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REVIEW 3 major objections 5 minor 39 references

Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessment

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read TaylorKAN, a Kolmogorov-Arnold network using second-order Taylor expansions as edge activations, consistently outperforms B-spline, orthogonal-polynomial, wavelet, and Fourier KAN variants in blind image quality score regression across…

desk verdict A competent but modest KAN-variant paper whose main empirical claim is undermined by an ambiguous hyperparameter-selection protocol; deserves review but needs clarification. read the letter →

arxiv 2505.21592 v1 pith:UMATMB5J submitted 2025-05-27 eess.IV cs.CVcs.LG

Ze Chen , Shaode Yu This is my paper
classification eess.IVcs.CVcs.LG
keywords blindimagequalityassessmentKolmogorov-ArnoldnetworkTaylorexpansionscoreregressiondimensionalityreductionprincipalcomponentanalysisauthenticdistortionsno-reference
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 TaylorKAN, a Kolmogorov-Arnold network variant that replaces B-splines and orthogonal polynomial bases with truncated Taylor series as learnable edge functions for blind image quality assessment. It claims that on five authentic-distortion databases, TaylorKAN consistently outperforms other KAN-related models in predicting human opinion scores, and that second-order local Taylor approximation is more effective for this regression task than global orthogonal expansions. It also argues that PCA compression and reduced network depth make the model substantially faster, with training-time reductions up to 12.6x while keeping accuracy nearly intact. If the claim holds, TaylorKAN offers an efficient regression head for high-dimensional deep features in quality assessment and similar score-prediction tasks.

What carries the argument

The load-bearing mechanism is the truncated Taylor expansion $f(x) \approx \sum_{n=0}^{N} \frac{f^{(n)}(a)}{n!}(x-a)^n$ used as the learnable univariate function on every KAN edge, with $N=2$ and expansion point $a=0$ after z-score standardization. Because the basis functions are simple powers of the input, the edge computation is a weighted sum of monomials, avoiding the knot selection needed for B-splines and the global basis of orthogonal polynomials; the paper argues this local approximation is what makes TaylorKAN accurate and cheap. Supporting machinery is the auto-layer configuration (four layers with widths chosen from the PCA-retained dimension) and PCA with $V_{\mathrm{ratio}} \ge \tau$ for $\tau \in \{0.90, 0.95\}$ and a floor of 64 components, which together shrink the per-forward cost $O(\sum_l d_l \cdot b \cdot d_{l+1})$ of the network.

What would settle it

Recompute the intra-database evaluation with PCA fitted strictly on the training partition and repeat the random split across several seeds, reporting mean and spread. If TaylorKAN's PLCC/SRCC advantage over FastKAN or BSRBFKAN does not persist under this protocol, the central claim of consistent KAN-family superiority would be contradicted.

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Extended reading notes

Core claim

The central discovery is that a KAN whose edge activations are monomials from a second-order Taylor expansion achieves the best or near-best PLCC and SRCC among twelve score-regression models on four of five databases, and is the top KAN variant on all five. Because every KAN model is given the same 2048-dimensional ResNet-50 features, the same PCA settings, and the same auto-configured four-layer width, the consistent margin over ChebyKAN, JacobiKAN, HermiteKAN, WavKAN, FourierKAN, BSRBFKAN, and FastKAN is attributed to the Taylor basis itself. The paper frames this as evidence that local, non-orthogonal approximation around a single expansion point captures the structure of quality-score mapping better than global orthogonal bases. Inter-database experiments show TaylorKAN ranks top most often when trained on BID, SPAQ, or FLIVE, supporting its generalization.

Load-bearing premise

The claim of consistent superiority assumes the PCA projection is fitted on the training partition alone and that the single 70/15/15 split represents typical performance; if test images leak into the PCA fit or the split is lucky, the reported correlations would no longer describe truly blind prediction.

