{"id":"02fa5dc5-17ba-4b43-9306-3218843a517f","arxiv_id":"2504.18833","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Kolmogorov-Arnold networks with a pretrain-prune-train-symbolize pipeline can rediscover known analytical solutions of the nonlinear Schrödinger equation and model intrapulse Raman scattering and supercontinuum generation in optical fibers with lower error than parameter-matched MLPs.","lead":"FiberKAN applies Kolmogorov-Arnold networks, a new type of neural network with learnable functions on connections, to rediscover known equations and model pulse propagation in optical fibers. The paper is a method demonstration: it shows KANs can recover analytical solutions of the nonlinear Schrödinger equation and beat equivalent-size MLPs on data-driven fiber simulations.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Self-steepening 'implicit discovery' is underdetermined: the network is given the target I as an input, so identity is a zero-error solution; the paper itself reports this failure mode.","rationale":"The reader's weakest_assumption is exactly the flaw I would stress: giving I as an input while predicting I makes the identity function a zero-loss solution, and Section IV-A admits that most SS failures are the identity shortcut. This is not a question of external consensus; the experiment is internally unable to identify the claimed implicit law. The explicit-soliton and IRS results are separate and plausible, so the paper should not be rejected outright, but the SS experiment should be rerun without target leakage or with an identifiability analysis. I therefore keep the reader's CONDITIONAL verdict. The absence of released code and data makes independent verification harder but is secondary. Concrete test: ablation of the I input and a derivative check on the learned mapping.","tokens_in":24705,"tokens_out":7675,"duration_ms":85567,"concrete_test":"Retrain the Section III-D MultKAN with the I input removed (inputs z,t; output I) under otherwise identical settings and report success rate and error over 100 seeds; if accuracy collapses relative to the 93% success rate, the original result depends on target leakage. Complementarily, after training the original model, evaluate the partial derivative ∂f/∂I at held-out points: the identity shortcut gives ≈1, whereas the claimed implicit equation gives a z- and t-dependent nontrivial derivative; if ∂f/∂I ≈ 1 over the domain, the learned mapping is effectively identity.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing weakness is the self-steepening experiment in Section III-D. The network inputs are (z, t, I) and the target is I, so the identity map f(z,t,I)=I is an exact solution of the supervised task with zero training and test error. The reported relation I=sech(t-3sIz) is also consistent with the data by construction, so error metrics cannot distinguish the alleged discovery from the trivial shortcut. This ambiguity is confirmed by the authors: Section IV-A states that 'in most failed cases, KANs discover the direct mapping relationship of I=I', and Table I sets lam_l1=0 in an attempt to avoid the identity solution. Because this is the only implicit-solution demonstration, the abstract's 'explicit, implicit, and non-analytical' discovery claim rests on an experiment in which the target is provided as an input. The explicit-soliton and IRS characterizations are not undermined by this issue, but the implicit-discovery subclaim is load-bearing for the paper's central narrative.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces FiberKAN, a KAN-based framework for 'scientific discovery and dynamic characterization' of nonlinear fiber-optic pulse propagation. For the explicit-solution cases (power attenuation, GVD, TOD, and the fundamental soliton), the authors generate datasets from the known analytical solutions, train MultKANs with a pretrain-prune-train-symbolize pipeline, and report recovery of the symbolic formulas with errors down to about 10^-11. For self-steepening, they attempt to discover the implicit intensity relation I(z,t)=sech(t-3sIz) by feeding I as an input feature. For intrapulse Raman scattering and supercontinuum generation, they train KANs and MLPs with comparable parameter counts and report lower maximum errors for the KAN. Additional sections evaluate success rates, computational cost, noise resistance, prior-knowledge embedding, hypothesis testing, transfer learning, and comparisons with PINNs and symbolic regression.","tokens_in":24887,"tokens_out":7404,"duration_ms":74301,"significance":"If the broad claim were fully supported, FiberKAN would be a useful demonstration that KANs can serve as interpretable surrogate models and symbolic-regression front-ends for fiber optics. The explicit-solution experiments are internally consistent, use held-out test losses, and the soliton recovery to 10^-11 is a clean positive result; the IRS statistical comparison (mean maximum error 0.0303 versus 0.0561 over 100 seeds) is a reasonable, if modest, evidence of a KAN advantage; and the computational-cost analysis is honest about KAN's slower training. However, the only implicit-solution experiment is underdetermined because the target intensity is provided as an input, so the central 'explicit, implicit, and non-analytical' claim is not currently supported. The 'discovery' demonstrations are also benchmark-style recoveries