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REVIEW 4 major objections 5 minor 13 references

A Comparative Analysis of MLP and Kolmogorov-Arnold Networks (KAN) for Faster-than-Nyquist (FTN) Signaling Detection

T0 review · 4 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read For FTN BPSK detection under AWGN, a Kolmogorov-Arnold Network with hidden width 4 and spline grid 5 achieves an 18.6x lower bit error rate at 10 dB than the best-tuned MLP (width 32), matching the BCJR reference.

desk verdict The 18.6x KAN-vs-MLP BER claim at 10 dB rests on about four test errors, and the 'parameter efficiency' framing is misleading; the actual contribution is a plausible first KAN-for-FTN comparison that is not yet demonstrated. read the letter →

arxiv 2608.02062 v1 pith:LXE3QQRN submitted 2026-08-03 eess.SP cs.LG

Sude Ertan , Osman Tokluoglu , Enver Cavus This is my paper
classification eess.SPcs.LG
keywords faster-than-NyquistsignalingKolmogorov-ArnoldnetworksMLPBPSKdetectionBCJRparameterefficiencybiterrorrate
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 argues that for faster-than-Nyquist BPSK detection in AWGN, a Kolmogorov-Arnold Network is both more accurate and more parameter-efficient than a well-tuned multilayer perceptron. Using a four-million-window dataset, the selected KAN (width 4, spline grid 5) beats the best MLP (width 32) at every SNR from 7 to 10 dB, and at 10 dB its bit error rate is 7.0e-6 versus 1.3e-4 for the MLP — an 18.6x improvement that matches the optimal BCJR sequence detector. The authors attribute the gap to KAN's edge-based spline nonlinearities, which capture the local inter-symbol interference structure more directly than node-based activations. If correct, this means near-optimal FTN detection can be achieved with a small, purely data-driven receiver, attractive for embedded systems.

What carries the argument

The load-bearing object is the Kolmogorov-Arnold edge parameterization: every connection carries a learnable B-spline phi_ij(x) = sum_m c_ijm B_m(x), with nonlinearity on edges rather than at nodes. In this architecture each of the 65 input samples contributes through its own spline function, so the network can model the FTN channel's local coupling pattern component by component. The paper's efficiency claim rests on the ratio eta = (BER improvement)/(parameter increase) = 18.6/1.83 ≈ 10.2, which quantifies how much more BER gain the KAN delivers per added parameter.

What would settle it

Run both detectors on a much larger test set at 10 dB (or average many independent training runs) and compute confidence intervals for the BERs; if the KAN and MLP intervals overlap, the claimed 18.6x advantage and the BCJR match do not hold.

Watch

Extended reading notes

Core claim

The central claim is that replacing fixed node activations with learnable univariate splines on each edge (the Kolmogorov-Arnold architecture) yields a receiver that dominates a width-swept MLP for FTN-BPSK detection. On a Monte Carlo dataset of 3,999,936 windows at tau=0.8 and SNR 7–10 dB, the KAN with hidden width 4 and grid size 5 reaches a 10 dB BER of 7.0e-6, equal to the BCJR reference and 18.6 times lower than the MLP's 1.3e-4, while using one eighth of the MLP's hidden width and about 1.83x parameters. The paper presents a parameter-efficiency metric eta = BER improvement / parameter increase ≈ 10.2, interpreting it as evidence that spline edge functions align with FTN's structured I

Load-bearing premise

The 10 dB BER numbers are statistically reliable, even though the KAN's test error count is only about 4 out of 600,000 windows; if those few errors are sampling noise, the 18.6x improvement and the match to BCJR could be largely luck.

Editorial extensions

If this is right

  • At 10 dB the selected KAN reaches the BCJR reference BER (7e-6), indicating near-optimal detection without the computational cost of sequence estimation.
  • The KAN outperforms the MLP at every tested SNR, with the gap widening at higher SNR, which the paper attributes to KAN's better modeling of fine decision boundaries.
  • The measured parameter efficiency (about 10.2x BER improvement per unit parameter increase at 10 dB) supports KAN as a more compact neural receiver for FTN signaling.