Editorial extensions

If this is right

  • KAN-based score regression can be made practical for high-dimensional features: PCA compression plus a four-layer TaylorKAN cuts training time by up to 12.6x with negligible PLCC/SRCC loss.
  • For BIQA regression on authentic distortions, local monomial bases appear better suited than global orthogonal bases, suggesting the underlying score function is locally smooth in the PCA-projected feature space.
  • The second-order expansion is the empirical sweet spot: orders 1, 3, and 4 underperform order 2 across databases, so the model benefits from just enough nonlinearity to fit the mapping without overfitting.
  • TaylorKAN transfers across databases, ranking top most often in inter-database tests; this suggests the learned feature-to-score mapping captures content-invariant quality patterns, not just database-specific biases.
  • A visible gap to modern deep BIQA models remains, so TaylorKAN is positioned as an efficient regression head for pre-trained features rather than a complete replacement for end-to-end learned quality assessment.

Reading between the lines

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

  • A direct extension would be to make the expansion point $a$ a learnable parameter per edge or per layer instead of fixing $a=0$ after standardization; if TaylorKAN's advantage comes from local approximation, adapting the center could improve accuracy on skewed score distributions like KonIQ and FLIVE.
  • The same local-monomial activation could be tested on other high-dimensional regression tasks, such as aesthetics scoring, compression-quality prediction, or deep-feature-based medical image grading, to see whether the 'local beats global' pattern is specific to IQA or generic.
  • Since SVR outperforms TaylorKAN precisely on the right-skewed datasets, a dataset-adaptive mixture or an ensemble of TaylorKAN and a kernel regressor might combine the strengths of both, but this is an untested hypothesis.
  • The PCA-leakage concern raised by the protocol description is testable by comparing eigenvalues computed on the full database versus training-only; we infer the authors likely intended training-only fitting, but the paper does not state it.
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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

3 major / 5 minor

Summary. The manuscript proposes TaylorKAN, a Kolmogorov-Arnold network variant in which the learnable edge functions are truncated Taylor series, and integrates it into a blind image quality assessment (BIQA) pipeline with PCA-based dimensionality reduction and an automated depth/width configuration. Experiments on five authentically distorted databases (BID, CLIVE, KonIQ, SPAQ, FLIVE) compare TaylorKAN with SVR, MLP, and nine KAN variants under intra-database and inter-database protocols. The paper reports that TaylorKAN consistently achieves the highest PLCC/SRCC among KAN-based models, is competitive with SVR, and reduces training time relative to several KAN variants. The authors interpret the results as evidence that local Taylor approximation is more effective than global orthogonal-function approximation for BIQA score regression.

Significance. If the reported results hold under a clean evaluation protocol, the contribution is practically useful: it shows that a simple, low-order Taylor activation can outperform B-spline and orthogonal-polynomial KAN variants on high-dimensional regression while being computationally cheaper, and it provides an efficient BIQA score-regression pipeline using pre-trained ResNet-50 features. The code is publicly available, and the evaluation spans five databases with both intra- and inter-database testing, which are strengths. However, the paper's central mechanistic claim that Taylor expansions are intrinsically better than global orthogonal bases is not yet established because the text does not rule out test-set-based order selection and does not specify whether PCA is fit on training data only. These protocol issues are load-bearing for the main comparison, so the manuscript needs revision before the conclusions can be accepted.