of formulas used to generate the data, which tempers the scientific-discovery framing. The manuscript does not provide code or data, limiting reproducibility.","major_comments":[{"comment":"The self-steepening 'implicit dynamics discovery' is underdetermined by the supervised task. The network receives I(z,t) as an input feature and is trained to output I(z,t), so the identity map f(z,t,I)=I is an exact zero-error solution on both training and test points. Removing the L1 regularization (Table I, lam_l1=0) does not suppress this solution; it only avoids penalizing non-identity structure, and Section IV-A explicitly reports that in most failed cases the KAN discovers exactly this I=I mapping. Because the data points satisfy I=sech(t-3sIz) by construction, the identity and the claimed implicit relation coincide on the data manifold, so the reported held-out error cannot distinguish the two. This is load-bearing: it is the only implicit-solution demonstration and the basis for the abstract's 'explicit, implicit, and non-analytical' taxonomy.","section":"Section III-D and Section IV-A, Table I"},{"comment":"The role of the symbolization step in the 'discovery' claim is underspecified. The manuscript states that each activation function is fitted to the 'closest' symbol from a candidate library and that coefficients are then fine-tuned, but it does not specify the candidate library, the similarity metric, or the selection criterion. Since the training data in Parts A-D are generated from the very formulas that are later 'discovered,' the reported 10^-11 accuracy (Section III-C) reflects, at least in part, the symbolic-regression postprocessor rather than the KAN alone. Reporting the pre-symbolization errors and the full symbolization protocol would clarify how much of the discovery is attributable to the KAN and would make the method reproducible.","section":"Section II-B and Section III-C"},{"comment":"The manuscript frames the method as discovering dynamics 'that have not yet been discovered and characterized' (Abstract; Section I), but every 'discovery' experiment in Parts A-D trains on data generated by exactly the analytical solution that is later recovered. This makes the experiments controlled recovery benchmarks, not discoveries of unknown dynamics. I recommend either adding a case with a genuinely unknown or numerically generated law, or explicitly reframing the claim as recovery/validation of known solutions.","section":"Section III (opening paragraph) and Section VI"}],"minor_comments":[{"comment":"The sentence 'the maximum error of KAN in the entire domain is almost one order of magnitude higher than that of MLP' appears to contradict Fig. 9(e) and (f) and the surrounding claim; please correct the typo and report the actual maximum errors.","section":"Section III-E, final paragraph"},{"comment":"There is a duplicated phrase: 'their performances remains constrained by the constrained by fundamental properties of MLPs' should read 'their performance remains constrained by fundamental properties of MLPs.'","section":"Section I, third paragraph"},{"comment":"The 'success rate' reported in Fig. 10 is never defined; please specify the criterion for a successful discovery (e.g., correct symbolic form with coefficient tolerance) and state how it is applied across the 100 trials.","section":"Section IV-A, Figure 10"},{"comment":"The comparison with PINN is qualitative ('several orders of magnitude higher', 'comparable accuracy'); please provide a direct numerical comparison under controlled settings or soften the claim.","section":"Section V-D"},{"comment":"No code or data availability statement is provided; since the method depends on many unspecified implementation details (spline initialization, pruning thresholds, symbol library), release of code would be important for reproducibility.","section":"General (reproducibility)"},{"comment":"The labels on the bars in Fig. 10 are difficult to read in the current reproduction; larger fonts or a table would help.","section":"Figure 10"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a competent application of KAN 2.0 to several known fiber-optics solutions. The main technical weakness is the self-steepening experiment, which cannot support the implicit-discovery claim as designed. If the authors can redesign that experiment (e.g., by not providing the target as an input, or by using an implicit-equation residual loss) or remove the implicit claim from the abstract, the rest of the paper is publishable after revision. The novelty is incremental relative to the KAN 2.0 framework and the authors' prior PINN work; the paper's value is primarily as a benchmark study."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, this is a genuinely early and fairly careful application of KANs/MultKANs to fiber optics: the authors recover several textbook NLSE solutions, report held-out errors, run 100-seed statistical tests, and compare against parameter-matched MLPs. Second, the paper's flagship 'implicit discovery' result for self-steepening is underdetermined, and the authors essentially admit it in Section IV-A. The network gets I as an input and I as the target, so identity is an exact solution; they disable L1 regularization to avoid it, and report that failed runs discover I=I. That means the abstract's 'explicit, implicit, non-analytical' trio overstates what is demonstrated.