Reading between the lines

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

  • The 10 dB result rests on very few KAN test errors (about 4 of 599,991 windows), so the 18.6x ratio and the exact BCJR match carry large statistical uncertainty; a larger test set or multi-seed averaging could substantially change the headline numbers.
  • The comparison used only tau=0.8 and BPSK; testing smaller time-packing factors or higher-order modulation would show whether KAN's edge-spline advantage grows with more severe ISI.
  • Parameter count is not the same as compute or latency; spline evaluations may have different hardware costs than dense layers, so the practical efficiency claim needs an inference-time benchmark.
  • If the advantage holds, it suggests learnable per-edge nonlinearities could replace fixed activations in other structured detection problems such as equalization or channel decoding.
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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

4 major / 5 minor

Summary. The paper presents an empirical comparison of an MLP and a Kolmogorov-Arnold Network (KAN) as symbol detectors for FTN-BPSK signaling with time-packing factor τ=0.8 over AWGN. Both detectors operate on a 65-sample received window and are trained on a Monte Carlo dataset of roughly 4 million labeled windows at SNRs 7–10 dB. The authors sweep MLP widths and two KAN configurations, select MLP width 32 and KAN w4_g5, and compare against a hard-decision baseline and the BCJR reference. They report that the KAN consistently outperforms the MLP, with an 18.6x lower BER at 10 dB (7.0e-6 vs 1.3e-4), that this matches the BCJR reference, and that the KAN is more parameter-efficient despite having 1.83x more parameters because its hidden width is one eighth that of the MLP.

Significance. If the claims were statistically supported, the paper would provide a useful data point on KANs for nonlinear sequence detection: a compact KAN with edge-wise splines could model FTN decision regions more accurately than a wider MLP, potentially reducing computational/hardware cost. The strengths are the controlled setting (same dataset, same window, same loss/optimizer), the inclusion of BCJR as a reference, and the relatively large training set. However, the headline quantitative claims are not supported by the evidence as reported.

major comments (4)
  1. [Table II and Section V] The 18.6x BER advantage at 10 dB rests on a KAN estimate with about 4 test errors. With a test set of 599,991 windows, BER 7.0e-6 corresponds to roughly 4 errors; the 95% Poisson CI for the KAN BER is approximately 2.7e-6 to 1.8e-5, and the CI for the MLP/KAN ratio spans about 6x to 60x. The BERs at 10 dB for KAN and BCJR are therefore statistically indistinguishable. The paper must report error counts, confidence intervals, and results over multiple seeds (or a much larger test set) before the headline and the 'reaches BCJR' conclusion can be accepted. At 7-9 dB the advantage is more stable because the error counts are larger, but the 10 dB claim is load-bearing and currently unsupported.
  2. [Eqs. (12)-(13), Table III, Abstract] The parameter-efficiency claim is internally inconsistent. Table III gives P_KAN≈3920 vs P_MLP=2145, i.e., KAN has 1.83x more parameters. The factor 1/8 refers only to hidden width, not parameter count. Defining η as (BER improvement)/(parameter increase) and obtaining 10.2 does not establish parameter efficiency; it simply rescales a BER ratio by a parameter ratio. A meaningful efficiency comparison would state BER as a function of parameter count or use a complexity-normalized metric. The conclusion 'more parameter-efficient' is contradicted by the paper's own Table III and should be corrected or qualified.
  3. [Sections III.B and IV] The KAN selection is not a fair comparison. The MLP width was swept over six values {8,16,32,64,128,256}, while only two KAN configurations (w4_g5 and w8_g3) were considered, and the selected KAN was chosen 'by jointly considering validation BER and parameter efficiency'—the same criterion later used as the main result. This creates a selection bias and makes it impossible to determine whether the reported advantage is specific to the chosen KAN configuration or to the particular grid/width combination. The authors should report full sweeps for both architectures and a pre-specified selection rule, with repeated training runs.
  4. [Section IV] The experimental protocol is underspecified. The number of epochs, learning rate, batch size, weight initialization, and early-stopping criteria are not given, and it is unclear whether separate models are trained for each SNR value or one model is evaluated across SNRs. The comparison is therefore not reproducible, and the observed differences could reflect training artifacts rather than architectural properties.
minor comments (5)
  1. [Eq. (11)] The variable k in the parameter count (G+k) is not defined. Specify the B-spline order and give the exact formula for PKAN.
  2. [Eqs. (8) and (11)] The phrasing 'was taken as follows' is ungrammatical and unclear; replace with a standard derivation sentence.
  3. [Figure 3] The BER-SNR curves would benefit from error bars or confidence bands, especially at 10 dB where the KAN point has very few errors.
  4. [Table II] In addition to normalized BER values, report the raw error counts (or number of test windows) so readers can assess statistical precision.
  5. [Section III.B] Please clarify which KAN variant is used (e.g., activation functions, residual connections, initialization), since KAN implementations can differ substantially.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the BER comparison is a direct empirical measurement, and the only definitional metric (η) is explicit and not used to manufacture the BER result.

