Unpaired Image Dehazing via Kolmogorov-Arnold Transformation of Latent Features

Le-Anh Tran

REVIEW 5 major objections 4 minor 56 references

Unpaired Image Dehazing via Kolmogorov-Arnold Transformation of Latent Features

T0 review · 5 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A KAN-based transformer reports the best unpaired dehazing numbers on SOTS-Outdoor and HSTS.

desk verdict Plausible KAN-based unpaired dehazing idea buried under a self-contradictory experimental section; the main numbers are unverifiable as written. read the letter →

arxiv 2502.07812 v1 pith:TKYF7LRX submitted 2025-02-08 cs.CV

Le-Anh Tran This is my paper · ORCID

classification cs.CV

keywords unpairedimagedehazingKolmogorov-ArnoldNetworksDual-GR-KANTransformercontrastivelearningadversarialtrainingrestorationvisiongenerativenetwork

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 tries to establish that an unpaired image-dehazing network whose transformer layers replace MLPs with Kolmogorov-Arnold Network layers can clear real haze without paired training data. Called UID-KAT, the model is trained on only 1,000 hazy and 1,000 clean images, using adversarial, identity, and patch-wise contrastive losses to map hazy features into clean features. On the public SOTS-Outdoor and HSTS benchmarks, the largest variant reports 24.57 dB PSNR and 0.917 SSIM and 27.16 dB PSNR and 0.930 SSIM, higher than prior unpaired dehazers such as UCL-Dehaze while using fewer MACs. A sympathetic reader would care because successful unpaired dehazing removes the need for paired hazy/clean data and because the result suggests KAN-based feature transformation is viable in generative image restoration.

What carries the argument

The load-bearing component is the Dual-GR-KAN Transformer, a vision-transformer block in which the usual MLP channel mixer and token mixer are both replaced by GR-KAN layers. GR-KAN layers learn univariate edge functions as rational functions with a Safe Padé activation that prevents the denominator from driving the output unbounded. The module patches a feature map of shape $H \times W \times C$ into $N$ tokens, runs two residual blocks each made of normalization plus GR-KAN, and unpatches back to the original shape. This design carries the argument by showing that KAN-based latent transformation, rather than attention or MLP mixing, is what the paper credits for stable GAN training and improved dehazing quality, and the patch-wise contrastive loss operates on the same $H \times W \times C$ feature maps.

What would settle it

Retrain every compared unpaired method on the same 1,000 hazy and 1,000 clean images with the exact batch size, epochs, learning-rate schedule, random crops, and evaluation code used for UID-KAT, then measure PSNR and SSIM on SOTS-Outdoor and HSTS; if UCL-Dehaze or HDUD matches or beats UID-KAT under matched conditions, the central claim fails. A second concrete test is to replace the GR-KAN layers with MLP or attention mixers at matched parameter count under the identical protocol; if the metrics do not drop, the KAN-specific contribution is not confirmed.

Watch

Extended reading notes

Core claim

The central discovery claimed by the paper is that a Kolmogorov-Arnold feature transformer can serve as the core of an unpaired dehazing generator and deliver better benchmark numbers than existing unpaired methods at lower computational cost. The generator is a ResNet-style encoder-decoder with self-calibrated convolutions and SiLU activations, but the nine residual blocks are replaced by nine Dual-GR-KAN Transformer modules, each applying GR-KAN layers to both token mixing and channel mixing in a patch-embedded latent space. Training combines a least-squares adversarial loss, an identity loss, and a patch-wise contrastive loss that pulls corresponding patches of hazy and restored images together while pushing away non-corresponding patches. Reported results for the base variant are 24.57 dB PSNR and 0.917 SSIM on SOTS-Outdoor and 27.16 dB PSNR and 0.930 SSIM on HSTS, with 18.08 million parameters and 38.28 GMACs, above the cited UCL-Dehaze results of 24.23 dB and 0.914 on SOTS-Outdoor and 26.03 dB and 0.919 on HSTS.

Load-bearing premise

The load-bearing premise is that Table II is an apples-to-apples comparison, meaning the baseline methods were evaluated under the same data sampling, training protocol, and evaluation code as UID-KAT; the paper's two Experimental Settings passages give conflicting protocols (batch size 4 vs 1, 400 vs 100 epochs, learning rate $10^{-4}$ vs $2 \times 10^{-4}$) and do not state that the baselines were re-run.

