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arxiv: 2607.01906 · v1 · pith:7DIQUKLBnew · submitted 2026-07-02 · 💻 cs.CV

SFKD: Spatial--Frequency Joint-Aware Heterogeneous Knowledge Distillation via Multi-Level Wavelet Spectral Interaction

Cuipeng Wang , Haipeng Wang This is my paper

Pith reviewed 2026-07-03 16:00 UTC · model grok-4.3

classification 💻 cs.CV
keywords knowledge distillationheterogeneous modelswavelet transformspatial-frequency interactionmodel compressioncomputer visionrepresentation transfer
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The pith

Heterogeneous knowledge distillation preserves transferable spatial semantics by decoupling representations with multi-level wavelet transforms and frequency filtering.

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

The paper establishes that spatial information in representations from models with differing inductive biases, such as CNNs and transformers, encodes global structural semantics that prior methods often discard or weaken due to spatial inconsistencies. To address this, it introduces a framework that applies multi-level discrete wavelet transform to explicitly separate these spatial components, refines them through a dual-stream dual-stage module, and pairs them with a Gaussian-filtered frequency loss for global energy capture. This joint spatial-frequency approach enables more effective knowledge transfer across both homogeneous and heterogeneous model pairs. Experiments on standard image benchmarks confirm improved performance, suggesting the method unlocks flexibility in distillation that homogeneous-only techniques miss.

Core claim

The SFKD framework applies multi-level discrete wavelet transform to explicitly decouple spatial information in heterogeneous representations. The resulting wavelet sub-bands are refined by a dual-stream dual-stage refinement module and combined with a Gaussian-filtered frequency loss to selectively capture informative global information, leveraging the complementary properties of wavelet spatial locality and Fourier global energy distributions to enable effective knowledge transfer despite architecture-specific biases.

What carries the argument

Multi-level discrete wavelet transform to decouple spatial information in heterogeneous representations, refined by dual-stream dual-stage module and integrated with Gaussian-filtered frequency loss.

Load-bearing premise

The spatial information encoded in heterogeneous representations contains transferable global structural semantics that can be recovered by multi-level discrete wavelet transform without introducing artifacts that harm distillation performance.

What would settle it

If the proposed method yields lower accuracy than existing heterogeneous distillation baselines on image classification benchmarks such as CIFAR-100 or ImageNet when distilling from a CNN teacher to a Vision Transformer student, the claim of superiority via wavelet-frequency interaction would be falsified.

Figures

Figures reproduced from arXiv: 2607.01906 by Cuipeng Wang, Haipeng Wang.

Figure 1
Figure 1. Figure 1: Illustration of heterogeneous feature maps, multi-level wavelet sub [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison between conventional heterogeneous distillation (a) and [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The architectural details of the ResConvBlock, TransBlock, and [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of the proposed 4D positional encoding, Gaussian low [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Most existing knowledge distillation methods focus on homogeneous models (e.g., CNN-to-CNN), thereby overlooking the flexibility and potential of knowledge transfer across heterogeneous models. Due to intrinsic inductive bias discrepancies between heterogeneous models that cause spatial distribution inconsistencies, prior heterogeneous distillation methods often weaken or discard spatial information in heterogeneous representations. However, the spatial information in representations often encodes transferable global structural semantics as well as architecture-specific local details, and therefore should not be directly ignored. To better leverage the spatial information encoded in heterogeneous representations, we propose a Spatial-Frequency Joint-Aware Heterogeneous Knowledge Distillation framework (SFKD). By leveraging the complementary properties of wavelet transform spatial locality and Fourier representations in characterizing global energy distributions, we first apply multi-level discrete wavelet transform to explicitly decouple spatial information. The resulting wavelet sub-bands are further refined by a dual-stream dual-stage refinement module, and finally combined with a Gaussian-filtered frequency loss to selectively capture informative global information. Extensive experiments on multiple benchmark datasets under both homogeneous and heterogeneous models demonstrate the superiority of our method.