full rationale

The paper's central claims are empirical: KAN and MLP are trained on the same dataset split, evaluated on the same test windows, and compared against the standard BCJR reference. No equation-level prediction reduces to a fitted input. The parameter-efficiency metric in Eq. (12), η = BER improvement / parameter increase, is explicitly defined by the authors, and Eq. (13) simply evaluates that definition using the measured BER ratio and parameter counts. This is a transparent choice of metric, not a hidden circular derivation. The KAN configuration was selected using validation BER and parameter efficiency, which is standard model selection rather than circularity; the selected configuration is then reported, not predicted from itself. The self-citations (Refs. [6]–[8]) are used as background or are not cited in the body; none carries the load of the central comparison. The main weakness of the paper is statistical: at 10 dB the KAN BER of 7.0e-6 corresponds to roughly 4 test errors, giving large Poisson uncertainty, so the 18.6x improvement and the exact match with BCJR are not numerically reliable. That is a correctness/statistical concern, not a circularity concern, and per the review rules it does not raise the circularity score. Overall, the result is self-contained against an external benchmark and no circular step is identifiable.

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

The paper is an empirical benchmark; its claims rest on hyperparameter choices and simulation assumptions rather than new theoretical constructs.

free parameters (3)
  • MLP hidden width = 32
    Selected by validation BER sweep over widths {8,16,32,64,128,256}; the comparison and efficiency claims depend on this choice.
  • KAN hidden width = 4
    Selected from the two tested KAN configurations (w4_g5, w8_g3) using validation BER and parameter efficiency; central to the compactness claim.
  • KAN spline grid size = 5
    Set to 5 in the selected w4_g5 configuration; influences parameter count and BER.
assumptions (3)
  • domain assumption FTN system model: BPSK symbols, linear pulse shaping, AWGN, and the discrete model in Eqs. (1)-(5) accurately describe the channel.
    The entire simulation is built on this model without comparison to a hardware testbed.
  • domain assumption BCJR is the optimal reference detector for the studied FTN channel.
    The paper treats BCJR BER as the performance ceiling; this is a standard result but not established for this specific simulation.
  • domain assumption The Monte Carlo dataset is representative and the train/validation/test split is independent.
    No analysis of dataset bias or overlap is given.

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Cite this review

Pith. "Pith review of A Comparative Analysis of MLP and Kolmogorov-Arnold Networks (KAN) for Faster-than-Nyquist (FTN) Signaling Detection." pith.science (2026). https://pith.science/paper/LXE3QQRN

@misc{pith2026260802062,
  author       = {Pith},
  title        = {Pith review of: A Comparative Analysis of MLP and Kolmogorov-Arnold Networks (KAN) for Faster-than-Nyquist (FTN) Signaling Detection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LXE3QQRN}},
  note         = {Machine review of arXiv:2608.02062}
}
read the original abstract

Faster-than-Nyquist signaling improves spectral ef- ficiency by deliberately introducing inter-symbol interference. Classical sequence detectors such as BCJR can approach optimal performance, but their computational cost grows rapidly with channel memory. This paper investigates data-driven FTN BPSK detection under AWGN through a direct comparison between multilayer perceptrons and Kolmogorov Arnold Networks. A large-scale Monte Carlo dataset containing nearly four million labeled windows is generated for a time-packing factor of zero point eight and signal-to-noise ratio values from seven to ten decibels. The best MLP obtained from width sweeping uses hidden width thirty two, whereas the selected KAN uses hidden width four with spline grid size five. At ten decibels, the MLP produces a bit error rate of one point three times ten to the minus four, while the KAN reaches seven times ten to the minus six. This corresponds to an eighteen point six times lower bit error rate while using only one eighth of the MLP hidden width. The results show that KAN provides a more effective and more parameter-efficient neural decision model than the MLP baseline for FTN BPSK detection.

Figures

Figures reproduced from arXiv: 2608.02062 by the authors.

Figure 1
Figure 1. FTN-BPSK transmission and neural-network-based [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Compared neural-network detector architectures. The [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. BER-SNR curves: FTN hard-decision baseline, best [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

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Reference graph

Works this paper leans on

13 extracted references · 1 linked inside Pith

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Reviewed August 4, 2026 · model on record in the stance chip above.