Bridging KAN and MLP: MJKAN, a Hybrid Architecture with Both Efficiency and Expressiveness

Hanseon Joo; Hayoung Choi; Minjong Cheon; Ook Lee

REVIEW 4 major objections 4 minor 17 references

Bridging KAN and MLP: MJKAN, a Hybrid Architecture with Both Efficiency and Expressiveness

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A hybrid layer claims KAN expressiveness at MLP-level cost.

desk verdict A KAN-inspired layer that never tests its central efficiency claim: no KAN baseline appears anywhere, and the one timing table shows MJKAN slower than MLP. read the letter →

arxiv 2507.04690 v1 pith:XAP7ZXNV submitted 2025-07-07 cs.LG cs.AIcs.CV

Hanseon Joo , Hayoung Choi , Ook Lee , Minjong Cheon This is my paper · ORCID

classification cs.LGcs.AIcs.CV

keywords Kolmogorov-ArnoldNetworksFiLMmodulationRadialBasisFunctionshybridarchitecturefunctionapproximationclassificationsizeMLP

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

This paper introduces MJKAN, a neural-network layer that replaces a KAN's spline edges with radial-basis-function expansions modulated by per-feature FiLM scaling and shifting. The authors argue that this design keeps the Kolmogorov-Arnold principle of summing learned univariate functions while reducing the computational burden of standard KANs. Their experiments show MJKAN matches or beats an MLP on function-regression tasks as the number of basis functions grows, and remains competitive with MLPs on image and text classification when the basis count is small. The paper's central conclusion is that MJKAN offers a practical middle ground between KAN expressiveness and MLP efficiency, with basis size acting as a capacity knob that must be tuned to avoid overfitting.

What carries the argument

The central object is the MJKANLayer: for each input dimension $x_i$, it computes a vector of $K$ Gaussian radial basis functions $\phi_{ij}(x_i)=\exp(-(x_i-c_j)^2/2\sigma^2)$, then forms modulation parameters $\gamma_i=\sum_j \phi_{ij}(x_i)\gamma_{ij}$ and $\beta_i=\sum_j \phi_{ij}(x_i)\beta_{ij}$ with learned vectors, producing output $y = \sum_i (\gamma_i x_i + \beta_i)$, optionally plus a base projection. This replaces the B-spline edge functions of a standard KAN with a simpler kernel expansion and an affine feature-wise modulation, which is what the paper claims reduces computation while preserving the additive univariate structure that gives KANs their expressive power.

What would settle it

Run MJKAN and a standard B-spline KAN with matched layer widths on CIFAR-10 for the same number of epochs, measuring wall-clock time, peak memory, and parameter count; if MJKAN is not faster or smaller at equal or better accuracy, the central efficiency claim is refuted.

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Extended reading notes

Core claim

The paper's central discovery is that a KAN-style layer can be built from two cheap ingredients—a radial-basis expansion of each input and a FiLM-style affine modulation per basis—so that each output logit is an additive sum of per-feature functions, exactly the Kolmogorov-Arnold decomposition. With this layer, the authors report that MJKAN achieves lower RMSE than an MLP on several symbolic regression tasks (e.g., reducing error on Local Bumps from 0.1955 to 0.1489 at K=50), while on MNIST, CIFAR-10/100, AG News, and SMS Spam it reaches accuracy close to MLP baselines provided the basis count is kept small. The authors interpret this as evidence that MJKAN inherits KAN's approximation strength without KAN's usual cost, at the price of a capacity–generalization trade-off controlled by the number of basis functions.

Load-bearing premise

The claim that MJKAN is efficient rests on the assumption that an RBF-plus-FiLM layer costs less to train and run than a standard spline-based KAN layer, but the paper never measures that comparison directly.

Editorial extensions

If this is right

If MJKAN works as claimed, it can serve as a drop-in replacement for fully connected layers across vision, language, regression, time-series, and physics tasks, since the layer has no domain-specific assumptions.
Because each output logit is a closed-form additive sum of per-feature functions, model decisions can be symbolically decomposed to show each input feature's exact contribution to each class.
Basis size becomes a key hyperparameter: small bases are needed for classification generalization, while larger bases improve function approximation.
The efficiency claim implies that KAN-style models become practical on standard hardware, assuming the RBF-FiLM layer is cheaper to run than spline-based KAN layers.

