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From KAN to GR-KAN: Advancing Speech Enhancement with KAN-Based Methodology

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read GR-KAN, a group-rational variant of Kolmogorov-Arnold Networks, improves speech enhancement quality in both time- and time-frequency-domain models while reducing parameters by up to 4x.

desk verdict Useful empirical application of GR-KAN to speech enhancement, but the Demucs parameter accounting is inconsistent and the headline mixes two comparisons. read the letter →

arxiv 2412.17778 v2 pith:RHRHJBHB submitted 2024-12-23 eess.AS cs.AIcs.LG

Haoyang Li , Yuchen Hu , Chen Chen , Sabato Marco Siniscalchi , Songting Liu , Eng Siong Chng This is my paper · ORCID
classification eess.AScs.AIcs.LG
keywords speechenhancementKolmogorov-ArnoldNetworksGR-KANrationalactivationfunctionstime-frequencydomaintime-domainparameterefficiencyPESQ
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 a scalable variant of Kolmogorov-Arnold Networks, called Group-Rational KAN (GR-KAN), can be dropped into existing speech enhancement models to improve objective speech quality while using far fewer parameters. The authors replace dense layers in the time-frequency-domain MP-SENet and ReLU activations in the time-domain Demucs with GR-KAN layers, and report consistent gains on the VoiceBank-DEMAND benchmark: up to 0.1 higher PESQ and up to four times fewer parameters. They also show that the original KAN, with spline activations on every edge, fails to scale to this task, adding about 50% parameters without improving MP-SENet. If these results hold, GR-KAN offers a plug-in path to better speech enhancement without redesigning the network.

What carries the argument

The load-bearing object is the GR-KAN layer, implemented as $\mathrm{LIN}(\mathrm{GR}(x))$: a group-wise rational activation $\mathrm{GR}$ followed by a linear matrix $\mathrm{LIN}$. Unlike a KAN layer, which places an independent spline on each edge, GR-KAN partitions input channels into $k$ groups and shares one rational function per group, which keeps parameters low, and it uses variance-preserving weight initialization for stable training. In MP-SENet the layer is inserted after the Bi-GRU inside each GRU-Transformer block; in Demucs its rational function replaces the ReLU nonlinearity in 1D CNN encoder/decoder blocks. This mechanism supplies the extra expressiveness for modeling harmonic and phase structure while avoiding the parameter blow-up that makes plain KAN fail.

What would settle it

Train the original and GR-KAN-adapted Demucs at depth 5 on VoiceBank-DEMAND across ten random seeds; if the mean PESQ difference between 2.990 and 2.896 falls below the standard deviation of the baseline, the claimed consistent improvement is not established.

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Extended reading notes

Core claim

The central claim is that GR-KAN layers—learnable rational functions shared across channel groups, followed by a linear projection—are expressive enough to capture the smooth, multiscale structure of speech, while remaining trainable at scale. On MP-SENet, replacing the dense layers inside the GRU-Transformer blocks with one GR-KAN layer raises PESQ from 3.561 (GELU baseline) to 3.588 at the same 2.26M parameters, and outperforms doubled dense-layer baselines. On causal Demucs, replacing ReLU with GR-KAN in the encoder/decoder lifts PESQ from 2.896 to 2.990 at depth 5, matching the depth-6 original, which has over four times the parameters. The paper presents this as the first consistent improvement from KAN-based methods in both time- and state-of-the-art time-frequency-domain speech enhancement.

Load-bearing premise

The load-bearing premise is that the reported Demucs gains, especially the +0.1 PESQ from depth 5, are larger than run-to-run variation; the paper gives no standard deviations or seed count for those tables.

Editorial extensions

If this is right

  • The same training recipes and loss functions as the original MP-SENet and Demucs can be kept; GR-KAN is a drop-in swap for dense layers or activations.
  • At depth 5, the GR-KAN-adapted Demucs matches the PESQ of the original depth-6 model while using about a quarter of the parameters, so parameter budgets can be redirected to depth or other capacity.
  • GR-KAN beats doubled dense-layer baselines in MP-SENet, suggesting that more parameters with conventional layers are not an equivalent substitute for the rational activation structure.
  • Plain KAN does not help time-frequency-domain speech enhancement at scale, so future KAN-style speech enhancement work should use GR-KAN's group-rational design rather than spline KAN.
  • The paper concludes that future speech enhancement and speech generation systems may benefit from adopting GR-KAN.