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 manuscript introduces SFKD, a Spatial-Frequency Joint-Aware Heterogeneous Knowledge Distillation framework. It applies multi-level discrete wavelet transform to decouple spatial information in heterogeneous representations, refines the resulting sub-bands via a dual-stream dual-stage module, and combines them with a Gaussian-filtered frequency loss to capture global energy distributions, claiming improved performance over prior methods on multiple benchmark datasets for both homogeneous and heterogeneous teacher-student pairs.

Significance. If the reported gains prove robust under controlled hyper-parameter sweeps and fair architectural comparisons, the work would offer a practical engineering contribution to heterogeneous distillation by explicitly preserving transferable global structural semantics that prior methods often discard due to inductive-bias mismatches. The use of complementary wavelet locality and Fourier global descriptors is a reasonable incremental step, though it rests entirely on empirical validation rather than a parameter-free derivation or theoretical guarantee.

minor comments (3)
  1. [Experiments] The abstract states that experiments demonstrate superiority, but the experimental section should include explicit ablation tables isolating the contribution of the dual-stream dual-stage refinement module versus the Gaussian-filtered frequency loss alone (e.g., Table X, rows for each component).
  2. Clarify the exact number of wavelet decomposition levels, the choice of wavelet basis, and any hyper-parameters of the Gaussian filter; these choices appear to affect the spatial-frequency interaction and should be reported with sensitivity analysis.
  3. [Experiments] Ensure all reported metrics include standard deviations over multiple random seeds and list the precise teacher-student architecture pairs (CNN-to-Transformer, etc.) with baseline re-implementations under identical training protocols.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our SFKD framework and the recommendation of minor revision. The assessment correctly identifies the empirical nature of the contribution and the use of wavelet-Fourier complementarity for heterogeneous distillation. No major comments were enumerated in the report, so we provide no point-by-point rebuttals below.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes an incremental engineering framework (SFKD) for heterogeneous knowledge distillation that combines multi-level discrete wavelet transform with Fourier-based frequency loss and a dual-stream refinement module. All load-bearing claims rest on empirical superiority demonstrated via experiments on external benchmark datasets under homogeneous and heterogeneous settings. No mathematical derivation chain, uniqueness theorem, or parameter-fitting step is presented that reduces by construction to self-defined quantities or self-citations. The method is externally falsifiable through standard distillation benchmarks and does not invoke self-referential definitions or ansatzes.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the untested premise that wavelet sub-bands preserve transferable semantics across architectures and that a Gaussian frequency filter selectively captures useful global information without discarding task-relevant content. No free parameters or invented entities are named in the abstract.

axioms (2)
  • domain assumption Wavelet sub-bands obtained from multi-level discrete wavelet transform on heterogeneous representations encode both global structural semantics and architecture-specific local details that are useful for distillation.
    Invoked in the motivation paragraph to justify retaining rather than discarding spatial information.
  • domain assumption Complementary properties of wavelet spatial locality and Fourier global energy distributions allow selective capture of informative global information via Gaussian filtering.
    Stated as the basis for combining the two transforms in the proposed pipeline.

pith-pipeline@v0.9.1-grok · 5715 in / 1397 out tokens · 23141 ms · 2026-07-03T16:00:22.020015+00:00 · methodology

discussion (0)

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Works this paper leans on

44 extracted references · 10 canonical work pages · 5 internal anchors

  1. [1]

    In: Proceedings of the IEEE/CVF conference on computer vision and pattern recog- nition

    Chen, P., Liu, S., Zhao, H., Jia, J.: Distilling knowledge via knowledge review. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recog- nition. pp. 5008–5017 (2021) 2, 14, 1, 4 16 C. Wang et al

    2021

  2. [2]

    Mathematics of computation19(90), 297–301 (1965) 10

    Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex fourier series. Mathematics of computation19(90), 297–301 (1965) 10

    1965

  3. [3]

    An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

    Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., et al.: An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929 (2020) 1, 3, 8, 9, 13

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  4. [4]

    In: Proceedings of the IEEE/CVF International Conference on Computer Vision

    Du, P., Li, H., Xu, H., Jeon, P.B., Lee, D., Ji, D., Yang, R., Zhu, F.: Diffusion transformer meets multi-level wavelet spectrum for single image super-resolution. In: Proceedings of the IEEE/CVF International Conference on Computer Vision. pp. 19700–19710 (2025) 7, 2