Editorial extensions

If this is right

Unpaired dehazing can be built from KAN-style transformers and trained on small unpaired image sets, removing the need for paired hazy/clean data in practical dehazing applications.
The Dual-GR-KAN Transformer can replace attention-based mixers in GAN training for ill-posed image translation, because the paper reports that attention-based mixers led to mode collapse while the dual GR-KAN setting trained stably.
The reported efficiency numbers imply that a competitive unpaired dehazer can run in roughly 0.02 seconds per image on a GPU, which matters for real-time or embedded use.
If the results hold, KAN layers are a viable alternative to MLPs for latent feature transformation in low-level vision, not only in classification or high-level tasks.

Reading between the lines

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

Editorial inference: because the framework trains on just 1,000 images per domain, the patch-wise contrastive loss may be doing much of the heavy lifting; a matched-parameter ablation that removes GR-KAN while keeping contrastive learning would tell whether KAN layers or the loss combination drive the reported gains.
Editorial inference: the authors' observation that attention-based mixing collapsed during GAN training is a generalizable design warning for unpaired restoration, and it suggests testing a stabilizer before using attention in adversarial restoration generators.
Editorial inference: the same Dual-GR-KAN transformation stage could be dropped into other unpaired restoration tasks such as deraining, denoising, or low-light enhancement, since the framework is not tied to the physics of haze.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear colleague,

The short version: this paper has a plausible, mildly novel idea — using GR-KAN layers for both token and channel mixing inside a transformer, plus CUT-style contrastive loss, for unpaired image dehazing — and the efficiency numbers are attractive. But as written, the main empirical claim is not verifiable, because the experimental section is internally contradictory. I'd trust nothing in Table II without a rewrite and a code check.

What's genuinely new: the specific combination of a Dual-GR-KAN Transformer (KAN in both mixer roles) with contrastive learning for unpaired dehazing doesn't appear in the cited literature, and the ablation structure would be informative once the tables are cleaned up. The paper also cites its nearest prior art (KAT, KAN-CUT, UCL-Dehaze) instead of pretending those don't exist. That's honest.

The soft spots are real and load-bearing. The text gives two conflicting training protocols: batch size 4, lr 1e-4, 400 epochs versus batch size 1, lr 2e-4, 100 epochs. The prose reports a "UID-KAT-L" with numbers that don't match any row of Table II. The ablation tables appear twice with different baselines (15.71 dB vs 23.01 dB). A "DCH loss" is praised in the ablation but never defined or placed in Eq. (17), and the manuscript contains "bla bla bla" and "Fig. X" placeholders. These aren't cosmetic typos; they prevent anyone from knowing what was actually run. The paper also never states whether baselines were re-run under matched conditions or simply quoted, which is essential for any SOTA claim. And it does not compare against KAN-CUT, the one prior KAN-based unpaired I2I method it cites, weakening the "first to apply KAN to unpaired dehazing" claim.

If the underlying experiments are real, the idea is worth pursuing. The reported MACs are low and the gains over UCL-Dehaze in Table II are plausible. I don't think the architecture should be dismissed. But the manuscript as it stands is not scientifically usable, and I would not want a student to benchmark against these numbers without the code running.

The intended reader is someone working on KANs for low-level vision or on unpaired dehazing. I would not cite it in this form, but I'd keep an eye on a revised version.

Recommendation: I'd send this back for major revision rather than desk-reject outright — the topic is relevant and the flaws are, on the surface, fixable. But the rewrite needs to reconcile the settings, define every loss, remove the placeholders, and release working code before the claim is taken seriously.

Referee Report

5 major / 4 minor

Summary. The paper proposes UID-KAT, an unpaired single-image dehazing framework that combines a KAN-based transformer module (the 'Dual-GR-KAN Transformer') with a PatchGAN discriminator and a patch-wise contrastive loss borrowed from CUT/UCL-Dehaze. The central claim is that UID-KAT achieves state-of-the-art dehazing performance on SOTS-Outdoor and HSTS while requiring fewer MACs than existing unpaired methods. The evidence for this claim is presented in Table II, which reports PSNR/SSIM for three UID-KAT variants against a set of prior-based and learning-based baselines.

