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REVIEW 4 major objections 6 minor 74 references

Kolmogorov-Arnold Network for Gene Regulatory Network Inference

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read scKAN uses a continuous Kolmogorov-Arnold network whose gradients yield signed, directed gene regulatory edges, outperforming tree-based models on the BEELINE benchmark.

desk verdict A solid, reproducible GRN inference method with an overstated SOTA claim and an untested causal interpretation of gradients. read the letter →

arxiv 2506.13740 v1 pith:QSGOQTJI submitted 2025-06-16 cs.CE

Tsz Pan Tong , Aoran Wang , George Panagopoulos , Jun Pang This is my paper
classification cs.CE
keywords Kolmogorov-Arnoldnetworkgeneregulatoryinferencesingle-cellRNA-seqexplainableAIgradientattributionactivationandinhibitionBEELINEbenchmarkone-vs-restmodels
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

scKAN replaces the tree predictors used by GENIE3 and GRNBOOST2 with a continuous Kolmogorov-Arnold network that reconstructs each gene's expression from all other genes. The paper claims that the partial derivatives of this learned function with respect to each input gene give both the strength and the sign (activation or inhibition) of regulatory edges, and that this overcomes a key limitation of tree models, which cannot distinguish regulation types. On the BEELINE benchmark, scKAN is reported to surpass the leading signed GRN inference models by 5.40% to 28.37% in AUROC and by 1.97% to 40.45% in AUPRC, while remaining competitive on networks of 71 and 104 genes. The paper also shows that evaluating gradients at specific cells yields cell-type-specific GRNs, and it explains why all one-vs-rest models struggle on branching differentiation trajectories.

What carries the argument

The central object is the one-vs-rest (OvR) regression formulation, in which each gene's expression is reconstructed from all other genes, and the replacement of tree models with a Kolmogorov-Arnold network (KAN) whose activation functions are third-order B-splines. The load-bearing mechanism is the gradient of the KAN predictor: the partial derivative with respect to gene j at a cell is treated as the signed regulatory weight of j on i, with strength standardized across genes (z-score) and edges sparsified by recording only those genes whose standardized magnitude exceeds 1 in a fraction of cells. This gradient readout is what gives scKAN its ability to label edges as activation or inhibition.

What would settle it

Train scKAN on a synthetic dataset generated from a known ground truth in which gene C drives A and B but A and B do not regulate each other; if the inferred network contains a confident edge between A and B, the gradient interpretation has produced a spurious regulatory claim. On real data, a sharper test is to compare scKAN's top-ranked signed edges with the results of perturbation experiments (e.g., knockout or overexpression), asking whether the predicted regulators actually change target expression when perturbed.

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Extended reading notes

Core claim

The discovery is a method, not a biological fact: for each target gene i, scKAN trains a third-order differentiable KAN model $f_{\text{KAN},i}$ to predict the expression of i from the expressions of all other genes, following the one-vs-rest formulation. The partial derivative of $f_{\text{KAN},i}$ with respect to input gene j, evaluated at a cell, is interpreted as the regulatory effect of j on i; averaging a z-scored version of these gradient magnitudes across cells and taking a majority vote on their signs yields a sparse, directed, signed adjacency matrix. The paper reports that this gradient-based construction outperforms existing signed GRN inference methods on the BEELINE benchmark and remains stable across ten runs.

Load-bearing premise

The load-bearing premise is that the partial derivative of the expression predictor with respect to a gene reflects a true regulatory influence, but the predictor is trained only for predictive accuracy, not causal identification, so correlated expression can make gradients track confounding or indirect associations instead of direct regulation.

Editorial extensions

If this is right

  • Signed, directed GRNs can be inferred from scRNA-seq alone without prior knowledge of the graph structure.
  • Cell-type-specific and lineage-specific GRNs become accessible by evaluating the learned gradients on subsets of cells.
  • The one-vs-rest family, including tree models and scKAN, will continue to struggle on branching trajectories because overlapping projections violate the assumption that expression is a function of other genes.
  • With only a few hundred parameters, the KAN predictor runs on a single GPU and scales to networks of about one hundred genes, a size relevant for small curated communities.