Reading between the lines

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

  • Our inference: the parameter savings suggest GR-KAN could be tested in larger speech enhancement backbones or in vocoders, where replacing expensive activations would be cheap to try.
  • Our inference: the group-sharing mechanism, rather than rational functions alone, may be the key to the result; an ablation that uses a rational-family activation in the same slots would isolate that factor.
  • Our inference: the method should transfer to non-speech audio restoration, such as music denoising, if the expressiveness claim about multiscale structure is general.
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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 / 6 minor

Summary. The paper proposes adapting Group-Rational KAN (GR-KAN), a rational-function variant of Kolmogorov-Arnold Networks, to two speech enhancement architectures: MP-SENet in the time-frequency domain and Demucs in the time domain. The authors first compare KAN and GR-KAN against MLP variants on a synthetic signal modeling task, then replace dense layers in MP-SENet with GR-KAN layers and ReLU activations in Demucs with GR-KAN activations. On VoiceBank-DEMAND they report that GR-KAN improves PESQ by up to 0.1 while requiring up to 4x fewer parameters than a deeper baseline, and claim the first successful use of KAN-based methods for consistent improvement in both time-domain and state-of-the-art time-frequency-domain speech enhancement.

Significance. If the reported gains are reproducible and the parameter counts are correct, the paper offers a practical drop-in replacement for dense layers and activations in existing SE models, with modest objective quality improvements at lower or equal parameter cost. The paper has clear strengths: the MP-SENet experiments are averaged over three runs with standard deviations, the comparison includes both conventional and learnable activations, and the negative result for KAN on MP-SENet is a useful data point consistent with prior scalability concerns. However, the central parameter-efficiency claim currently rests on an apparent inconsistency in the Demucs parameter accounting, and the Demucs results lack variance information, so the headline improvement could be within run-to-run noise. The circularity burden is minimal, as GR-KAN is an externally proposed method and all comparisons are against external baselines.

major comments (3)
  1. [Section 3.3 and Table 4] Table 4 reports the same #P for the original Demucs and the GR-KAN adapted Demucs at every depth (4.702, 18.868, 75.512M), yet Section 3.3 states that the zero-parameter ReLU activations in the encoders and decoders were replaced by GR-KAN activations (GR from Eq. 4), and GR-KAN rational functions have trainable coefficients. If those coefficients are trainable, the GR-KAN model must have strictly more trainable parameters than the baseline. The identical numbers strongly suggest that the rational-function coefficients were excluded from #P. Please clarify exactly which parameters are included in the reported counts, and if the coefficients were omitted, recount and recompute all parameter-efficiency conclusions.
  2. [Abstract and Table 4] The abstract's claim that 'GR-KAN requires up to 4x fewer parameters while improving PESQ by up to 0.1' is not supported by any single comparison in Table 4. The 4x ratio comes from comparing GR-KAN depth 5 (18.868M) with original depth 6 (75.512M), while the +0.1 PESQ improvement (2.896 to 2.990) comes from comparing GR-KAN depth 5 with original depth 5 at identical reported parameter counts. No row or pair of rows demonstrates both a 4x parameter reduction and a 0.1 PESQ gain simultaneously. The authors should either report a matched experiment that shows both outcomes in one comparison or rephrase the abstract to state the two findings separately and accurately.
  3. [Tables 3 and 4] The Demucs results in Tables 3 and 4 are reported as point estimates without standard deviations, confidence intervals, or the number of seeds, unlike Table 2 where MP-SENet results are averaged over three runs with standard deviations. Since the headline gains are approximately 0.1 PESQ (e.g., 2.896 to 2.990 at depth 5, and 2.977 to 3.018 at depth 6), it is currently impossible to judge whether these differences exceed run-to-run variation. Please report multi-run statistics for the Demucs experiments, or at minimum provide a variance estimate and a significance test, before claiming consistent improvement.
minor comments (6)
  1. [Abstract] There is a typo: 'V oicebank-DEMAND' should be 'VoiceBank-DEMAND'.
  2. [Section 2.2, Eq. (3)] The text uses 'scaler' where 'scalar' is intended; please correct the wording.
  3. [Section 3.3] The phrase 'To further access scalability' should read 'To further assess scalability'.
  4. [Table 3] The column headers 'KAN Enc' and 'KAN Dec' are misleading because the adapted model uses GR-KAN activations, not KAN activations; rename the headers to 'GR-KAN Enc' and 'GR-KAN Dec'.
  5. [Section 3.3] The Demucs adaptation uses only the GR rational-function part of Eq. (4) rather than the full GR-KAN layer; please specify the group size, rational-function degree, and any other GR-KAN hyperparameters used for the Demucs experiments, as these are not reported.
  6. [Section 5] The claim of 'first successful use of KAN-based methods' is stronger than the evidence supports, given that only two model architectures are tested and no comparison is made against other KAN variants or other recent activation-replacement methods on the same benchmark; consider softening the novelty claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: GR-KAN is an externally developed method, evaluated against external baselines on a standard benchmark.

