{"id":"1f2bd378-25cd-4c1b-8fad-4149e03cd0eb","arxiv_id":"2412.15373","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A KAN-based framework with a first-layer proximal operator detects Granger causal relationships in simulated VAR and Lorenz-96 time series, with accuracy comparable to cMLP baselines.","lead":"The authors apply Kolmogorov-Arnold networks (KANs) to Granger causality detection, adding a proximal sparsity step to the first layer to identify causal parents in time series. They report accuracy comparable to, and slightly better than, multilayer perceptron baselines on simulated VAR and Lorenz-96 data.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claim that GC-KAN outperforms MLPs rests on cMLP numbers borrowed from Tank et al. under different architectures and dataset conditions, so the comparative evidence is not yet established; a controlled equal-footing rerun is needed.","rationale":"The reader correctly notes that Eq. 18 is underspecified, and my reading confirms that ambiguity: phi is a function, not a scalar weight, and the paper does not explicitly connect Eq. 18 to the |phi|_1 norm defined in Eq. 11. However, I see the uncontrolled baseline comparison as the more load-bearing issue, because the central claim is explicitly comparative ('potential to outperform MLPs'). If the only cMLP numbers are imported from another paper, then differences in architecture size, data draws, and hyperparameters are confounded with the KAN-versus-MLP comparison. The paper does have independent value: the proximal sparsity step applied to first-layer KAN edges is a reasonable adaptation, the synthetic setup is clearly described, and the appendix figure gives qualitative support for the pruning mechanism. No internal inconsistency makes the method impossible; rather, the evidence chain for the headline claim is incomplete. The reader's CONDITIONAL verdict remains appropriate: with controlled equal-footing baselines, an explicit Eq. 18 metric, and released code, the comparison could be settled; without them, the claim of outperformance is unverified. I therefore do not change the verdict.","tokens_in":9417,"tokens_out":4803,"duration_ms":46547,"concrete_test":"Re-run cMLP with the Hierarchical Group Lasso in the same codebase under identical data-generating processes, lag p=5, n=20, sample sizes T in {250,500,1000}, with matched parameter budgets (same hidden-neuron count and/or same total trainable parameters) and at least 20 seeds, then report AUROC deltas with confidence intervals. If GC-KAN does not beat cMLP on the majority of settings where Tables I-II claim improvement, the 'outperform MLPs' claim should be downgraded. In the same code release, specify exactly how |phi| in Eq. 18 is computed (e.g., the Eq. 11 norm over training inputs, or raw spline coefficients) and regenerate the reported ROC curves from that explicit metric.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing assumption behind the central claim that GC-KAN outperforms MLPs is that the comparison is a fair, same-setting benchmark. That assumption is not met. Tables I and II state that cMLP results are 'taken directly from [15]', while GC-KAN scores are generated by the authors on their own simulated data. The cMLP baseline has 100 hidden neurons and was optimized with the Hierarchical Group Lasso by Tank et al.; GC-KAN uses 1 hidden neuron for VAR and 10 for Lorenz-96. Different hidden counts mean different capacities, and different data draws, preprocessing, and initialization can produce run-to-run differences that a borrowed baseline cannot control. The reported margins (e.g., 99.3 vs 98.4 at T=1000 VAR(1); 95.9 vs 95.1 at VAR(2)) are small and not accompanied by matched-condition intervals. The one equal-hidden-neuron comparison (Lorenz-96, 10 hidden, T=1000, F=40: about 94% vs 95.7%) is a single point and also comes from a different source. A secondary but real reproducibility gap is Eq. 18: C_{j,k} is written as a sum of |phi_{j,k,i}|, but phi is a function. Eq. 11 defines |phi|_1 as an average over training inputs, yet the paper never states that Eq. 18 uses this norm, so the causal scoring rule that produces the ROC curves is not exactly specified. Either issue alone would be serious; together they mean the headline comparative claim is not yet supported by the evidence provided.