Significance. If the reported numbers were reliable, the contribution would be of interest: it would show that replacing MLP-based mixers with GR-KAN layers inside a transformer block yields a favorable accuracy-efficiency trade-off for unpaired dehazing (e.g., UID-KAT-B at 38.28 GMACs versus UCL-Dehaze at 78.85 GMACs with comparable or better PSNR). The application of KANs to ill-posed unpaired image restoration is a plausible and timely direction, and the architecture description in Section III-B is reasonably clear. However, as submitted, the manuscript contains multiple internal contradictions in the training protocol, the model nomenclature, the ablation tables, and even the main quantitative table, so the quantitative evidence cannot be accepted as reported.

major comments (5)

[Section IV-A, 'Experimental Settings'] The paper contains two mutually contradictory descriptions of the training protocol. The first states a batch size of 4, a learning rate of 10^-4 decayed uniformly to zero, and 400 epochs; the second states a batch size of 1, a learning rate of 2×10^-4 for the first 50 epochs linearly reduced to zero over the remaining 50, and 100 epochs. No statement indicates which protocol produced the results in Table II, so the main empirical results are not reproducible from the manuscript.
[Section IV-B, 'Quantitative Evaluations'] The prose reports that 'UID-KAT-L achieves the best performance among all methods, with a PSNR of 24.63 dB and an SSIM of 0.919 for the SOTS-Outdoor dataset, and a PSNR of 26.57 dB and an SSIM of 0.929 for the HSTS dataset.' However, Table I defines only UID-KAT-T, UID-KAT-S, and UID-KAT-B, and Table II lists UID-KAT-B as 24.57 dB/0.917 on SOTS-Outdoor and 27.16 dB/0.930 on HSTS. The prose describes a nonexistent variant with different numbers than the table, so the reported state-of-the-art claim is internally inconsistent.
[Section IV-C, Tables III (both versions)] The ablation tables are self-contradictory. The first Table III shows a baseline of 15.71 dB PSNR/0.769 SSIM, while the second Table III shows a baseline of 23.01 dB/0.894 SSIM; these are not reconcilable. The first Table III also contains malformed entries, such as a '+SCConv' row with no PSNR value and a 'ResConv→Dual-GR-KAN' row with repeated '23.28' values in place of a coherent metric. As a result, the ablation claims about the contributions of SCConv, SiLU, and the Dual-GR-KAN transformer are not supported by consistent data.
[Section IV-C, ablation text and Table III] The manuscript mentions a 'DCH Loss' in the ablation study and in Table III, claiming that it improves visual quality without significant quantitative gain, but this loss is never defined and does not appear in the integrated loss L_final in Eq. (17). An undefined loss cannot be evaluated or reproduced, and the sentence 'DCH Loss, even though it does not give a significant improvement...' is presented without any equation, reference, or description.
[General manuscript quality, Sections IV-A through IV-C] The manuscript contains duplicated paragraphs: the entire 'Experimental Settings' and 'Quantitative Evaluations' subsections appear twice verbatim, and the ablation section is also partially duplicated. It also contains placeholder text such as 'as bla bla bla' and 'as can be noticed in Fig. X'. The qualitative section discusses methods (AOD-Net, GCANet, PFDN, FFA-Net, DehazeFormer-S) that are not listed in Table II and do not appear in the quantitative comparison. These issues prevent the reader from determining which results are actual and which are editorial artifacts, so the paper is not in a citable form.

minor comments (4)

[Figure numbering] Figure numbering is inconsistent and duplicate figure captions appear (e.g., Fig. 3, Fig. 4, Fig. 5 are reused with different content in different sections; the 'Effects of different mixer configurations' figure is numbered both Fig. 7 and Fig. 8).
[References and notation] Reference numbering is incorrect: Adam optimizer is cited as [52] in one 'Experimental Settings' paragraph and as [54] in the other; Eq. (10) uses 'm/n' for the rational function degree while n is also used for the number of contrastive patches in Eq. (15), creating notational confusion.
[Section IV-B, first paragraph] The text says 'the performance comparison presented in Table I highlights the effectiveness' but the comparison is actually in Table II; Table I only lists model variants.
[Table II caption and baselines] The paper does not state whether the baseline numbers in Table II were re-run under the same protocol or quoted from their original publications, so even the valid rows of the comparison cannot be verified as matched.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: benchmark claims are empirical measurements, not derived from their inputs; unresolved reproducibility defects are correctness risks, not circularity.