    2025

  5. [5]

    In: European conference on computer vision

    Finder, S.E., Amoyal, R., Treister, E., Freifeld, O.: Wavelet convolutions for large receptive fields. In: European conference on computer vision. pp. 363–380. Springer (2024) 7, 2

    2024

  6. [6]

    Georg-August- Universitat, Gottingen

    Haar, A.: Zur theorie der orthogonalen funktionensysteme. Georg-August- Universitat, Gottingen. (1909) 6

    1909

  7. [7]

    Advances in Neural Information Processing Systems36, 79570–79582 (2023) 3, 5, 12, 13, 14, 1, 4, 7

    Hao, Z., Guo, J., Han, K., Tang, Y., Hu, H., Wang, Y., Xu, C.: One-for-all: Bridge the gap between heterogeneous architectures in knowledge distillation. Advances in Neural Information Processing Systems36, 79570–79582 (2023) 3, 5, 12, 13, 14, 1, 4, 7

    2023

  8. [8]

    He,K.,Zhang,X.,Ren,S.,Sun,J.:Deepresiduallearningforimagerecognition.In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 770–778 (2016) 1, 3

    2016

  9. [9]

    In: Proceedings of the IEEE/CVF international conference on computer vision

    Heo,B.,Kim,J.,Yun,S.,Park,H.,Kwak,N.,Choi,J.Y.:Acomprehensiveoverhaul of feature distillation. In: Proceedings of the IEEE/CVF international conference on computer vision. pp. 1921–1930 (2019) 2, 14, 1, 4

    1921

  10. [10]

    Distilling the Knowledge in a Neural Network

    Hinton, G.: Distilling the knowledge in a neural network. arXiv preprint arXiv:1503.02531 (2015) 2, 12, 13, 1, 4

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  11. [11]

    MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications

    Howard, A.G., Zhu, M., Chen, B., Kalenichenko, D., Wang, W., Weyand, T., An- dreetto, M., Adam, H.: Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861 (2017) 3

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  12. [12]

    Advances in Neural Information Processing Systems35, 33716– 33727 (2022) 2, 12, 13, 14, 1, 4

    Huang, T., You, S., Wang, F., Qian, C., Xu, C.: Knowledge distillation from a stronger teacher. Advances in Neural Information Processing Systems35, 33716– 33727 (2022) 2, 12, 13, 14, 1, 4

    2022

  13. [13]

    IEEE Transactions on Multimedia26, 7058–7073 (2024) 7, 9

    Huang, Y., Huang, J., Liu, J., Yan, M., Dong, Y., Lv, J., Chen, C., Chen, S.: Wavedm: Wavelet-based diffusion models for image restoration. IEEE Transactions on Multimedia26, 7058–7073 (2024) 7, 9

    2024

  14. [14]

    In: Proceedings of the IEEE/CVF international conference on computer vision

    Jiang, L., Dai, B., Wu, W., Loy, C.C.: Focal frequency loss for image reconstruc- tion and synthesis. In: Proceedings of the IEEE/CVF international conference on computer vision. pp. 13919–13929 (2021) 11, 3

    2021

  15. [15]

    Krizhevsky, A., Hinton, G., et al.: Learning multiple layers of features from tiny images (2009) 3

    2009

  16. [16]

    In: Proceedings of the IEEE/CVF International Conference on Computer Vision

    Li, G., Wang, Q., Yan, K., Ding, S., Gao, Y., Xia, G.S.: Fuse before transfer: Knowledge fusion for heterogeneous distillation. In: Proceedings of the IEEE/CVF International Conference on Computer Vision. pp. 3445–3454 (2025) 3, 5, 12, 13, 14, 15, 1, 2, 4

    2025

  17. [17]

    In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

    Li, J., Hassani, A., Walton, S., Shi, H.: Convmlp: Hierarchical convolutional mlps for vision. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 6307–6316 (2023) 2, 1

    2023

  18. [18]

    Neural Networks177, 106378 (2024) 7, 2 SFKD 17

    Li, J., Cheng, B., Chen, Y., Gao, G., Shi, J., Zeng, T.: Ewt: Efficient wavelet- transformer for single image denoising. Neural Networks177, 106378 (2024) 7, 2 SFKD 17