Reading between the lines

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

  • Extrapolating from the paper's benchmark results, scKAN's gradient interpretation is likely to inherit the confounding structure of scRNA-seq; combining it with known perturbation data or causal-dynamics models is the natural next test.
  • The sparsification rule (z-score threshold of 1) is a fixed heuristic; an adaptive threshold tuned by validation or a learned sparsity prior might improve recall of weak but real regulators.
  • The paper's own furcation analysis implies that OvR architectures cannot represent one-to-many mappings; conditional or multi-branch predictors, or mixture models, would be a direct architectural fix worth testing.
  • Because the KAN is third-order differentiable, second derivatives (curvature of the Waddington landscape) could encode regulatory interactions between pairs of inputs, a testable extension the paper mentions only as future work.
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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 / 6 minor

Summary. The manuscript introduces scKAN, a method for signed, directed gene regulatory network (GRN) inference from single-cell RNA-seq data. Following the One-vs-Rest formulation of GENIE3 and GRNBOOST2, scKAN trains a Kolmogorov-Arnold network to reconstruct each gene's expression from all the other genes, then derives the GRN from the gradient of the learned predictor: the gradients are computed at each cell, z-scored across input genes (Eq. 8), and converted into a signed adjacency matrix by thresholding with majority-vote sign (Eq. 9). The method is evaluated on the BEELINE benchmark (six synthetic and four curated network types, ten 2000-cell datasets each), with additional scalability experiments on 71-gene and 104-gene networks extracted from CollecTRI. The authors claim that scKAN surpasses the leading signed GRN baselines by 5.40%–28.37% in AUROC and by 1.97%–40.45% in AUPRC, but the body of the paper restricts this claim to the LI, LL, CY, and curated datasets and states that scKAN 'faced difficulties' on the furcating datasets (BF, BFC, TF). An ablation study compares KAN versus MLP predictors and raw gradients versus SHAP explanations, and Section 6.2 analyzes a shared weakness of all OvR models on bifurcating topologies.

Significance. If the qualified claims hold up under significance testing, this is a genuine advance for signed GRN inference: scKAN is the only One-vs-Rest-family method among the compared baselines that outputs signed, directed edges, and it achieves the best AUROC and AUPRC on the linear (LI, LL), cyclic (CY), and curated (mCAD, VSC, HSC, GSD) network types while remaining competitive in run time. The paper's concrete strengths are a public code repository, a large experimental effort (more than 2,300 runs), a fair comparison against BEELINE baselines with optimized hyperparameters, an informative ablation (KAN vs MLP; gradient vs SHAP), and an unusually honest limitations section (Section 6.3) that notes zero-inflation, self-loops, and non-identifiability. The toy example in Section 6.2 is a useful illustration of why OvR models fail on furcating topologies, and the gradient-clustering extension in Section 6.1 offers cell-type-specific GRNs that tree-based models cannot produce. The main caveats are the overstated abstract claim, the absence of significance tests, and the untested gradient-to-regulation interpretation, all of which are fixable in revision.