full rationale

This paper does not derive its own fitting equations; it imports GR-KAN from prior work [28] by different authors and then substitutes it into MP-SENet and Demucs. All performance claims are empirical comparisons against externally defined baselines (Voicebank-DEMAND, PESQ/CSIG/CBAK/COVL/STOI), and no reported result is obtained by solving for a parameter that was fitted to the same target. The "4x fewer parameters" claim is a comparison of published model sizes, not a construction-level identity. The identical #P values for baseline and GR-KAN Demucs in Table 4, alongside the paper's statement that ReLU activations were replaced by parameterized GR-KAN rational activations, is a parameter-accounting inconsistency that deserves a correctness review, but it is not circularity: no metric is defined in terms of another reported quantity, and the central comparisons are external. The signal-modeling experiment in Section 3.1 also uses a synthetic task with no dependence on the SE benchmark results. Therefore the circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new entities are introduced. GR-KAN, rational functions, and group sharing are prior work. The main hand-chosen hyperparameter is the group size k=8, with KAN baseline hyperparameters also fixed.

free parameters (2)
  • GR-KAN group size k = 8
    Set in Sec. 4.1 without a sweep; the central comparison uses this single hand-chosen value.
  • KAN grid size and spline order = grid=5, order=3
    Used for the KAN baseline that fails on MP-SENet; the conclusion that KAN does not scale depends on this configuration.
assumptions (4)
  • standard math Kolmogorov-Arnold theorem underlies KAN expressiveness
    Invoked in Sec. 2.1 as the theoretical basis for KAN's representational power.
  • domain assumption GR-KAN architecture from [28] works as described
    The paper adopts rational functions, group sharing, and variance-preserving initialization from Yang and Wang without re-deriving them.
  • domain assumption VoiceBank-DEMAND protocol from [33] is correctly followed
    The benchmark, SNR conditions, and train/test split are assumed to be standard as in the cited dataset paper.
  • domain assumption Replacing dense layers or ReLU with GR-KAN is a fair architectural comparison
    The paper does not control for the extra rational parameters or the variance-preserving init, so the comparison implicitly assumes these are the only differences.

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Cite this review

Pith. "Pith review of From KAN to GR-KAN: Advancing Speech Enhancement with KAN-Based Methodology." pith.science (2026). https://pith.science/paper/RHRHJBHB

@misc{pith2026241217778,
  author       = {Pith},
  title        = {Pith review of: From KAN to GR-KAN: Advancing Speech Enhancement with KAN-Based Methodology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RHRHJBHB}},
  note         = {Machine review of arXiv:2412.17778}
}
read the original abstract

Deep neural network (DNN)-based speech enhancement (SE) usually uses conventional activation functions, which lack the expressiveness to capture complex multiscale structures needed for high-fidelity SE. Group-Rational KAN (GR-KAN), a variant of Kolmogorov-Arnold Networks (KAN), retains KAN's expressiveness while improving scalability on complex tasks. We adapt GR-KAN to existing DNN-based SE by replacing dense layers with GR-KAN layers in the time-frequency (T-F) domain MP-SENet and adapting GR-KAN's activations into the 1D CNN layers in the time-domain Demucs. Results on Voicebank-DEMAND show that GR-KAN requires up to 4x fewer parameters while improving PESQ by up to 0.1. In contrast, KAN, facing scalability issues, outperforms MLP on a small-scale signal modeling task but fails to improve MP-SENet. We demonstrate the first successful use of KAN-based methods for consistent improvement in both time- and SoTA TF-domain SE, establishing GR-KAN as a promising alternative for SE.