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces GC-KAN, a Kolmogorov-Arnold network based framework for nonlinear Granger causality detection. Each target time series is modeled by a KAN whose first-layer spline activations map lagged inputs to hidden neurons; sparsity is encouraged by L1 and entropy regularization plus a proximal soft-thresholding step applied to the first layer. The method is evaluated on synthetic VAR(1), VAR(2), and Lorenz-96 data with known ground truth, and AUROC scores are compared with cMLP results taken from Tank et al. [15]. The authors report comparable or slightly better accuracy for GC-KAN in several settings and argue that KANs offer a more parameter-efficient and interpretable alternative to MLPs for sparse high-dimensional Granger causality detection.","tokens_in":9784,"tokens_out":3900,"duration_ms":34460,"significance":"If the central claim were fully supported, the paper would make a useful contribution by adapting KANs to nonlinear Granger causality with an explicit sparsification mechanism and a compact architecture. The proximal-operator idea is a sensible adaptation of the cMLP pipeline to spline-based networks, and evaluating on synthetic systems with known ground truth is appropriate. The manuscript is also honest in reporting that many differences are small. However, the evidence for the headline claim that GC-KAN can outperform MLPs is weakened by an unequal benchmark: cMLP results are borrowed from [15] with a 100-hidden-neuron architecture and a different data pipeline, while GC-KAN results are generated in-house with 1 or 10 hidden neurons. In addition, the causal contribution metric in Eq. (18) is not fully specified because the norm of a spline function is not defined. A matched-condition rerun and a precise definition of the contribution score would be needed before the comparative claim can be accepted.","major_comments":[{"comment":"The headline comparison is not made on equal footing. The cMLP AUROC values are \"taken directly from [15]\" and correspond to a 100-hidden-neuron cMLP optimized with Hierarchical Group Lasso on data from a different pipeline, whereas the GC-KAN results are produced by the authors with 1 (VAR) or 10 (Lorenz-96) hidden neurons on their own simulated data. The reported margins (e.g., 99.3 vs 98.4 at T=1000 in VAR(1), and 95.7 vs 95.5 at T=1000, F=40 in Lorenz-96) are small, and no matched-condition standard deviations are provided for the borrowed baseline. Consequently, the central claim that GC-KAN has the potential to outperform MLPs in Granger causality detection is not supported by controlled evidence; the authors should rerun cMLP under identical data, preprocessing, and capacity settings.","section":"Section III, Tables I and II"},{"comment":"The Granger contribution C_{j,k} is defined as a sum of |φ_{j,k,i}|, but φ_{j,k,i} is a learnable spline function, not a scalar. The paper never states whether the absolute value refers to the L1 norm defined in Eq. (11), the absolute value evaluated at a particular input, or some other functional norm. Since this quantity is used to construct the binary Granger causality matrix that underlies the ROC curves, the causal scoring rule is not mathematically specified and the experiments are not reproducible as written. Please define the norm explicitly.","section":"Eq. (18) in Section II.C.2"},{"comment":"The conclusion that GC-KAN shows \"stronger performances in low-sample-size settings\" for Lorenz-96 is overstated. At F=10, T=250 the AUROC values are 86.9±0.5 for GC-KAN versus 86.6±0.2 for cMLP, which is within the reported standard deviations; the only non-overlapping low-sample advantage appears at F=40, T=250 (86.3±0.2 vs 84.0±0.5). The claim should be qualified to refer to that specific setting.","section":"Section IV and Table II"}],"minor_comments":[{"comment":"The phrase \"10 add hidden neurons\" should read \"10 additional hidden neurons.