Reading between the lines

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

Beyond the paper: the reported basis-size sensitivity suggests that regularizing the modulation parameters (e.g., weight decay on $\gamma$ and $\beta$) or using adaptive basis placement could recover some of the lost accuracy at K=50, a testable extension the paper does not run.
Beyond the paper: because the logits decompose additively over features, MJKAN could double as an interpretability tool—feature-attribution maps are exact by construction rather than approximate—though the paper only notes the closed form and does not exploit it.
Beyond the paper: the efficiency claim is only argued structurally; a direct head-to-head timing and parameter benchmark against a B-spline KAN would settle whether 'MLP-like cost' holds, since the paper's only timing table compares MJKAN to an MLP and shows MJKAN slower.
Beyond the paper: the architecture is generic enough that applying FiLM modulation to other kernel families (e.g., Fourier features or wavelets) is a natural next step, potentially preserving the same trade-off profile.

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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

The paper proposes MJKAN, a layer that feeds each input through an RBF expansion and then applies FiLM-style per-feature modulation before summing. That combination is reasonable and worth a look in itself. Credit where it's due: the paper is unusually honest about classification results, reporting that MJKAN loses to MLP on MNIST, CIFAR-10/100, AG News, and SMS Spam, and it clearly documents the overfitting trend as the basis count grows. The closed-form per-feature expression in the conclusion is a nice touch, even if underdeveloped.

The soft spots are load-bearing, not cosmetic. The abstract and intro promise faster inference and higher accuracy than prior KAN variants, but no KAN baseline appears in any experiment. Every table compares MJKAN to an MLP, and the only timing table (Table 1) shows MJKAN slower than MLP on all three vision datasets. That directly contradicts the efficiency half of the central claim. The regression results are also weaker than advertised: MJKAN wins only at the largest basis size (K=50) on all five functions, and the authors appear to have selected that setting after seeing the test performance. No error bars, no multiple seeds, no parameter counts. The reference list contains obvious placeholders like "Doe and Smith [2021]" and "Lee and Park [2022]", which is a serious integrity problem and undermines confidence in the related-work discussion.

I do not think the paper deserves a serious referee in its current form. The missing KAN baseline alone makes the main claim untestable, and the fabricated-looking references are disqualifying. If the authors added a real KAN comparison (e.g., EfficientKAN or a standard B-spline KAN), fixed the references, and reported variance, the architecture would be worth another look. As submitted, it is a modest empirical note with an unsupported headline.

For a reading group, it could be a useful case study in how KAN papers overclaim without baselines, but I would not cite it in my own work.

Referee Report

4 major / 4 minor

Summary. The paper proposes MJKAN, a neural network layer that combines FiLM-style feature-wise modulation with radial basis function (RBF) activations, intended as a hybrid between KANs and MLPs. The authors claim this layer inherits KAN-like expressiveness while being more computationally efficient and practical. Experiments are reported on MNIST, CIFAR-10/100, AG News, SMS Spam, and five synthetic 1D function-regression tasks, comparing MJKAN with an MLP baseline across varying RBF basis counts. The main conclusions are that MJKAN outperforms MLP on function regression when the basis size is chosen large enough, is competitive with MLP on classification when the basis size is small, and is computationally more efficient than KANs, although no KAN model is included in any experiment.

Significance. If the central claims were established, MJKAN would be a useful contribution to the growing family of KAN-inspired layers, particularly for tasks requiring localized or compositional function approximation. The paper does provide explicit layer equations and a broad set of empirical settings. However, the current manuscript does not substantiate its central efficiency claim (no KAN baseline is ever run), and the regression-superiority claim rests on post hoc selection of basis size with no error bars or repeated-seed analysis. One narrative sentence in Section 4.2 is directly contradicted by the paper's own Table 3. As a result, the claimed significance is not yet supported by the evidence presented.

major comments (4)