Figures

Figures reproduced from arXiv: 2412.17778 by the authors.

Figure 1
Figure 1. Architecture of (a) the Overall MP-SENet (b) the GR￾KAN adapted GRU-Transformer Block. variants, with either conventional or learnable activation func￾tions. The synthetic signal consists of dynamic, artificial sylla￾bles (150–250ms) with irregular pauses (20–100ms). The base frequency of each syllable fluctuates nonlinearly around 5 Hz, modulated by sine and cosine functions for smooth transitions. The amplitude of… view at source ↗
Figure 2
Figure 2. Architecture of the GR-KAN adapted Causal Demucs, where we replace all ReLU activations in the Encoder and De￾coder blocks with GR-KAN activations. Please note that the last Decoder block does not have the GR-KAN activations. adapted causal Demucs, where we have replaced the ReLU ac￾tivation functions in the original Encoders and Decoders with the GR-KAN activation functions (GR from Eq. 4). This setup differs sligh… view at source ↗
Figure 3
Figure 3. Comparison of MLP (ReLU), MLP (GELU) and GR-KAN on fitting an artificial signal with speech dynamics against conventional MLP methods in speech enhancement [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Training-Free Intelligibility-Guided Observation Addition for Noisy ASR

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    Mixing noisy and enhanced speech with weights derived from the recognizer's confidence on each signal reduces ASR word error rate without any additional training.

  2. "KAN you hear me?" Exploring Kolmogorov-Arnold Networks for Spoken Language Understanding

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    Placing a KAN layer between two linear layers improves spoken language understanding accuracy over linear-only baselines on several speech-intent datasets.

  3. Pushing the Performance of Synthetic Speech Detection with Kolmogorov-Arnold Networks and Self-Supervised Learning Models

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    Swapping the MLP projector for a GR-KAN layer in XLSR-Conformer reduces equal error rates on ASVspoof 2021 LA and DF, reaching 0.70% EER on the variable-length LA set.

Reference graph

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    Traditional SE solutions are based on digital signal processing solutions, such as Wiener filtering [1], spectral subtraction [2] and min- imum mean squared error estimation [3]

    Introduction Speech enhancement (SE) reduces noise and distortion to im- prove speech clarity, benefiting applications like hearing aids, telecommunications and voice recognition systems. Traditional SE solutions are based on digital signal processing solutions, such as Wiener filtering [1], spectral subtraction [2] and min- imum mean squared error estima...

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    Preliminaries 2.1. KAN: Kolmogorov-Arnold Network The Kolmogorov-Arnold theorem [32] asserts that any continu- ous function can be represented as a composition of univariate continuous functions of a finite number of variables. A KAN layer L is thus a composition of learnable univariate functions, ϕ(s), as shown in Eq. (1): L(x) = PI i=1 ϕi,1(xi) . . . PI...

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    KAN and GR-KAN in SE 3.1. Analysis on small-scale signal modeling We first evaluate KAN and GR-KAN solutions on a small-scale signal modeling task using a 5 second synthetic signal with sam- pling rate of 100. Results are compared against several MLP Figure 1: Architecture of (a) the Overall MP-SENet (b) the GR- KAN adapted GRU-Transformer Block. variants...

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    Experimental Setup The V oiceBank-DEMAND [33], a widely recognized SE benchmark, is used to assess our KAN-based models

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    Conclusion This work explores the use of KAN and its variant, GR-KAN, to enhance existing DNN-based SE solutions. We begin by demonstrating the superior expressiveness of KAN-based meth- ods over MLPs with conventional and learnable activation func- tions through a small-scale signal modeling task. We then ex- plain KAN’s inability to scale to complex SE ...

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.