major comments (4)
  1. [Abstract; Section 5.2 (Fig. 3)] The abstract's claim that 'scKAN surpasses and improves the leading signed GRN inference models ranging from 5.40% to 28.37% in AUROC and from 1.97% to 40.45% in AUPRC' is not supported by the full results in Fig. 3. On the signed BEELINE ground truth, GRNVBEM outperforms scKAN in AUROC on BF (69.42 vs 63.11), BFC (78.05 vs 69.46), and TF (68.11 vs 57.85), and in AUPRC on BF (35.29 vs 27.07) and BFC (35.23 vs 29.20). The reported ranges therefore appear to be computed only over the seven network types where scKAN is the best signed model (LI, LL, CY, mCAD, VSC, HSC, GSD), and the 'second-best' baseline changes from dataset to dataset (GRNVBEM on some, SINCERITIES on others). The body of Section 5.2 does acknowledge the furcating weakness, but the abstract and the Contributions bullet repeat the unqualified claim, which is misleading as a headline. Please rewrite these statements to name the dataset classes where the superiority holds and to report the deficits on BF, BFC, and TF.
  2. [Section 5.1-5.2; Fig. 9] No statistical significance tests are reported for any of the headline comparisons. The standard deviations in Fig. 9 show substantial overlap on several datasets; for example, signed AUROC on LI is 91.48±2.43 for scKAN versus 76.67±16.17 for GRNVBEM, and on TF the gap between scKAN (57.85) and GRNVBEM (68.11) is comparable to the magnitude of the reported standard deviations. Since each network type was evaluated on 10 BoolODE datasets, paired significance tests (e.g., Wilcoxon signed-rank or paired t-test over the 10 runs) are feasible and should be reported for all 10 dataset types. This would also clarify whether the favorable comparisons on LI, LL, CY, and the curated datasets are established beyond noise.
  3. [Section 4 (Eqs. 8-9); Section 6.3] The mapping from the gradient of a reconstruction-trained predictor to a signed regulatory effect (Eqs. 8-9) is an assumption that is not validated. The predictor f_{KAN,i} is trained to reconstruct gene i's expression from the other genes; with correlated regulators, partial derivatives can reflect confounding or an arbitrary split of credit among co-expressed inputs, so the inferred sign and strength of an edge need not correspond to a direct regulatory relationship. The authors acknowledge in Section 6.3 that 'the inferred biological system is not identifiable,' but no experiment tests how often the gradient signs match the true signs. Because the signed BEELINE evaluation does not decompose performance into structure recovery and sign accuracy, I recommend (a) reporting sign accuracy among true-positive edges, and (b) adding a controlled experiment with correlated regulators, or explicitly restricting the central claims to benchmark ranking performance while flagging the identifiability issue in the main text rather than only in the limitations.
  4. [Section 4 (Eq. 9); Section 5.1] The method's free parameters, notably the sparsification threshold (z-score > 1 in Eq. 9), the spline order, the grid size, and the early-stopping criterion, are fixed without any sensitivity analysis. The z-score threshold directly controls the edge set and will therefore influence AUROC and AUPRC, and the paper's performance comparisons could depend on this choice. A sensitivity analysis over the threshold (and ideally over the spline order and grid size) for at least a few representative network types would strengthen the claim that the reported improvements are a property of the method rather than of a particular threshold.
minor comments (6)
  1. [Section 4 (Eq. 9)] Eq. 9 uses s_{i,j,p} in the indicator, but the z-score is defined as s_{j,i,p} in Eq. 8; please make the subscript ordering consistent.
  2. [Section 5.1] The early-stopping rule uses the gap between train and test loss, so the held-out expression data influence the training loop; either call this split a validation set or justify why using it in the stopping rule does not affect the validity of the benchmark comparison.
  3. [Section 6.2; Contributions] The Contributions bullet promises a 'proof' of the furcating-data weakness, but Section 6.2 provides a toy example and an argument, not a proof; the conclusion depends on the constructed multi-valued target, so the wording should be softened to 'explanation and illustration.'
  4. [Section 5.3; Fig. 5] The SHAP deep explainer is designed for deep MLP architectures; its application to KAN models should be justified, or the SHAP baselines should be described as approximate XAI references.
  5. [Fig. 4] The run-time comparison in Fig. 4 mixes hardware (scKAN on a V100 GPU, baselines on CPU), which makes the scaling comparison hard to interpret; a GPU/CPU label or a CPU-only run of scKAN would help.
  6. [Section 5.2] The phrase 'scKAN has the best average AUROC and AUPRC in all datasets' is ambiguous and, taken literally, is incorrect (for unsigned AUROC in Fig. 2, PPCOR beats scKAN on BF and PIDC beats scKAN on CY); the intended claim is presumably the best average across all datasets, which should be stated precisely.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: scKAN is an empirical, externally benchmarked method whose central result does not reduce to its inputs.