\"","section":"Section III.B"},{"comment":"The caption states that the data are generated from an n=10 VAR(3) model, while Section III.A describes the VAR experiments as n=20 VAR(1) and VAR(2). This inconsistency should be resolved.","section":"Fig. 1 caption"},{"comment":"The GC-KAN loss omits the summation over time steps t=p,...,T that appears in the cMLP loss of Eq. (5). Please make the notation consistent.","section":"Eq. (14)"},{"comment":"The proximal operator is written as Prox_{λprox}, but the soft-thresholding rule uses ηλprox as the threshold. The role of the learning rate η in the definition of the proximal map should be clarified.","section":"Eqs. (16)-(17)"}],"recommendation":"major_revision","confidential_remarks":"The paper would be considerably strengthened by an open-source implementation and a matched-baseline rerun. As submitted, the experimental evidence for the main claim relies on borrowed numbers from Tank et al. (2021), which is a serious limitation for a methods paper. I recommend major revision rather than rejection because the framework itself is plausible and the central issues (equal-footing comparison and precise definition of the contribution score) are fixable within the scope of the manuscript."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I read the GC-KAN paper. Short version: the method is reasonable, the evaluation is not.\n\nWhat's actually new: replacing the MLP in Tank et al.'s component-wise framework with a KAN, and adding a proximal soft-thresholding step on the first-layer weights (both base and spline) so that irrelevant lags get exactly zero contribution. That's a clean, simple extension and the appendix figure shows it works as advertised. The paper is clearly written, the synthetic setups (VAR and Lorenz-96) are standard, and using AUROC over a range of proximal strengths is a sensible way to measure detection.\n\nThe soft spots are mostly about whether the main claim holds. The headline comparison against cMLP uses numbers taken directly from Tank et al., with 100 hidden neurons and hierarchical group lasso, while GC-KAN uses 1 hidden neuron for VAR and 10 for Lorenz-96. Those are different architectures, different data draws, different preprocessing—so the reported margins (99.3 vs 98.4, 95.9 vs 95.1) aren't evidence of superiority. The one equal-capacity comparison they mention (10 hidden neurons, Lorenz-96, T=1000, F=40) is a single point from another source and still not matched on data. The abstract says 'outperform', but the actual numbers are mixed: GC-KAN is worse at low sample sizes for VAR and only marginally better elsewhere. The conclusion is more measured, but the framing overstates.\n\nThere's also a genuine technical ambiguity: Eq. 18 defines the Granger contribution C_{j,k} as a sum over hidden neurons of |phi_{j,k,i}|, where phi is a spline function, not a scalar. The paper defines an L1 norm for activation functions in Eq. 11, so a charitable reading is that Eq. 18 uses that norm, but the paper never says so. That needs to be explicit. And there's no code release, which makes it hard to check the ROC construction.\n\nNone of these are fatal to the idea. The method is coherent, the proximal sparsity step is a real contribution, and the synthetic experiments are a reasonable starting point. But the central comparative claim needs an equal-footing rerun: same data, same tuning budget, same hidden size for at least one configuration, and ideally code. I'd send this to a referee—it's the kind of paper where a careful revision with a controlled baseline would make it solid—but it isn't ready as is.\n\nFor your reading group, it's worth a slot if you want a concrete example of KANs applied to causal discovery with a methodological caveat to discuss. I wouldn't cite it in its current form; I'd wait for the revised version.","headline":"GC-KAN is a sensible combination of KANs and component-wise neural Granger causality, with a clean proximal sparsity trick that does produce exact zeros, but the paper's central claim that KANs outperform MLPs is not supported by the current evaluation—the cMLP baselines are borrowed from another paper under different conditions, and Eq. 18 is underspecified.","tokens_in":10295,"tokens_out":3377,"would_cite":false,"duration_ms":28374,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62M10","68T07"],"pacs":[],"model":"deepseek-v4-flash","headline":"Kolmogorov-Arnold networks, with learnable spline edge functions and a first-layer proximal threshold, can match or slightly beat multilayer perceptrons at detecting sparse Granger causal relationships in time series.","keywords":["Granger causality","Kolmogorov-Arnold Networks","nonlinear time series","sparsity-inducing