    2024

  19. [19]

    IEEE Transactions on Pattern Analysis and Machine Intelligence45(10), 12581–12600 (2023) 2, 1

    Li, K., Wang, Y., Zhang, J., Gao, P., Song, G., Liu, Y., Li, H., Qiao, Y.: Uniformer: Unifying convolution and self-attention for visual recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence45(10), 12581–12600 (2023) 2, 1

    2023

  20. [20]

    arXiv preprint arXiv:2304.11832 (2023) 2, 11, 14, 15, 1, 4

    Liu, D., Kan, M., Shan, S., Chen, X.: Function-consistent feature distillation. arXiv preprint arXiv:2304.11832 (2023) 2, 11, 14, 15, 1, 4

    work page arXiv 2023

  21. [21]

    Liu, Z., Lin, Y., Cao, Y., Hu, H., Wei, Y., Zhang, Z., Lin, S., Guo, B.: Swin transformer:Hierarchicalvisiontransformerusingshiftedwindows.In:Proceedings of the IEEE/CVF international conference on computer vision. pp. 10012–10022 (2021) 1, 3

    2021

  22. [22]

    In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition

    Liu, Z., Mao, H., Wu, C.Y., Feichtenhofer, C., Darrell, T., Xie, S.: A convnet for the 2020s. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 11976–11986 (2022) 1, 3

    2022

  23. [23]

    Elsevier (1999) 7, 14

    Mallat, S.: A wavelet tour of signal processing. Elsevier (1999) 7, 14

    1999

  24. [24]

    In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

    Miao, Y., Deng, J., Han, J.: Waveface: Authentic face restoration with efficient frequency recovery. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 6583–6592 (2024) 7, 9

    2024

  25. [25]

    Proceedings of the IEEE69(5), 529–541 (2005) 11, 3, 6

    Oppenheim, A.V., Lim, J.S.: The importance of phase in signals. Proceedings of the IEEE69(5), 529–541 (2005) 11, 3, 6

    2005

  26. [26]

    Park, N., Kim, S.: How do vision transformers work? arXiv preprint arXiv:2202.06709 (2022) 3, 7

    work page arXiv 2022

  27. [27]

    In: Pro- ceedings of the IEEE/CVF conference on computer vision and pattern recognition

    Park, W., Kim, D., Lu, Y., Cho, M.: Relational knowledge distillation. In: Pro- ceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 3967–3976 (2019) 2, 12, 13, 1, 4

    2019

  28. [28]

    In: Proceedings of the IEEE/CVF international conference on computer vision

    Peng, B., Jin, X., Liu, J., Li, D., Wu, Y., Liu, Y., Zhou, S., Zhang, Z.: Corre- lation congruence for knowledge distillation. In: Proceedings of the IEEE/CVF international conference on computer vision. pp. 5007–5016 (2019) 2, 12, 13, 1, 4

    2019

  29. [29]

    Raghu, M., Unterthiner, T., Kornblith, S., Zhang, C., Dosovitskiy, A.: Do vision transformers see like convolutional neural networks? Advances in neural informa- tion processing systems34, 12116–12128 (2021) 3, 7

    2021

  30. [30]

    FitNets: Hints for Thin Deep Nets

    Romero, A., Ballas, N., Kahou, S.E., Chassang, A., Gatta, C., Bengio, Y.: Fitnets: Hints for thin deep nets. arXiv preprint arXiv:1412.6550 (2014) 2, 12, 13, 1, 4, 7

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  31. [31]

    International journal of computer vision115, 211–252 (2015) 3

    Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., et al.: Imagenet large scale visual recog- nition challenge. International journal of computer vision115, 211–252 (2015) 3

    2015

  32. [32]

    In: Proceedings of the IEEE conference on computer vision and pattern recognition

    Sandler, M., Howard, A., Zhu, M., Zhmoginov, A., Chen, L.C.: Mobilenetv2: In- verted residuals and linear bottlenecks. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 4510–4520 (2018) 1, 3

    2018

  33. [33]