full rationale

The derivation chain is self-contained and empirically falsifiable. scKAN trains a KAN predictor f_{KAN,i} to reconstruct each gene's expression from all other genes (Eq. 7), then constructs the GRN adjacency matrix from gradients of that predictor via Eqs. (8)-(9). No ground-truth edge information is used during training or sparsification; the thresholding in Eq. (9) is a heuristic applied to gradients, not a fit to the BEELINE labels. The central performance claim is evaluated against external BEELINE ground-truth networks, so the AUROC/AUPRC improvements are not equivalent to the model's inputs by construction. The only self-citation visible in the main text, reference [6] in Section 3.3 supporting the general statement that KAN excels in graph regression, is motivational and non-load-bearing: the paper's use of KAN rests on continuity, universal approximation, and the OvR formulation, not on that cited result. No uniqueness theorem is imported from prior author work, and no ansatz is smuggled in via self-citation. The gradient-to-regulation mapping in Eq. (8) is a causal heuristic rather than a proven identification, but that is a correctness and interpretability concern, not circularity; the paper itself acknowledges non-identifiability in Section 6.3. The abstract's universal SOTA phrasing is questionable given the furcating-dataset results in Fig. 3, but that is an empirical/statistical issue distinct from circular reasoning.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The method introduces no new physical or biological entities. Its main extra assumptions are the smoothness of the regulatory mapping, the causal validity of gradients, and the representativeness of the simulator. Several hand-chosen hyperparameters influence the results but are not fitted to the ground-truth networks.

free parameters (6)
  • Sparsification z-score threshold = 1
    Eq. (9): edges are kept when the per-cell standardized gradient magnitude exceeds 1. The threshold is chosen by hand to enforce sparsity; no sensitivity analysis is reported.
  • Spline order k = 3
    Section 4: set to 3 to ensure third-order differentiability. Not tuned per dataset.
  • B-spline grid size G = 10
    Section 4: balances model granularity. Not tuned per dataset.
  • Hidden layer widths = 2d+1, 2(2d+1)+1, 2d+1
    Section 4: follows Liu et al. recommendation; depends on input dimension d=g-1.
  • Learning rate = 1e-4
    Section 5.1: Adam optimizer. Chosen a priori.
  • Early stopping gap and patience = 0.0005 gap, 10 epochs
    Section 5.1: stopping when train-test loss gap exceeds threshold.
assumptions (5)
  • standard math Kolmogorov-Arnold representation theorem and universal approximation guarantee that a KAN can approximate the true gene regulatory function f_i.
    Section 3.3 uses these theorems to justify replacing trees with KANs.
  • domain assumption Gene expression dynamics can be represented as a smooth continuous differentiable function (Waddington landscape).
    Section 1 and 4 motivate KAN by claiming cellular dynamics are continuous at measurement resolution.
  • ad hoc to paper The partial derivative of the fitted predictor with respect to an input gene is a valid measure of that gene's regulatory effect on the target.
    Section 4, Eq. (8): gradient sign and magnitude are interpreted as activation and inhibition strength. This is not derived from causal inference theory and can fail under confounding.
  • domain assumption BoolODE-simulated BEELINE datasets are representative enough that benchmark performance transfers to real scRNA-seq data.
    Section 5 uses only synthetic and curated simulated data; Section 6.3 acknowledges that real data are not evaluated.
  • domain assumption Using held-out expression test loss for early stopping does not leak information about the ground-truth GRN.
    Section 5.1 argues test loss is only used to detect overfitting of expression prediction, not GRN labels.

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Cite this review

Pith. "Pith review of Kolmogorov-Arnold Network for Gene Regulatory Network Inference." pith.science (2026). https://pith.science/paper/QSGOQTJI

@misc{pith2026250613740,
  author       = {Pith},
  title        = {Pith review of: Kolmogorov-Arnold Network for Gene Regulatory Network Inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QSGOQTJI}},
  note         = {Machine review of arXiv:2506.13740}
}
read the original abstract

Gene regulation is central to understanding cellular processes and development, potentially leading to the discovery of new treatments for diseases and personalized medicine. Inferring gene regulatory networks (GRNs) from single-cell RNA sequencing (scRNA-seq) data presents significant challenges due to its high dimensionality and complexity. Existing tree-based models, such as GENIE3 and GRNBOOST2, demonstrated scalability and explainability in GRN inference, but they cannot distinguish regulation types nor effectively capture continuous cellular dynamics. In this paper, we introduce scKAN, a novel model that employs a Kolmogorov-Arnold network (KAN) with explainable AI to infer GRNs from scRNA-seq data. By modeling gene expression as differentiable functions matching the smooth nature of cellular dynamics, scKAN can accurately and precisely detect activation and inhibition regulations through explainable AI and geometric tools. We conducted extensive experiments on the BEELINE benchmark, and scKAN surpasses and improves the leading signed GRN inference models ranging from 5.40\% to 28.37\% in AUROC and from 1.97\% to 40.45\% in AUPRC. These results highlight the potential of scKAN in capturing the underlying biological processes in gene regulation without prior knowledge of the graph structure.