major comments (3)
  1. [Sec. III.E and Sec. IV.D.2 (Fig. 3)] The paper states in Sec. III.E that TaylorKAN's expansion order is set to 2 and that other KAN models use default parameter settings, while Sec. IV.D.2 and Fig. 3 report that second-order expansion achieves the highest PLCC/SRCC across databases and is adopted. The text does not state whether the curves in Fig. 3 are computed on the validation or test partition. If test performance was used to select order 2, TaylorKAN has effectively been selected on the test set while ChebyKAN, JacobiKAN, HermiteKAN, WavKAN, FourierKAN, and B-spline variants receive no equivalent hyperparameter search (for example over polynomial degree or number of basis functions). This conflates basis-family choice with favorable hyperparameter selection and invalidates the abstract's mechanistic conclusion that local Taylor approximation is more effective than global orthogonal-function approximation. The authors must specify the partition used for order selection and, if it was the test set, re-select the order on validation data; in either case, the compared KAN variants should be given a comparable validation-based tuning budget.
  2. [Sec. III.C.1 and Sec. III.E] Eq. (7) defines the cumulative explained-variance ratio from eigenvalues of 'a dataset X', and Sec. III.E describes the data split into training/validation/test but never states that PCA is fitted on the training partition only. If the covariance matrix is computed from the full database before the split, the projection axes encode test-image content, violating the blind-test assumption and potentially inflating all intra- and inter-database PLCC/SRCC values. The manuscript must state explicitly that PCA is fit on training images only, and if the current implementation used full-data PCA, the experiments must be rerun with training-only PCA. This is load-bearing because dimensionality reduction is part of the proposed pipeline and affects every reported comparison.
  3. [Sec. III.E and Tables II, IV] All results are based on a single fixed 70/15/15 split using one random seed. Tables II and IV therefore report point estimates without any measure of variance across splits, and the claims of 'consistently outperforms' across five databases rest on differences that may be within split-to-split noise. The authors should report results over multiple seeds or splits (mean and standard deviation) or at least verify that the main TaylorKAN-versus-baseline gaps persist across several splits. This is particularly important because the significance markers in Table II are computed on a single test partition, which does not capture the variability of the evaluation protocol.
minor comments (5)
  1. [Sec. III.C.1] The notation is inconsistent: the text uses 'V ratio' in the prose and Eq. (7) uses 'Vratio' without a subscript, while Fig. 2 uses 'V ratio'. Please unify the notation for the explained-variance ratio.
  2. [Sec. II.D and Appendix A] HermiteKAN is described in Appendix A and mentioned in Sec. II.D without a citation, whereas ChebyKAN and JacobiKAN have references. A reference for the HermiteKAN implementation should be added or the absence justified.
  3. [Sec. IV.D.2 and Fig. 3] Figure 3 reports that second-order Taylor expansion is best but provides no numerical values, confidence intervals, or statistical test; given that this figure is used to justify the chosen order, the exact metric values on the relevant partition should be reported in the text or caption.
  4. [Sec. V and Table VI] The comparison with deep BIQA models such as SFA, HyperIQA, DB-CNN, QPT-ResNet50, and QCN is presented as a 'current achievement' table, but these methods use different feature extractors, training procedures, and possibly different evaluation protocols. The table should be described as indicative rather than as a head-to-head ranking, or the protocols must be aligned.
  5. [Sec. I and Appendix B] The learning-rate grid in Appendix B lists values ending at 1e-2, while Sec. III.E states the grid goes to 5e-2. The discrepancy should be resolved so the reported hyperparameter search is unambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: TaylorKAN's reported advantage rests on an independent empirical comparison, not on a derivation that reduces to its inputs.

full rationale

The paper's central claim is empirical: TaylorKAN, a KAN whose edge functions are truncated Taylor polynomials, is compared against twelve other KAN variants and several BIQA methods on five databases under a common feature-extraction and train/validation/test protocol. The Taylor expansion formula (Eq. 4) is a mathematical definition of the activation family, not an equation that defines the target PLCC/SRCC; the reported metrics are measured on held-out test partitions, so the superiority claim is not equivalent by construction to the choice of activation. The expansion order is fixed to 2 in Section III.E ('For TaylorKAN, its expansion order is set to 2, and the other KAN models use default parameter settings'), and Figure 3 is presented as an ablation showing the sensitivity to order. If the order or other hyperparameters had been selected using test-set curves, that would be a data-leakage/correctness concern, but the paper does not state that Figure 3 or the grid search in III.E was evaluated on the test partition, and the inference 'order 2 is best' is an empirical observation rather than a logical consequence of the model definition. The self-citation to the authors' earlier KAN-for-BIQA study [25] is used to motivate the high-dimensional-feature difficulty, but the current paper independently reproduces KAN's limited performance in Table II, so the citation is not load-bearing. No uniqueness theorem, no ansatz smuggled via citation, and no renaming of a known result as a new derivation were found. Under the stated rules, the absence of a demonstrated reduction of the claimed result to its own inputs yields a no-circularity verdict.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. Its free parameters are method hyperparameters, and two of them (Taylor order and PCA variance ratio) are selected using target-dataset outcomes. The axioms are standard mathematical background plus domain assumptions about the quality relevance of ResNet-50 features and PCA variance.

