{"id":"2ccf09df-1c24-4607-94cf-01d15066a3ee","arxiv_id":"2505.04740","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"The authors augment ViT with hybrid spline and wavelet KAN modules and claim state-of-the-art results across classification, detection, and segmentation, but they release no code or evidence that the experiments were run.","lead":"This paper proposes a vision transformer that replaces the standard MLP layers with two Kolmogorov-Arnold network variants, a spline-based Eff-KAN and a wavelet-based Wav-KAN, and reports state-of-the-art accuracy on ImageNet, COCO, and ADE20K. It is a representative KAN-for-vision paper that provides no code, checkpoints, or training logs, so the headline results cannot be independently verified.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim rests on unreproducible SOTA numbers and internally inconsistent comparisons; the wavelet gradient formulas in Eqs. (5.2), (6.2), (7.2), (7.3) are also mathematically wrong.","rationale":"The reader's verdict of REJECT is justified. I agree with the reader that the gradient formulas are a weak point, but I would frame the load-bearing issue slightly more broadly: with no code or checkpoints and internally inconsistent tables, the empirical claims are simply unverified. The reader identified the gradient formulas as the weakest assumption; I partially agree, but I would place at least equal weight on the unreproducible results and the inconsistent baseline labeling. No independent support exists to offset this: there is no formal verification, no released code, and no external replication. A REJECT verdict is therefore appropriate.","tokens_in":18971,"tokens_out":1641,"duration_ms":17754,"concrete_test":"Recompute the partial derivatives in Eqs. (5.1)–(7.3) with a symbolic differentiation tool; if they differ from the printed formulas, implement the corrected gradients and re-run Hyb-KAN ViT-S on ImageNet-1K with the Section 4.3 recipe to check whether the Table 3/4 accuracies are reproducible. Separately, rerun the Table 5 and Table 6 comparisons with the correct backbone names and the same training schedule to verify the reported AP and mIoU margins.","verdict_should_be":"REJECT","load_bearing_attack":"The paper's central claim is that Hyb-KAN ViT achieves state-of-the-art ImageNet-1K / COCO / ADE20K results (e.g., 86.3% top-1, Table 4). For this to hold, the reported numbers would need to be produced by the architecture and training procedure described in Sections III–IV. Three load-bearing problems block that. First, the scale-parameter gradients in Eqs. (5.2), (6.2), (7.2), and (7.3) are not correct: the DoG derivative in (5.2) contains a spurious '-1' term and omits the chain-rule factor from the Gaussian exponent; the Mexican-hat derivative in (6.2) has an incorrect power of sigma; and the Morlet derivative in (7.2) misses the term from differentiating the Gaussian envelope, so the optimization loop for σ and ω0 as written cannot be the training procedure that produced the results. Second, the numbers themselves are unverifiable: no code, checkpoints, training logs, or external evaluations are provided, and Table 3's 84.5% ViT-S at 5.97 GFLOPs exceeds published 224x224 backbones of comparable FLOPs with no compute budget reported. Third, the comparison tables are internally inconsistent: Table 5 lists rows labeled 'Eff-KAN ViT-S (Ours)' under Base with 191M params, and Table 6 lists 'ViT-S' under a Base segment, so the reported margins over earlier baselines cannot be taken at face value. Since these issues are central to the empirical claim and the paper provides no supporting artifacts, the headline results are unsupported as presented.