Figures

Figures reproduced from arXiv: 2506.13740 by the authors.

Figure 1
Figure 1. A graphical summary of scKAN. For each gene i, we remove its gene expres￾sion and train an independent model fKAN,i to recover its expression. We extract the gradients from the models to infer the GRN after standardization and sparsification. 4 Methodology Our method consists of the following three steps. Preprocessing. We start by creating a copy of the gene expression matrix for each gene i, and removing the i-th … view at source ↗
Figure 2
Figure 2. Average AUROC (left) and AUPRC (right) of directed GRN inference models with unsigned ground-truth on different datasets out of 10 runs. Synthetic and curated datasets are separated by a vertical line. the network density. SHD measures the closeness of the predicted and ground￾truth networks, while FDR measures the edge prediction error. SHD is a positive real number and the FDR ranges from 0 to 100%. Smaller values… view at source ↗
Figure 3
Figure 3. Average AUROC (left) and AUPRC (right) of directed GRN inference models with signed ground-truth on different datasets out of 10 runs. in [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Model elapsed time on different dataset sizes in log-log scale. Vertical bars indicate standard deviations at each data point. BF BFC LI LL CY TF mCAD VSC HSC GSD MLP (same arch.) MLP (width-wise) MLP (depth-wise) KAN (SHAP, deep) KAN (SHAP, grad) scKAN (Ours) 57.04 61…
Figure 5
Figure 5. Figure 5: Average AUROC (left) and AUPRC (right) of models in the ablation study on different datasets out of 10 runs. 5.3 Ablation Study Compared with other OvR models, our model replaces the tree model with a KAN model, an alternative to MLP, and replaces the importance score …
Figure 6
Figure 6. Figure 6: UMAP visualization of the gene expression and gradient pattern colored by pseudotime and gradient cluster. Inferred cell-type specific GRNs are shown in (c). 6.2 Weakness of OvR Models We empirically demonstrated the capability and scalability of scKAN to infer directe…
Figure 7
Figure 7. Figure 7: (a) Simulations of gene expression with blue and red branches. (b) Underlying GRN of the 3-gene toy example. For the dataset with both branches and the dataset with the red branch, GENIE3 infers GRN both, GRN r, respectively: GRN both =   0 0.48 0.47 0.92 0 0.53 0.08…
Figure 8
Figure 8. Figure 8: Standard deviation of AUROC (left) and AUPRC (right) of directed GRN inference models with unsigned ground-truth on different datasets out of 10 runs. Syn￾thetic and curated datasets are separated by a vertical line. scKAN has a stable performance across different data…
Figure 9
Figure 9. Figure 9: Standard deviation of AUROC (left) and AUPRC (right) of directed GRN in￾ference models with signed ground-truth on different datasets out of 10 runs. Synthetic and curated datasets are separated by a vertical line [PITH_FULL_IMAGE:figures/full_fig_p023_9.png]
Figure 10
Figure 10. Figure 10: Standard deviation of AUROC (left) and AUPRC (right) of models in the ablation study on different datasets out of 10 runs. Synthetic and curated datasets are separated by a vertical line [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]
Figure 11
Figure 11. Figure 11: Average (a) and standard deviation (b) of the Structured Hamming Distance of directed GRN inference models with unsigned ground-truth out of 10 runs. Synthetic and curated datasets are separated by a vertical line. BF BFC LI LL CY TF mCAD VSC HSC GSD PPCOR LEAP SCODE …
Figure 12
Figure 12. Figure 12: Average (a) and standard deviation (b) of the False Discovery Rate of directed GRN inference models with unsigned ground-truth out of 10 runs. Synthetic and cu￾rated datasets are separated by a vertical line. reveal the underlying GRNs. Integrating prior knowledge and…

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Pith tools

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