[Section 1, Section 4.1, Table 1] The paper's central efficiency claim is untested. The abstract and conclusion state that MJKAN improves computational efficiency relative to KANs, but no KAN baseline (B-spline KAN, EfficientKAN, or any other KAN variant) appears in any table or figure. Table 1, the only timing comparison, compares MJKAN with an MLP and shows MJKAN slower on all three vision datasets: MNIST 124.57 s vs 120.84 s, CIFAR-10 127.7 s vs 115.2 s, and CIFAR-100 125.3 s vs 115.5 s. No parameter counts, FLOPs, or memory measurements are reported for any model. Therefore the load-bearing claim that MJKAN is more efficient than KANs is unsupported by the paper's own experiments, and the only timing data actively undermine the broader efficiency rhetoric.
[Section 4.2, Table 3] The regression superiority claim is based on post hoc selection of the basis size and is partly contradicted by the reported numbers. For every task in Table 3, the best MJKAN point is at K=50, and the text highlights these best cases, but no error bars, confidence intervals, or multiple-seed results are provided, so it is impossible to tell whether the improvements are statistically meaningful. More seriously, the text says that for Global Pattern, 'MJKAN achieves lower RMSE with moderate basis counts (e.g., K=25),' yet Table 3 lists MJKAN(K=25) RMSE as 0.2329 versus MLP's 0.0840, which is substantially worse. This internal contradiction undermines the narrative of consistent regression improvement and requires correction or clarification.
[Section 3.2] The theoretical motivation via the Kolmogorov–Arnold theorem is asserted rather than demonstrated. The paper states that MJKAN 'aligns with' KAT by modeling univariate functions, linear mixing, and outer functions, but no theorem or proof shows that the specific FiLM-modulated RBF architecture can represent or approximate the required univariate functions, nor that it inherits the approximation guarantees of KANs. The claim in Section 1 that fixing the modulation parameters to trivial values reduces the layer to a standard KAN is also not established, since a standard KAN uses B-spline edge functions and a different parameterization. As it stands, the phrase 'inherits the theoretical advantages of KANs' is a rhetorical claim, not a supported result.
[Section 4 overall] The empirical comparisons lack standard reproducibility information. The paper does not report learning rates, batch sizes, number of training runs, seeds, hardware, or model parameter counts for the evaluated architectures. Table 3 reports RMSE values without variance, and Tables 1, 2, and 4 report accuracies without error bars or significance tests. Without these details, the claimed accuracy differences (e.g., 96.6 vs 97.9 on MNIST) cannot be distinguished from run-to-run noise, and the experiments cannot be independently reproduced.

minor comments (4)

[References] Several references appear to be placeholders or non-verifiable entries, notably 'J. Doe and A. Smith' (J. Sci. Comput. 2021) and 'P. Chen et al.' (ICML 2023). These are not standard citation names and should be either replaced with real, verifiable works or removed.
[Section 1] The contribution bullet states 'MJKAN is the first KAN variant to incorporate feature-wise affine modulation,' but no literature search or comparison is provided to support this novelty claim.
[Section 3.2] The phrase 'Base is an optional nonlinear linear residual update' is self-contradictory; 'nonlinear linear' should be clarified.
[Figure 1] The regression figure is described in the text as showing predicted versus ground-truth curves, but the subplots are not clearly labeled with the task names and basis sizes in the caption, making it difficult to verify the RMSE values in Table 3.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: MJKAN is an empirical architecture proposal whose reported results come from training on external benchmarks, not from reducing its claims to its inputs.

full rationale

The paper is an empirical architecture study rather than a formal derivation chain, and I find no load-bearing step where a claimed result reduces by construction to its own inputs. The MJKAN layer is defined by explicit equations (RBF expansion, FiLM modulation, summation), and the reported accuracies and RMSEs come from training that model on standard external benchmarks; no fitted parameter is later renamed as an independent prediction. The Kolmogorov-Arnold theorem is cited from Kolmogorov and Arnold as external motivation, and the paper's mapping of FiLM_i to the theorem's univariate functions is an interpretive analogy, not a derivation that presupposes the conclusion, so any weakness there is an overclaim or correctness risk rather than circularity. The efficiency claim of faster inference than prior KAN variants is never tested against any KAN baseline, and the only timing table shows MJKAN slower than an MLP, but an unsupported empirical claim is a missing comparison, not a circular reduction. The only overlapping-author citations (Cheon 2024a,b) appear in background descriptions of KANs and are not load-bearing for MJKAN's central contribution. Function-regression RMSEs appear to be in-sample fits, which limits their generalization evidence but does not constitute a fitted input being called a prediction in the circular sense defined here. Overall, the central architecture and its evaluations are self-contained, so the circularity score is 0.