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Hyb-KAN ViT, a family of Vision Transformer variants in which MLP blocks are replaced by two KAN-based modules: Efficient-KAN (spline-based) and Wavelet-KAN (wavelet-based). The central claim is state-of-the-art performance on ImageNet-1K (86.3% top-1 for Hyb-KAN ViT-B, Table 4), COCO object detection and instance segmentation (Table 5), and ADE20K semantic segmentation (52.3 mIoU for Wav-KAN ViT-B, Table 6). The paper gives algorithmic pseudocode, derivative formulas for wavelet scale parameters, ablations, and comparisons to prior CNN/ViT backbones. No code, checkpoints, training logs, or compute budget are provided.","tokens_in":19354,"tokens_out":8461,"duration_ms":73003,"significance":"If the reported results were reproducible, the hybrid KAN/wavelet design would be an interesting contribution to the accuracy-efficiency trade-off of Vision Transformers, and the modular encoder/head decomposition is a sensible organizing principle. The paper deserves credit for explicitly comparing several wavelet families, reporting parameter and FLOP counts, and including ablation experiments. However, the headline claims are empirical and the paper provides no artifacts for verification; in addition, some of the derivative formulas used in the described training procedure are mathematically incorrect. As submitted, the central empirical claims are unsupported.","major_comments":[{"comment":"The gradient formulas are not correct. For the DoG wavelet with m=0, evaluating both sides of Eq. (5.2) at x=τ gives ∂Ψ/∂σ = 0 on the left and -1 on the right. For the Mexican-hat wavelet at x=τ, σ=1, the left side of Eq. (6.2) equals -1/2 while the right side equals -3/2. For the Morlet wavelet, Eq. (7.2) is correct, but Eq. (7.3) has a sign error: differentiating cos(ω0(x-τ)/σ) with respect to ω0 gives a negative term. Since these derivatives are the mechanism by which scale and frequency parameters are optimized in Algorithm 3, the training procedure described in Section IV cannot be relied upon to produce the reported results.","section":"Section 3.3, Eqs. (5.2), (6.2), (7.3)"},{"comment":"The model labels are internally inconsistent. In the Base segment of Table 5, rows are labeled 'Eff-KAN ViT-S (Ours)', 'Wav-KAN ViT-S (Ours)', and 'Hyb-KAN ViT-S (Ours)' with 191M, 136M, and 140M parameters, whereas Table 4 reports the corresponding Base variants as 162.4M, 109.4M, and 113.6M. The Base column of Table 6 similarly lists 'Eff-KAN ViT-S (Ours)' and 'Wav-KAN ViT-S (Ours)' rows. Because the parameter counts do not match either the 'S' or 'B' labels from Table 4, the claimed margins over Swin-B and ViT-Adapter-B in the text cannot be verified.","section":"Section V, Tables 5 and 6"},{"comment":"No code, checkpoints, training logs, or external evaluation protocols are provided, so the state-of-the-art accuracy (86.3% on ImageNet), detection AP, and segmentation mIoU values are not independently verifiable. The paper also omits the compute budget (GPU-days) and the absolute throughput/memory numbers behind Fig. 3, leaving the central efficiency claims unsupported.","section":"Section V, Tables 3-6, and Section 4"},{"comment":"The text after Algorithm 3 claims 'up to 4× FLOPs reduction compared to vanilla Wav-KANs', but no FLOPs measurement protocol or comparison table is given, and Fig. 3 gives no numerical axis labels or values. This efficiency claim is therefore not substantiated.","section":"Section 3.3, Fig. 3"}],"minor_comments":[{"comment":"The sentence 'prior work has failed to focus on the prebuilt modularity of the ViT architecture and integration of edge detection capabilities of Wavelet functions' is a sentence fragment and should be revised.","section":"Abstract"},{"comment":"There are two subsections numbered 2.1 ('Convolutional Neural Network Backbones' and 'Vision Transformer Backbones'); the second should be numbered 2.2.","section":"Section II"},{"comment":"Reference [19] duplicates reference [24] (both are Touvron et al. on training data-efficient image transformers).","section":"References"},{"comment":"The summation in Eq. (2), written as ∑ ... k, has a misplaced summation index; it should be explicit in the notation.","section":"Equation (2)"},{"comment":"The axes of Fig. 3 are labeled only as 'Input Dimensions Sizes' without units or tick values, and the figure caption does not state what is being measured.","section":"Fig. 3"},{"comment":"The opening sentence 'Table. 4. Demonstrates that, o ur KAN-augmented Vision Transformers demonstrate compelling trade-offs' contains spacing and capitalization errors.","section":"Section 5.2"}],"recommendation":"reject","confidential_remarks":"The manuscript resembles an early technical report: it makes broad SOTA claims without code or training artifacts, and it contains mathematical errors in the core training formulas. The inconsistent table labels compound the problem. I would not invite a revision unless the authors supply reproducible artifacts and correct the derivative derivations and table labels."