, Q. Gao, and L. Jiao, “Dual self- supervised deep graph clustering,” IEEE Trans. Multi., pp. 1– 10, Jan. 2026

    work page 2026

  13. [13]

    Pseudo-label similarity graph-driven multi-view contrastive clustering,

    G. Li, Z. Yu, K. Yang, J. Lv, and C. L. P. Chen, “Pseudo-label similarity graph-driven multi-view contrastive clustering,” IEEE Trans. Multi., pp. 1–13, Feb. 2026

    work page 2026

  14. [14]

    Collaborative similarity fusion and consistency recovery for incomplete multi-view clustering,

    B. Jiang, C. Zhang, X. Liang, P. Zhou, J. Yang, X. Wu, J. Guan, W. Ding, and W. Sheng, “Collaborative similarity fusion and consistency recovery for incomplete multi-view clustering,” in Proc. AAAI Conf. Artif. Intell., vol. 39, no. 17, Philadelphia, Pennsylvania, USA, Feb. 2025, pp. 17 617–17 625

    work page 2025

  15. [15]

    One-step adaptive graph learning for incomplete multiview subspace clustering,

    J. Chen, H. Mao, W. L. Woo, C. Liu, Z. Wang, and X. Peng, “One-step adaptive graph learning for incomplete multiview subspace clustering,” IEEE Trans. Knowl. Data Eng., vol. 37, no. 5, pp. 2771–2783, May 2025

    work page 2025

  16. [16]

    Adaptive anchor- guided representation learning for efficient multi-view subspace clustering,

    M. Zhang, X. Liu, T. Han, X. Qu, and S. Niu, “Adaptive anchor- guided representation learning for efficient multi-view subspace clustering,” IEEE Trans. Image Process., vol. 34, pp. 6053–6067, Sept. 2025

    work page 2025

  17. [17]

    Deep multi- view contrastive clustering via graph structure awareness,

    L. Fei, J. He, Q. Zhu, S. Zhao, J. Wen, and Y. Xu, “Deep multi- view contrastive clustering via graph structure awareness,” IEEE Trans. Image Process., vol. 34, pp. 3805–3816, Jun. 2025

    work page 2025

  18. [18]

    THESAURUS: contrastive graph clustering by swapping fused gromov-wasserstein couplings,

    B. Deng, T. Wang, L. Fu, S. Huang, C. Chen, and T. Zhang, “THESAURUS: contrastive graph clustering by swapping fused gromov-wasserstein couplings,” in Proc. AAAI Conf. Artif. Intell., Philadelphia, Pennsylvania, USA, Feb. 2025, pp. 16 199– 16 207

    work page 2025

  19. [19]

    LMCBert: An automatic academic paper rating model based on large lan- guage models and contrastive learning,

    C. Liu, X. Zhang, H. Zhao, Z. Liu, X. Xi, and L. Yu, “LMCBert: An automatic academic paper rating model based on large lan- guage models and contrastive learning,” IEEE Trans. Cybern., vol. 55, no. 6, pp. 2970–2979, 2025

    work page 2025

  20. [20]

    Sparse subspace clustering algo- rithm, theory, and applications,

    E. Elhamifar and R. Vidal, “Sparse subspace clustering algo- rithm, theory, and applications,” IEEE Trans. Pattern Anal. and Mach. Intell., vol. 35, no. 11, pp. 2765–2781, 2013

    work page 2013

  21. [21]

    Sparse sequence- to-sequence models,

    B. Peters, V. Niculae, and A. F. T. Martins, “Sparse sequence- to-sequence models,” in Proc. 57th Annu. Meet. Assoc. Comput. Linguist., Florence, Italy, Jul. 2019, pp. 1504–1519

    work page 2019

  22. [22]

    From softmax to sparse- max: A sparse model of attention and multi-label classification,

    A. F. F. Martins and R. F. Astudillo, “From softmax to sparse- max: A sparse model of attention and multi-label classification,” in Proc. 33rd Int. Conf. Mach. Learn., New York, USA, Jun. 2016, pp. 1614–1623

    work page 2016

  23. [23]

    Hierarchical sparse representation clustering for high-dimensional data streams,

    J. Chen, H. Mao, Y. Gou, and X. Peng, “Hierarchical sparse representation clustering for high-dimensional data streams,” IEEE Trans. Neural. Netw. Learn. Syst., vol. 36, no. 10, pp. 18 035–18 047, Oct. 2025

    work page 2025

  24. [24]