full rationale

UID-KAT is an empirical architecture paper. Its derivation chain, Eqs. (1)-(17), consists of the standard Kolmogorov-Arnold representation theorem, the GR-KAN parameterization from [15], and well-known LSGAN/identity/patch-wise contrastive losses; the final loss is a weighted sum, not a self-referential identity. The claimed state-of-the-art is a benchmark measurement reported in Table II, and the numbers are not obtained by fitting parameters to the test set or by defining the model in terms of its own output. The author's self-citations (e.g., [1,2,8,14,21,27,29]) are background or comparison references and carry none of the load for the central KAN-transformer claim. There is no uniqueness theorem imported from the authors, and no ansatz is smuggled in solely via self-citation: GR-KAN and the contrastive loss are attributed to external works [15,19]. The manuscript does contain serious non-circularity defects: Section IV-A gives mutually incompatible training protocols (batch size 4/400 epochs/1e-4 vs batch size 1/100 epochs/2e-4), the text reports a nonexistent 'UID-KAT-L' with numbers different from Table II, Tables III-IV are internally inconsistent and contain misplaced values, 'DCH Loss' is never defined or included in Eq. (17), and placeholders such as 'bla bla bla' and 'Fig. X' appear. Additionally, the ablation study selects hyperparameters (activation, patch size, mixer configuration) using the SOTS-Outdoor and HSTS evaluation sets, which biases the reported SOTA but does not make the prediction equivalent to its input by construction. These issues undermine the verifiability of the empirical comparison, but independent re-runs could falsify the table; therefore no circular step is identified.

Assumptions & free parameters 5 free parameters · 5 assumptions · 1 invented entities

This paper does not derive anything from first principles. The generator is assembled from known components: a ResNet backbone, SCConv, PatchGAN, CUT-style contrastive loss, and GR-KAN layers. The free choices are architectural sizes, loss weights, patch size, and training schedules. The main unstated assumptions are that unpaired RESIDE subsets suffice for generalization, that patch alignment survives flattening and pixel shuffle, and that Safe Pade activation is stable in GAN training.

free parameters (5)

Loss balancing weights (lambda_1, lambda_2, lambda_3) = 1, 1, 5
Inherited from UCL-Dehaze [11] and not re-validated in this paper. These weights directly shape the integrated loss in Eq. (17).
Contrastive temperature tau = 0.07
Taken from CUT [19]. It controls the sharpness of the contrastive distribution in Eq. (15).
Transformer patch size P = 4 x 4
Selected after an ablation over 4 x 4, 8 x 8, and 16 x 16 in Table VII, i.e., chosen on data rather than derived.
Number of Dual-GR-KAN blocks = 9 (tiny/small), 5 (base)
Table I lists different block counts for variants, while the text elsewhere says nine residual blocks are replaced. This is a hand-chosen architectural degree of freedom.
First-stage channel width = 16 (T), 32 (S), 64 (B)
The three model variants are sized by hand to hit different MAC budgets; no selection criterion is given.

assumptions (5)

standard math Kolmogorov-Arnold representation theorem justifies KAN layers.
Invoked in Section II-D to motivate KANs, but the actual layer uses learned rational functions from GR-KAN, not the theorem's exact construction, so the theorem is only background motivation.
domain assumption A random subset of 1,000 hazy images from OTS, RTTS, and URHI and 1,000 clean images from OTS and ITS is representative enough to generalize to SOTS-Outdoor and HSTS.
This is the entire training distribution for the model. Section IV-A defines the sampling, and the evaluation is on different RESIDE splits, but representativeness is asserted, not demonstrated.
domain assumption Patch embedding and unembedding preserve spatial alignment for the contrastive loss.
The Dual-GR-KAN Transformer flattens patches and later uses pixel shuffle to restore RHxWxC. The patch-wise contrastive loss in Eq. (16) assumes that positive patches from the restored image correspond spatially to patches in the input image.
domain assumption Adversarial and contrastive losses are sufficient for unpaired hazy-to-clean mapping.
The framework uses no cycle consistency and no paired supervision. It assumes that PatchGAN plus the NCE loss can isolate the hazy-to-clean direction without additional constraints.
ad hoc to paper The Safe Pade activation with an absolute value denominator prevents rational function poles from destabilizing training.
Eq. (11) is introduced to avoid Q(x) tending to zero, but no stability analysis or empirical evidence is provided beyond the final benchmark numbers.

invented entities (1)

Dual-GR-KAN Transformer
purpose: Replaces MLP-based token and channel mixing in the generator's latent transformation stage.
This is the paper's main architectural contribution. Its only evidence is benchmark performance; there is no independent falsifiable handle outside the reported experiments.