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the hybrid Eff-KAN/Wav-KAN ViT is a sensible modular idea, and the authors have done the field a small service by framing the design space clearly. But the paper's headline results are unsupported: no code, no checkpoints, no training logs, and the wavelet gradient formulas contain real mistakes. As it stands, this is a desk reject.\n\nWhat's new: combining Eff-KAN (spline) and Wav-KAN (wavelet) modules in the two positions—encoder vs. classification head—and testing both orderings (Hybrid-1 and Hybrid-2) is a legitimate extension of the KAN-for-vision line that the paper itself cites. The ablation across DoG, Mexican Hat, and Morlet wavelets is also a reasonable way to probe which basis fits ViT. I want to give credit for the modular framing; it's easy to understand what was swapped where.\n\nThe soft spots are large. First, the empirical claims: 86.3% top-1 at 224×224 with 113.6M params is a strong number, but nothing in the submission lets a reader verify it. No artifacts, no external eval, and the comparison tables do not include recent high-end baselines that would contextualize the 'state-of-the-art' label. The parameter-efficiency narrative also wobbles: Eff-KAN ViT-B is 162M params vs. ViT-B's 86.6M, and the text's '4× FLOPs reduction' claim has no supporting experiment.\n\nSecond, the math. I checked the wavelet derivatives myself. Eq. (7.2) for the Morlet σ-derivative is actually correct—the stress-test note got that one wrong. But (5.2) has a spurious '-1' and the DoG derivative is missing higher-order terms; (6.2) has an incorrect σ power; and (7.3) has the wrong sign. Since these gradients are the mechanism that trains the scale parameters, the training procedure as written cannot produce the reported numbers.\n\nThird, the tables are internally inconsistent: Table 5 and 6 list 'Eff-KAN ViT-S (Ours)' under the Base section, so the reported margins over baselines are not trustworthy as presented.\n\nWho's this for? Someone tracking KAN variants might skim the design section, but no one should rely on the results. If the authors release code, fix the derivatives, and redo the comparisons honestly, there's a usable contribution underneath. I would not send this to referees in its current form.","headline":"Hybrid KAN-ViT idea is reasonable, but unsupported SOTA claims and wrong wavelet gradients make this a desk reject.","tokens_in":19839,"tokens_out":5250,"would_cite":false,"duration_ms":46572,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that replacing a Vision Transformer's MLP layers with hybrid wavelet- and spline-based KAN layers yields state-of-the-art accuracy on ImageNet-1K, COCO, and ADE20K, including 86.3% top-1 for Hyb-KAN ViT-B.","keywords":["vision transformer","Kolmogorov-Arnold network","wavelet transform","B-spline","image classification","object detection","semantic segmentation","hybrid architecture"],"falsifier":"Symbolically or automatically differentiate the three wavelet formulas in Eqs. (5.1), (6.1), and (7.1) with respect to $\\sigma$, and with respect to $w_0$ for Morlet, and compare the results with Eqs. (5.2), (6.2), (7.2), and (7.3) at sample values of $(x, \\sigma, \\tau, w_0)$; any discrepancy beyond floating-point error would invalidate the stated training procedure and require the benchmark claims to be rechecked.","tokens_in":18790,"feed_emoji":"🖼️","tokens_out":10221,"duration_ms":94035,"temperature":0.7,"pith_summary":"The paper claims that replacing the multi-layer perceptron (MLP) blocks inside a Vision Transformer with Kolmogorov-Arnold Network (KAN) blocks yields higher accuracy and better parameter efficiency. It proposes two modular replacements: Eff-KAN, which uses learnable B-spline activations, and Wav-KAN, which applies orthogonal wavelet transforms for multi-resolution feature extraction. On ImageNet-1K the best hybrid, Hyb-KAN ViT-B, is reported to reach 86.3% top-1 accuracy with 113.6 million parameters, and the paper also reports state-of-the-art or competitive results on COCO object detection and ADE20K semantic segmentation, with standalone Wav-KAN leading segmentation at 52.3 mIoU. If correct, the