Assumptions & free parameters 2 free parameters · 2 assumptions · 0 invented entities

The only task-specific free parameter visible is the basis count K, which is tuned per benchmark. The RBF centers and width are said to be fixed or learnable but are not specified. No new physical entities are introduced; the proposed layer is the architecture itself.

free parameters (2)

basis_size_K = 5, 10, 25, 50 per task
The number of RBF bases is chosen per task to produce the best reported accuracy or RMSE; no principled selection rule is given.
RBF_center_and_width = not specified
The paper says centers are 'learnable or fixed' and width sigma is 'fixed', but does not state the values or schedule; these control the basis function shapes.

assumptions (2)

standard math Kolmogorov-Arnold representation theorem provides a valid motivation for summing univariate functions.
The theorem is a true result about continuous functions, but the paper does not prove that the FiLM-RBF layer implements it efficiently or that it inherits approximation bounds.
ad hoc to paper The FiLM-modulated RBF layer is at least as expressive as a standard KAN layer.
This is asserted in Section 3 and the conclusion, but no universal approximation proof or comparison to spline KANs is given.

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Cite this review

Pith. "Pith review of Bridging KAN and MLP: MJKAN, a Hybrid Architecture with Both Efficiency and Expressiveness." pith.science (2026). https://pith.science/paper/XAP7ZXNV

@misc{pith2026250704690,
  author       = {Pith},
  title        = {Pith review of: Bridging KAN and MLP: MJKAN, a Hybrid Architecture with Both Efficiency and Expressiveness},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XAP7ZXNV}},
  note         = {Machine review of arXiv:2507.04690}
}

read the original abstract

Kolmogorov-Arnold Networks (KANs) have garnered attention for replacing fixed activation functions with learnable univariate functions, but they exhibit practical limitations, including high computational costs and performance deficits in general classification tasks. In this paper, we propose the Modulation Joint KAN (MJKAN), a novel neural network layer designed to overcome these challenges. MJKAN integrates a FiLM (Feature-wise Linear Modulation)-like mechanism with Radial Basis Function (RBF) activations, creating a hybrid architecture that combines the non-linear expressive power of KANs with the efficiency of Multilayer Perceptrons (MLPs). We empirically validated MJKAN's performance across a diverse set of benchmarks, including function regression, image classification (MNIST, CIFAR-10/100), and natural language processing (AG News, SMS Spam). The results demonstrate that MJKAN achieves superior approximation capabilities in function regression tasks, significantly outperforming MLPs, with performance improving as the number of basis functions increases. Conversely, in image and text classification, its performance was competitive with MLPs but revealed a critical dependency on the number of basis functions. We found that a smaller basis size was crucial for better generalization, highlighting that the model's capacity must be carefully tuned to the complexity of the data to prevent overfitting. In conclusion, MJKAN offers a flexible architecture that inherits the theoretical advantages of KANs while improving computational efficiency and practical viability.

Figures

Figures reproduced from arXiv: 2507.04690 by the authors.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

17 extracted references · 12 canonical work pages

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

A. N. Kolmogorov. On the representation of continuous functions of several variables by superposition of continuous functions of one variable and addition. Dokl. Akad. Nauk SSSR, 114: 0 953--956, 1957

work page 1957

[2] [2]

V. I. Arnold. On functions of three variables. Soviet Math. Dokl., 5: 0 521--524, 1957

work page 1957

[3] [3]

Kliger, S

D. Kliger, S. Goldberg, and R. Rimon. Kernel activation networks: A new paradigm for neural function approximation. In Proc. NeurIPS, 2023

work page 2023

[4] [4]

Doe and A

J. Doe and A. Smith. Learnable activation networks for pde solvers. J. Sci. Comput., 89 0 (2): 0 123--147, 2021

work page 2021

[5] [5]

Lee and Y

M. Lee and Y. Park. Kans for scientific data modeling. Comput. Phys. Comm., 275: 0 108323, 2022

work page 2022

[6] [6]

Chen et al

P. Chen et al. An empirical study of kernel activation networks vs. mlps. In ICML, 2023

work page 2023

[7] [7]

Kumar and L

R. Kumar and L. Zhang. Hardware acceleration of kans on fpgas. IEEE Trans. VLSI Syst., 30 0 (11): 0 1825--1837, 2022

work page 2022

[8] [8]

Gupta and T

S. Gupta and T. Johnson. Challenges in training high-dimensional functional parameters. Neural Netw., 134: 0 167--179, 2021

work page 2021