free parameters (3)
  • Taylor expansion order = 2
    Selected after observing Figure 3; order 2 yields the highest PLCC/SRCC on test subsets of the five databases.
  • PCA variance ratio tau = 0.95 (main results; 0.90 also tested)
    Hand-chosen; controls k, the number of PCs, and therefore the model input dimension; main-table numbers likely use 0.95, though the paper does not state this per database.
  • Auto-config hidden widths = [input_dim, 64/128/256/512, 16/32/64/128, 1]
    Ad hoc rules from Algorithm 1; shared by all KAN models in the comparison, but still hand-picked architecture choices.
assumptions (4)
  • standard math Kolmogorov-Arnold representation theorem
    Used in Section II.A to justify KAN as a finite sum of univariate functions.
  • domain assumption ResNet-50 features are quality-relevant
    Section III.B uses the last FC layer of ResNet-50 as the feature extractor; the entire method inherits its quality representation.
  • domain assumption PCA variance is a proxy for quality-relevant variance
    Section III.C.1 keeps PCs by explained variance ratio; nothing guarantees variance-preserving components are the quality-discriminative ones.
  • domain assumption MOS labels are reliable ground truth
    All metrics (PLCC/SRCC) are computed against ground-truth MOS from the five databases.

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Cite this review

Pith. "Pith review of Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessment." pith.science (2026). https://pith.science/paper/UMATMB5J

@misc{pith2026250521592,
  author       = {Pith},
  title        = {Pith review of: Taylor expansion-based Kolmogorov-Arnold network for blind image quality assessment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UMATMB5J}},
  note         = {Machine review of arXiv:2505.21592}
}
read the original abstract

Kolmogorov-Arnold Network (KAN) has attracted growing interest for its strong function approximation capability. In our previous work, KAN and its variants were explored in score regression for blind image quality assessment (BIQA). However, these models encounter challenges when processing high-dimensional features, leading to limited performance gains and increased computational cost. To address these issues, we propose TaylorKAN that leverages the Taylor expansions as learnable activation functions to enhance local approximation capability. To improve the computational efficiency, network depth reduction and feature dimensionality compression are integrated into the TaylorKAN-based score regression pipeline. On five databases (BID, CLIVE, KonIQ, SPAQ, and FLIVE) with authentic distortions, extensive experiments demonstrate that TaylorKAN consistently outperforms the other KAN-related models, indicating that the local approximation via Taylor expansions is more effective than global approximation using orthogonal functions. Its generalization capacity is validated through inter-database experiments. The findings highlight the potential of TaylorKAN as an efficient and robust model for high-dimensional score regression.

Figures

Figures reproduced from arXiv: 2505.21592 by the authors.

Figure 1
Figure 1. Architectures of KAN and TaylorKAN. Unlike B-splines, Taylor series require no piecewise mod￾eling or control point optimization. Thus, they eliminate the need for pre-processing steps such as knot selection, making them a simpler alternative for approximating local function behavior around a given expansion point. D. The difference between KAN and TaylorKAN [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The effect of changing variance ratio Vratio on the number of remaining PCs. TABLE V: The factors on computational efficiency Dataset LNo. Vratio PLCC SRCC Time (s) CLIVE 6 1.00 0.792 0.771 43.18 4 1.00 0.788 0.755 4.671 (× 9.2) 4 0.95 0.783 0.753 3.421 (× 12.6) KonIQ 6 1.00 0.851 0.831 239.1 4 1.00 0.844 0.830 52.33 (× 4.6) 4 0.95 0.830 0.816 37.85 (× 6.3) V. DISCUSSION TaylorKAN achieves the best performance among… view at source ↗
Figure 3
Figure 3. The effect of Taylor expansion orders on score regres [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Performance of TaylorKAN across different learning rates. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: The distribution of MOS values of the five image databases. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.