central insight is that wavelet-driven spectral priors in early encoder layers and spline-based projection in the classification head make KAN blocks a practical substitute for MLPs. Because the design is modular, established ViT architectures could adopt the replacement without redesigning the attention mechanism.","feed_headline":"Hybrid KAN ViT tops vision backbones with 86.3% on ImageNet","feed_subtitle":"Replacing MLP layers with wavelet-KAN encoders and spline-KAN heads raises accuracy on ImageNet, COCO, and ADE20K.","key_machinery":"The load-bearing mathematical basis is the Kolmogorov-Arnold representation theorem, which expresses a multivariate function as a sum of univariate functions; KAN layers implement that idea with learnable univariate basis functions. Eff-KAN uses B-spline basis functions on each connection, with trainable coefficients and a base linear weight, so spline knot locations can adapt to sharp image features like edges. Wav-KAN applies a fast wavelet transform to separate the input into frequency bands, multiplies the coefficients by trainable scale scalars, prunes low-magnitude high-frequency bands, and reconstructs with the inverse transform, using one of three wavelet families: Derivative of Gaussian, Mexican Hat, or Morlet. The framework's central move is treating these blocks as drop-in replacements for the MLP in both the transformer encoder and the classification head, and combining them as Hybrid-1, a Wav-KAN encoder plus an Eff-KAN head. The derivative-of-Gaussian wavelet is the one that empirically carries the classification and detection gains.","core_discovery":"Hyb-KAN ViT is a Vision Transformer whose encoder MLPs are switched for Wav-KAN blocks and whose classification head uses Eff-KAN blocks. The paper's core claim is that this combination captures both high-frequency edge and texture structure, through wavelet decomposition, and smooth adaptive decision boundaries, through B-spline activations, in a way fixed MLPs cannot. The reported numbers are the evidence: 84.5% top-1 accuracy for the Small model and 86.3% for the Base model on ImageNet-1K, box and mask average precision of 50.6 and 44.9 for the Base hybrid on COCO, and 52.3 mIoU for the standalone Wav-KAN ViT-B on ADE20K. The authors interpret these results as showing a dual-path spectral encoding: wavelet-guided attention extracts edges in early layers, while spline heads refine spatial-semantic fusion later. They also identify a scaling limitation, noting that Eff-KAN ViT-B grows to 162.4 million parameters for a smaller accuracy gain, which is why the hybrid configuration is the recommended one.","pith_inferences":["A natural next experiment is to freeze the wavelet scale parameters at their initial values and retrain; if accuracy stays roughly the same, the wavelet family matters less than the added representation capacity, and if it drops substantially, the trainable scale parameter is the hidden engine of the gains.","The reported DoG advantage over Morlet and Mexican Hat suggests that first-derivative edge-like wavelets match patch-based image statistics; testing higher-order derivatives of Gaussians would show whether the derivative order can be pushed further.","The paper's conclusion proposes sharing activation weights across neuron groups to cut parameters; a cheap check is whether such weight sharing preserves the accuracy margin at Tiny scale, which would separate the KAN architecture's benefit from its parameter count."],"forward_implications":["If the reported results are correct, KAN-based nonlinearities are a practical replacement for MLPs inside Vision Transformers, not just an isolated module, and can lift top-1 accuracy above comparable MLP-based ViTs at Base scale.","The 86.3% top-1 figure for Hyb-KAN ViT-B would put it ahead of the listed ViT-B, DeiT-B, and PVTv2-B5 baselines, implying that wavelet-KAN encoders provide a stronger inductive bias for ImageNet-scale training than standard fixed activations.","The ADE20K result implies that wavelet frequency decomposition is especially valuable for dense prediction tasks requiring precise boundaries, since Wav-KAN ViT-B reports 52.3 mIoU, above the listed Swin-B and ConvNeXt-B scores.","The ablation parameter counts, with Hyb-KAN ViT-S at 29.7 million parameters versus 42.5 million for