regularization","proximal gradient","neural causal discovery","Lorenz-96","interpretable machine learning"],"falsifier":"Train a GC-KAN on the paper's VAR(1) data and recompute $C_{j,k}$ with two natural definitions of $|\\varphi|$, such as the $L^2$ norm over the training inputs and the $\\ell^1$ norm of the B-spline coefficients; if the two rankings of candidate parents disagree, the causal extraction rule is not well-defined.","tokens_in":9206,"feed_emoji":"📈","tokens_out":8325,"duration_ms":68006,"temperature":0.7,"pith_summary":"This paper argues that Kolmogorov-Arnold Networks (KANs), which place learnable spline functions on network edges, can serve as the engine for nonlinear Granger causality detection instead of the multilayer perceptrons used in current neural Granger causality models. It introduces GC-KAN, a framework that trains one small KAN per target time series with an L1-plus-entropy sparsity penalty and a proximal soft-threshold step on the first layer, so that lagged inputs that do not help predict the target are driven to exactly zero weight. On synthetic vector autoregressive data and on the chaotic Lorenz-96 system, GC-KAN matches the component-wise multilayer perceptron baseline and edges ahead at high sample sizes for VAR and at low sample sizes for Lorenz-96. The intended payoff is a parameter-efficient, interpretable way to discover which time series cause which others in high-dimensional nonlinear settings.","feed_headline":"KANs match or top MLPs on sparse Granger causality","feed_subtitle":"Proximal-trained spline networks find causal parents in VAR and Lorenz-96 with fewer parameters.","key_machinery":"The carrying object is the KAN's first edge layer, $\\Phi_0 = W_{\\mathrm{base}}\\sigma(z) + W_{\\mathrm{spline}}\\,\\mathrm{spline}(z)$, where each connection is a learnable B-spline function rather than a scalar weight. Causality is extracted from this layer by summing the magnitudes of the first-layer functions that map each lagged input to each hidden neuron, and the proximal update $w \\leftarrow \\operatorname{sign}(w)\\max(|w|-\\eta\\lambda_{\\mathrm{prox}},0)$ is applied only to $W_{\\mathrm{base}}$ and $W_{\\mathrm{spline}}$ so that weak functions become exactly zero. The L1 and entropy penalties on the whole layer encourage sparse and balanced use of the splines, and the deliberately small architectures (one or ten hidden neurons) keep the resulting causal map readable. The mechanism converts the question 'does series $j$ Granger-cause series $i$?' into 'does the corresponding first-layer spline contribution survive proximal thresholding?'","core_discovery":"The central claim is that replacing the scalar input weights of a component-wise neural Granger model with KAN's learnable spline functions, and adding a proximal operator that soft-thresholds only the first-layer functions, yields a Granger causality detector that is at least as accurate as the established MLP baseline and more directly interpretable. Concretely, the paper defines GC-KAN, in which each target series is modeled by a KAN fed with all lagged series, and after training the Granger contribution of lag $k$ of series $j$ is read off as $C_{j,k}=\\sum_{i=1}^{n_{\\text{hidden}}}|\\varphi_{j,k,i}|$. Because the proximal step forces irrelevant first-layer functions to exact zero, causal parents can be identified from the nonzero contributions without manual thresholding. In experiments, GC-KAN's AUROC is comparable to cMLP with hierarchical group lasso, with the largest reported margins on VAR(1) and VAR(2) at $T=1000$ and on Lorenz-96 with forcing $F=10$ at $T=250$.","pith_inferences":["The paper's contribution score assumes a well-defined magnitude for each spline function $\\varphi_{j,k,i}$, but no norm is specified; choosing different natural norms, such as the $L^2$ norm over inputs or the $\\ell^1$ norm of B-spline coefficients, could change the ranking of candidate causal parents.","A natural follow-up is to group lags of the same variable inside GC-KAN, mirroring the hierarchical group lasso, which would add automatic lag-order selection to the spline-based detector.","The authors' suggestion that KANs can fit symbolic functions implies a concrete next step: converting each surviving first-layer spline into an explicit symbolic expression, which would