    SIAM (1996) 7, 14

    Strang, G., Nguyen, T.: Wavelets and filter banks. SIAM (1996) 7, 14

    1996

  34. [34]

    arXiv preprint arXiv:1910.10699 (2019),https://arxiv.org/abs/1910.10699, accessed: 2026-06-29 4, 7, 14, 29, 32, 44, 45, 47, 52, 56 20 Aizierjiang Aiersilan

    Tian, Y., Krishnan, D., Isola, P.: Contrastive representation distillation. arXiv preprint arXiv:1910.10699 (2019) 2, 12, 13, 14, 1, 4

    work page arXiv 1910

  35. [35]

    Advances in neural information processing systems34, 24261–24272 (2021) 1, 3

    Tolstikhin, I.O., Houlsby, N., Kolesnikov, A., Beyer, L., Zhai, X., Unterthiner, T., Yung, J., Steiner, A., Keysers, D., Uszkoreit, J., et al.: Mlp-mixer: An all- mlp architecture for vision. Advances in neural information processing systems34, 24261–24272 (2021) 1, 3

    2021

  36. [36]

    IEEE transactions on pattern analysis and machine intelligence45(4), 5314–5321 (2022) 1, 3

    Touvron, H., Bojanowski, P., Caron, M., Cord, M., El-Nouby, A., Grave, E., Izac- ard, G., Joulin, A., Synnaeve, G., Verbeek, J., et al.: Resmlp: Feedforward networks for image classification with data-efficient training. IEEE transactions on pattern analysis and machine intelligence45(4), 5314–5321 (2022) 1, 3

    2022

  37. [37]

    In: International conference on machine learning

    Touvron, H., Cord, M., Douze, M., Massa, F., Sablayrolles, A., Jégou, H.: Training data-efficient image transformers & distillation through attention. In: International conference on machine learning. pp. 10347–10357. PMLR (2021) 1, 3 18 C. Wang et al

    2021

  38. [38]

    In: Wavelet applications in signal and image processing V

    Unser, M.A.: Ten good reasons for using spline wavelets. In: Wavelet applications in signal and image processing V. vol. 3169, pp. 422–431. SPIE (1997) 7, 9, 14, 6

    1997

  39. [39]

    Vetterli, M., Kovacevic, J.: Wavelets and subband coding, vol. 87. Prentice Hall PTR Englewood Cliffs, NJ (1995) 7, 9, 14, 6

    1995

  40. [40]

    IEEE Transactions on Circuits and Systems for Video Technology (2025) 7, 9

    Wang, Q., Li, Z., Zhang, S., Chi, N., Dai, Q.: Wavefusion: A novel wavelet vision transformer with saliency-guided enhancement for multimodal image fusion. IEEE Transactions on Circuits and Systems for Video Technology (2025) 7, 9

    2025

  41. [41]

    arXiv preprint arXiv:2405.18524 (2024) 3, 5, 1

    Wu, H., Xiao, L., Zhang, X., Miao, Y.: Aligning in a compact space: Con- trastive knowledge distillation between heterogeneous architectures. arXiv preprint arXiv:2405.18524 (2024) 3, 5, 1

    work page arXiv 2024

  42. [42]

    In: European conference on computer vision

    Yao, T., Pan, Y., Li, Y., Ngo, C.W., Mei, T.: Wave-vit: Unifying wavelet and trans- formers for visual representation learning. In: European conference on computer vision. pp. 328–345. Springer (2022) 7, 2

    2022

  43. [43]

    Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer

    Zagoruyko, S., Komodakis, N.: Paying more attention to attention: Improving the performance of convolutional neural networks via attention transfer. arXiv preprint arXiv:1612.03928 (2016) 14, 1, 4

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  44. [44]

    In: Proceedings of the IEEE/CVF Conference on computer vision and pattern recognition

    Zhao, B., Cui, Q., Song, R., Qiu, Y., Liang, J.: Decoupled knowledge distillation. In: Proceedings of the IEEE/CVF Conference on computer vision and pattern recognition. pp. 11953–11962 (2022) 2, 12, 13, 14, 1, 4 SFKD: Spatial–Frequency Joint-Aware Heterogeneous Knowledge Distillation via Multi-Level Wavelet Spectral Interaction (Appendix) Cuipeng Wang1,2...

    work page arXiv 2022