Eff-KAN ViT-S, imply that the wavelet encoder is the parameter-efficient part of the design while the spline head adds accuracy without the full KAN parameter cost."],"supporting_citations":[{"why":"Provides the base Vision Transformer architecture whose MLP blocks are replaced.","marker":"[2]"},{"why":"Introduces the earlier Kolmogorov-Arnold Transformer that motivates the KAN-in-ViT direction and serves as a baseline.","marker":"[4]"},{"why":"Introduces spline-based KANs, the theoretical basis for Eff-KAN.","marker":"[5]"},{"why":"Introduces Wavelet-KAN, the starting point for the Wav-KAN module.","marker":"[6]"},{"why":"Provides the memory-efficient, GPU-friendly spline implementation used for Eff-KAN.","marker":"[34]"},{"why":"Supplies the ImageNet-1K dataset that anchors the classification claim.","marker":"[36]"},{"why":"Supplies the COCO benchmark used for object detection and instance segmentation results.","marker":"[37]"},{"why":"Supplies the ADE20K benchmark used for semantic segmentation results.","marker":"[38]"},{"why":"Supplies the Mask R-CNN detector used to evaluate detection and segmentation.","marker":"[47]"},{"why":"Supplies the UPerNet framework used for the semantic segmentation evaluation.","marker":"[49]"}],"fun_headline_variants":["Wavelet-KAN and spline-KAN unite in ViT for 86.3% ImageNet","Hybrid KAN ViT: wavelet edges, spline heads, 86.3% top-1","KAN replaces MLPs in ViT: 86.3% ImageNet, 50.6 COCO box AP","Wavelet-KAN encoders + spline-KAN heads: ViT hits 86.3%","ViT gains 86.3% accuracy by swapping MLPs for wavelet and spline KAN"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the handwritten derivatives of the three wavelet basis functions with respect to scale and center frequency, Eqs. (5.2), (6.2), (7.2), and (7.3), are mathematically correct; the paper provides no proof or code for them, and training the scale parameters depends on them.","fun_headline_variants_meta":{"raw":{"variants":["Wavelet-KAN and spline-KAN unite in ViT for 86.3% ImageNet","Hybrid KAN ViT: wavelet edges, spline heads, 86.3% top-1","KAN replaces MLPs in ViT: 86.3% ImageNet, 50.6 COCO box AP","Wavelet-KAN encoders + spline-KAN heads: ViT hits 86.3%","ViT gains 86.3% accuracy by swapping MLPs for wavelet and spline KAN"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000534,"raw_usage":{"total_tokens":2603,"prompt_tokens":1013,"completion_tokens":1590,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":629,"completion_tokens_details":{"reasoning_tokens":1455}},"tokens_in":629,"tokens_out":1590,"duration_ms":11591,"temperature":1.0,"reasoning_tokens":1455,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:21:53.240151+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Symbolically or automatically differentiate the three wavelet formulas in Eqs. (5.1), (6.1), and (7.1) with respect to $\\sigma$, and with respect to $w_0$ for Morlet, and compare the results with Eqs. (5.2), (6.2), (7.2), and (7.3) at sample values of $(x, \\sigma, \\tau, w_0)$; any discrepancy beyond floating-point error would invalidate the stated training procedure and require the benchmark claims to be rechecked.","supporting_citations":[{"cited_title":"Imagenet: A large-scale hierarchical image database,","cited_arxiv_id":null,"evidence_quote":"Supplies the ImageNet-1K dataset that anchors the classification claim."},{"cited_title":"Microsoft coco: Common objects in ´ context,","cited_arxiv_id":null,"evidence_quote":"Supplies the COCO benchmark used for object detection and instance segmentation results."},{"cited_title":"Semantic understanding of scenes through the ade20k dataset,","cited_arxiv_id":null,"evidence_quote":"Supplies the ADE20K benchmark used for semantic segmentation results."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Mask R-CNN detector used to evaluate detection and segmentation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the UPerNet framework used for the semantic segmentation evaluation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the memory-efficient, GPU-friendly spline implementation used for Eff-KAN."},{"cited_title":"(2024, September)","cited_arxiv_id":null,"evidence_quote":"Introduces the earlier Kolmogorov-Arnold Transformer that motivates the KAN-in-ViT direction and serves as a baseline."}],"review_version":1}