turn GC-KAN into a dynamical-law extractor rather than only a causal detector.","The reported advantages appear mainly in compact architectures, so an equal-parameter comparison, rather than equal-neuron comparison, would clarify whether the gain comes from spline flexibility or from model size."],"forward_implications":["GC-KAN with a single hidden neuron matches or beats cMLP with 100 hidden neurons on VAR data at $T=500$ and $T=1000$, so KAN-based detection can be much more parameter-efficient.","Because the proximal step zeros out irrelevant inputs, GC-KAN can produce a Granger causality matrix directly from the trained network, without a manual pruning threshold.","On Lorenz-96 with $F=10$ and $T=250$, GC-KAN slightly outperforms cMLP, suggesting spline activations help in low-sample nonlinear regimes.","If the pattern holds, KAN-based frameworks are a viable route for causal discovery in high-dimensional physical and economic time series."],"supporting_citations":[{"why":"Defines Granger causality, the predictive notion the paper operationalizes.","marker":"[8]"},{"why":"Introduces KANs and the L1/entropy pruning that GC-KAN adapts for sparsity.","marker":"[11]"},{"why":"Defines the cMLP/cLSTM neural Granger causality framework and provides the baseline results and synthetic settings GC-KAN is compared against.","marker":"[15]"},{"why":"Formulates the hierarchical group lasso penalty used by the cMLP baseline.","marker":"[13]"},{"why":"Specifies the Lorenz-96 chaotic system used as the nonlinear test bed.","marker":"[9]"},{"why":"Supplies the B-spline basis used in the KAN edge functions.","marker":"[7]"}],"fun_headline_variants":["GC-KAN: spline nets top MLPs on sparse Granger causality","Proximal KANs find causal parents without manual thresholding","KANs match or beat MLPs on sparse Granger discovery","Spline-based Granger detector reads off causal links directly","GC-KAN: fewer parameters, clearer causal picture than MLP"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that every first-layer spline function has a well-defined magnitude so that the contribution score $C_{j,k}$ in Eq.~18 can be computed; the paper never states how the magnitude of a spline function is measured.","fun_headline_variants_meta":{"raw":{"variants":["GC-KAN: spline nets top MLPs on sparse Granger causality","Proximal KANs find causal parents without manual thresholding","KANs match or beat MLPs on sparse Granger discovery","Spline-based Granger detector reads off causal links directly","GC-KAN: fewer parameters, clearer causal picture than MLP"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000222,"raw_usage":{"total_tokens":1475,"prompt_tokens":987,"completion_tokens":488,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":603,"completion_tokens_details":{"reasoning_tokens":397}},"tokens_in":603,"tokens_out":488,"duration_ms":4151,"temperature":1.0,"reasoning_tokens":397,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T11:28:18.561277+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train a GC-KAN on the paper's VAR(1) data and recompute $C_{j,k}$ with two natural definitions of $|\\varphi|$, such as the $L^2$ norm over the training inputs and the $\\ell^1$ norm of the B-spline coefficients; if the two rankings of candidate parents disagree, the causal extraction rule is not well-defined.","supporting_citations":[{"cited_title":"Nonlinear system identification: NARMAX methods in the time, frequency, and spatio- temporal domains","cited_arxiv_id":null,"evidence_quote":"Specifies the Lorenz-96 chaotic system used as the nonlinear test bed."},{"cited_title":"Multi- variate granger causality and generalized variance","cited_arxiv_id":null,"evidence_quote":"Supplies the B-spline basis used in the KAN edge functions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines Granger causality, the predictive notion the paper operationalizes."},{"cited_title":"Analyzing multiple nonlinear time series with extended granger causality","cited_arxiv_id":null,"evidence_quote":"Introduces KANs and the L1/entropy pruning that GC-KAN adapts for sparsity."},{"cited_title":"High dimensional forecasting via in- terpretable vector autoregression","cited_arxiv_id":null,"evidence_quote":"Formulates the hierarchical group lasso penalty used by the cMLP baseline."}],"review_version":1}