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Cite this review

Pith. "Pith review of Unpaired Image Dehazing via Kolmogorov-Arnold Transformation of Latent Features." pith.science (2026). https://pith.science/paper/TKYF7LRX

@misc{pith2026250207812,
  author       = {Pith},
  title        = {Pith review of: Unpaired Image Dehazing via Kolmogorov-Arnold Transformation of Latent Features},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TKYF7LRX}},
  note         = {Machine review of arXiv:2502.07812}
}

read the original abstract

This paper proposes an innovative framework for Unsupervised Image Dehazing via Kolmogorov-Arnold Transformation, termed UID-KAT. Image dehazing is recognized as a challenging and ill-posed vision task that requires complex transformations and interpretations in the feature space. Recent advancements have introduced Kolmogorov-Arnold Networks (KANs), inspired by the Kolmogorov-Arnold representation theorem, as promising alternatives to Multi-Layer Perceptrons (MLPs) since KANs can leverage their polynomial foundation to more efficiently approximate complex functions while requiring fewer layers than MLPs. Motivated by this potential, this paper explores the use of KANs combined with adversarial training and contrastive learning to model the intricate relationship between hazy and clear images. Adversarial training is employed due to its capacity in producing high-fidelity images, and contrastive learning promotes the model's emphasis on significant features while suppressing the influence of irrelevant information. The proposed UID-KAT framework is trained in an unsupervised setting to take advantage of the abundance of real-world data and address the challenge of preparing paired hazy/clean images. Experimental results show that UID-KAT achieves state-of-the-art dehazing performance across multiple datasets and scenarios, outperforming existing unpaired methods while reducing model complexity. The source code for this work is publicly available at https://github.com/tranleanh/uid-kat.

Figures

Figures reproduced from arXiv: 2502.07812 by the authors.

**Figure 2.** The proposed UID-KAT framework. the encoder and decoder for preserving low-level information. To ensure semantic fidelity and structural consistency, patch-level contrastive learning is employed which helps to maximize mutual information between corresponding patches in a learned feature space. The networks are trained using a combination of multiple loss functions, collectively enhancing visual quality, structural… view at source ↗

**Figure 4.** Typical visual results on SOTS-Outdoor. Fig. 3: Typical visual results on SOTS-Outdoor. Fig. 4: Typical visual results on SOTS-Outdoor. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

Figures from the paper (5 more)

**Figure 5.** Figure 5: Typical visual results on HSTS. Fig. 5: Typical visual results on HSTS. Fig. 4: Typical visual results on HSTS [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Typical visual results on natural data. Fig. 5: Typical visual results on natural data [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 6.** Figure 6: Effects of integrated components. Fig. 6: Effects of modifications to the baseline. Fig. 6: Effects of integrated components. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Effects of different mixer configurations (Token mixer/Channel mixer). Fig. 7: Effects of different mixer configurations (Token mixer/Channel mixer). Fig. 7: Effects of different mixer configurations (token mixer/channel mixer). [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Abstracted architecture of GR-KAN transformer. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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L. Li, Y . Dong, W. Ren, J. Pan, C. Gao, N. Sang, and M.-H. Yang, “Semi- supervised image dehazing,” IEEE Transactions on Image Processing , vol. 29, pp. 2766–2779, 2019

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S. An, X. Huang, L. Wang, L. Wang, and Z. Zheng, “Semi-supervised image dehazing network,” The Visual Computer , vol. 38, no. 6, pp. 2041–2055, 2022

2022
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D. Engin, A. Genc ¸, and H. Kemal Ekenel, “Cycle-dehaze: Enhanced cyclegan for single image dehazing,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops , 2018, pp. 825–833

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B. Li, Y . Gou, S. Gu, J. Z. Liu, J. T. Zhou, and X. Peng, “You only look yourself: Unsupervised and untrained single image dehazing neural network,” International Journal of Computer Vision, vol. 129, no. 5, pp. 1754–1767, 2021

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C.-L. Guo, Q. Yan, S. Anwar, R. Cong, W. Ren, and C. Li, “Image dehazing transformer with transmission-aware 3d position embedding,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2022, pp. 5812–5820

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Y . Wang, J. Xiong, X. Yan, and M. Wei, “Uscformer: Unified trans- former with semantically contrastive learning for image dehazing,” IEEE Transactions on Intelligent Transportation Systems , vol. 24, no. 10, pp. 11 321–11 333, 2023

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S. Elfwing, E. Uchibe, and K. Doya, “Sigmoid-weighted linear units for neural network function approximation in reinforcement learning,” Neural networks, vol. 107, pp. 3–11, 2018

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N. H. Kaplan, “Real-world image dehazing with improved joint en- hancement and exposure fusion,” Journal of Visual Communication and Image Representation, vol. 90, p. 103720, 2023

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

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