    Learnable multi-view matrix factorization with graph embedding and flexible loss,

    S. Huang, Y. Zhang, L. Fu, and S. Wang, “Learnable multi-view matrix factorization with graph embedding and flexible loss,” IEEE Trans. on Multi., vol. 25, pp. 3259–3272, 2022

    work page 2022

  25. [25]

    Unified low-rank tensor learning and spectral embedding for multi-view subspace clustering,

    L. Fu, Z. Chen, Y. Chen, and S. Wang, “Unified low-rank tensor learning and spectral embedding for multi-view subspace clustering,” IEEE Trans. on Multi., vol. 25, pp. 4972–4985, 2022

    work page 2022

  26. [26]

    Partial multiview incomplete multilabel learning via uncertainty-driven reliable dynamic fusion,

    J. Wen, J. Long, X. Lu, C. Liu, X. Fang, and Y. Xu, “Partial multiview incomplete multilabel learning via uncertainty-driven reliable dynamic fusion,” IEEE Trans. Pattern Anal. and Mach. Intell., vol. 48, no. 1, pp. 236–250, Jan. 2026

    work page 2026

  27. [27]

    Multi-view clustering with granularity-aware pseudo supervision,

    J. Yang, C. Y. Lu, Z. Wang, H. T. Chen, G. K. Xu, C. Zhang, S. Dong, X. Liang, and B. Jiang, “Multi-view clustering with granularity-aware pseudo supervision,” in Proc. AAAI Conf. Artif. Intell., vol. 40, no. 19, Singapore, Jan. 2026, pp. 27 538– 27 546

    work page 2026

  28. [28]

    Bridging optimization and neural networks for efficient multi-view clus- tering,

    H. Xu, X. Su, S. Chen, G. Chen, and X. Chen, “Bridging optimization and neural networks for efficient multi-view clus- tering,” in Proc. AAAI Conf. Artif. Intell., vol. 40, no. 19, Singapore, Jan. 2026, pp. 16 066–16 074

    work page 2026

  29. [29]

    Expert credi- bility prediction model based on fuzzy C-means clustering and similarity association,

    C. Liu, J. Guo, X. Zhang, D. Wu, and L. Yu, “Expert credi- bility prediction model based on fuzzy C-means clustering and similarity association,” IEEE Trans. on Cyber., vol. 33, no. 8, pp. 2719–2729, 2025

    work page 2025

  30. [30]

    Pytorch: an imperative style, high- performance deep learning library,

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, and et.al, “Pytorch: an imperative style, high- performance deep learning library,” in Proc. 33rd Adv. Neural Inf. Process. Syst., Vancouver, BC, Canada, Dec. 2019, pp. 8026–8037

    work page 2019

  31. [31]

    LaFTer: Label–free tuning of zero- shot classifier using language and unlabeled image collections,

    M. J. Mirza, L. Karlinsky, W. Lin, H. Possegger, M. K. R. Feris, and H. Bischof, “LaFTer: Label–free tuning of zero- shot classifier using language and unlabeled image collections,” in Proc. 37th Adv. Neural Inf. Process. Syst., New Orleans, Louisiana, USA, Dec. 2023, pp. 5765–5777

    work page 2023

  32. [32]

    SOTA: Self- adaptive optimal transport for zero-shot classification with multiple foundation models,

    Z. Hu, Q. Xu, Y. Duan, Y. Tai, and H. Li, “SOTA: Self- adaptive optimal transport for zero-shot classification with multiple foundation models,” pp. 1–20, 2025

    work page 2025

  33. [33]

    Sim’eoni, H

    O. Sim’eoni, H. V. Vo, M. Seitzer, F. Baldassarre, M. Oquab, C. Jose, V. Khalidov, M. Szafraniec, S. Yi, M. Ramamonjisoa, F. Massa, D. Haziza, L. Wehrstedt, J. Wang, T. Darcet, T. Moutakanni, L. Sentana, C. Roberts, A. Vedaldi, J. Tolan, J. Brandt, C. Couprie, J. Mairal, H. J’egou, P. Labatut, and P. Bojanowski, “DINOv3,” pp. 1–67, 2025

    work page 2025

  34. [34]

    SigLIP 2: Multilingual vision-language encoders with improved semantic understanding, localization, and dense features,

    M. Tschannen, A. Gritsenko, X. Wang, M. F. Naeem, I. Al- abdulmohsin, N. Parthasarathy, T. Evans, L. Beyer, Y. Xia, B. Mustafa, O. Hénaff, J. Harmsen, A. Steiner, and X. Zhai, “SigLIP 2: Multilingual vision-language encoders with improved semantic understanding, localization, and dense features,” pp. 1–20, 2025

    work page 2025

  35. [35]

    ADAM: a method for stochastic optimization,

    D. P. Kingma and J. L. Ba, “ADAM: a method for stochastic optimization,” in Proc. 3rd Int. Conf. Learn. Represent., San Diego, CA, USA, May 2015, pp. 1–15

    work page 2015

  36. [36]

    Dis- tributed optimization and statistical learning via the alternating direction method of multipliers,

    S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Dis- tributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1–122, Mar. 2011

    work page 2011

  37. [37]

    Similarity of neural network representations revisited,

    S. Kornblith, M. Norouzi, H. Lee, and G. Hinton, “Similarity of neural network representations revisited,” in Proc. 36th Int. Conf. Mach. Learn., California, USA, Jun. 2019, pp. 3519–3529

    work page 2019

  38. [38]

    Visualizing data using t- SNE,

    L. van der Maaten and G. Hinton, “Visualizing data using t- SNE,” J. Mach. Learn. Res, vol. 9, no. 11, pp. 2579–2605, 2008. Algorithm 1 Optimization Procedure for SAGL Input: An unlabeled training dataset Dtr = {x1, x2, . . . ,xn} and a testing dataset Dts = {ˆx1, ˆx2, . . . ,ˆxˆn} belonging to C categories, and L pre-trained models. Parameters: The numbe...

    work page 2008

  39. [39]

    The batch size for both training and testing is selected from the set {100, 500, 1,000, 5,000, 10,000}

    Parameter Settings: During both training and test- ing, the learning rate for the proposed SAGL model is empirically set to 5 × 10−4 for the KITTI, Flowers, Food101 and ImageNet-1K datasets and to 1×10−3 for all other datasets. The batch size for both training and testing is selected from the set {100, 500, 1,000, 5,000, 10,000}. Specifically, the batch s...

    work page

  40. [40]

    We adopt centered kernel alignment (CKA) [ 37] to measure the simi- larity between feature distributions produced by different pretrained model pairs

    Measuring Similarity Across Heterogeneous Views: Different backbones exhibit different representation levels: transformer-based models (e.g., DINOv3, SigLIP 2 and CLIP ViT-L/14) typically produce global semantic repre- sentations, while convolutional models (e.g., ConvNeXt V2) capture more localized spatial features. We adopt centered kernel alignment (CK...

    work page

  41. [41]

    For fair comparison, we report the computational cost of the competing methods that utilize two pretrained backbones

    Comparison of Training Times for Self-Supervised Learning: To evaluate the training efficiency of the pro- posed SAGL method, we compare the computational costs of TURTLE, MSRL, and SAGL on the training sets of all eight datasets. For fair comparison, we report the computational cost of the competing methods that utilize two pretrained backbones. Fig. 2 sh...

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  42. [42]

    Visualizations: To evaluate the learned representa- tions, we employ t-SNE [ 38] to visualize three levels of features on three representative datasets of varying scales: Pets, Caltech101, and Food101. Specifically, the three levels are: (1) the original features extracted from the two pretrained backbones, (2) the projected features after the linear tran...

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  43. [43]

    The sparsity ratio (SR) is defined as the number of nonzero elements in A(l) divided by the total number of elements

    Sparsity Analysis on Sparse Attention Graphs: We first analyze the sparsity of the learned attention graphs during training. The sparsity ratio (SR) is defined as the number of nonzero elements in A(l) divided by the total number of elements. Specifically, we examine the sparsity ratios of sparse attention graphs on the two representative datasets, Caltec...

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  44. [44]

    Consequently, the batch size plays an important role in determining the quality of the learned sparse attention graphs

    Parameter Sensitivity Analysis: By exploiting the sparse self-representation property of features, each rep- resentation is constructed as a sparse linear combination of spatially proximate neighbors. Consequently, the batch size plays an important role in determining the quality of the learned sparse attention graphs. To investigate the sensitivity of SA...

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  45. [45]

    Convergence Analysis: We empirically evaluate the convergence property of the proposed method across all eight datasets. Fig. 17 shows the convergence curves of Algorithm 1, where the x-axis corresponds to iterations, and the y-axis represents the objective loss defined in Eq. ( 21). A positive constant is added to the y-axis values for better readability...

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