\n\nThe explicit-solution demos (attenuation, GVD, TOD, soliton) are consistent and plausible. Recovering sech(t)exp(iz/2) to about 1e-11 after symbolization is a nice result, and the 93% success rate for SS with 5000 points at least shows the pipeline can often find the intended relation, even if that experiment cannot distinguish it from identity. The IRS characterization with a 608-parameter KAN versus a 618-parameter MLP (mean max errors 0.0303 vs 0.0561) is a fair, if modest, comparison. The computational cost analysis is rough but honest about KAN being slower to train and about inference being comparable.\n\nThe self-steepening case is the load-bearing weakness. Since I is both input and output, the reported relation I = sech(t - 3sIz) is also consistent with the data by construction; no error metric separates discovery from shortcut. Fixing this requires either training without I as input (as in the other cases) or validating on an implicit relation where I is not trivially recoverable. At minimum, the abstract and conclusion should stop claiming 'implicit' discovery until a non-identity formulation is shown.\n\nThere is also a contradictory sentence in Section III-E: the text says the maximum error of KAN is 'almost one order of magnitude higher' than MLP, then uses that to claim KAN is better. Probably a typo for 'lower', but as written it undermines the supercontinuum comparison. No code or data is released, and the 'discovery' is benchmark-style fitting to known formulas, so the novelty is in the domain application, not in new physics.\n\nWho benefits? Researchers in AI-for-optics looking for a concrete KAN baseline and a worked example of the pretrain-prune-train-symbolize pipeline. It deserves a serious referee, but I would send it back with a request for code and data and a fix or reframing of the self-steepening claim. With those changes it could be a solid subfield contribution.","headline":"A competent early KAN-for-fiber-optics paper whose explicit-solution results are solid but whose 'implicit discovery' claim is undercut by feeding the target as an input.","tokens_in":25452,"tokens_out":2439,"would_cite":true,"duration_ms":24701,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Kolmogorov-Arnold networks can rediscover and characterize solutions of the nonlinear Schrödinger equation governing fiber optics, including implicit and non-analytic cases, with accuracy exceeding MLPs at the same parameter count.","keywords":["Kolmogorov-Arnold networks","nonlinear fiber optics","nonlinear Schrödinger equation","scientific discovery","symbolic regression","self-steepening","intrapulse Raman scattering","supercontinuum generation"],"falsifier":"Re-run the Section III-D self-steepening experiment and inspect the post-pruning network: if the edge from the input I to the output I survives with a weight near 1 and the other edges account for only a small correction, or if predictions outside the training range match the identity mapping rather than sech(t-3sIz), then the implicit-discovery claim is falsified.","tokens_in":24487,"feed_emoji":"⚛️","tokens_out":11094,"duration_ms":97285,"temperature":0.7,"pith_summary":"The paper proposes FiberKAN, a Kolmogorov-Arnold Network framework for scientific discovery in nonlinear fiber optics. It argues that replacing MLPs' fixed node activations with learnable edge activations lets a small, interpretable network recover explicit analytical solutions (power attenuation, dispersion, solitons), an implicit self-steepening solution, and characterize non-analytical intrapulse Raman scattering and supercontinuum dynamics. Across these tasks the KANs match or beat MLPs of comparable trainable-parameter count, and after symbolization the soliton solution is recovered to errors around 1e-11. The claim matters because it points to a route toward automated extraction of physical laws from optical data, not just black-box fitting.","feed_headline":"A 608-parameter KAN rediscovers the optical soliton","feed_subtitle":"A transparent network beats larger MLPs at extracting soliton, self-steepening, and Raman-scattering dynamics.","key_machinery":"The central object is the Kolmogorov-Arnold Network (KAN) and its multiplicative variant MultKAN, which implement the Kolmogorov-Arnold representation theorem by placing learnable univariate activation functions (B-splines) on network edges instead of fixed nonlinearities on nodes. In FiberKAN this machinery is driven through a four-step cycle—pretraining, pruning, training, symbolization—during which redundant edges and nodes are eliminated, the remaining splines are visualized and fitted to elementary functions, and the symbolic coefficients are fine-tuned to machine precision. The multiplication nodes of MultKAN are what let the network represent separable products such as sech(ω) cos(β_k ω^k z / k!) directly, and the absence of node nonlinearities is what makes each edge interpretable in physical terms.","core_discovery":"The central claim is that Kolmogorov-Arnold Networks, because their activation functions live on edges and are learnable splines, are capable of discovering and characterizing the dynamics of nonlinear fiber-optic systems described by the nonlinear Schrödinger equation. In the explicit-solution cases, a two-layer MultKAN with 608 parameters rediscovers the fundamental soliton h(z,t)=sech(t)exp(iz/2), and after symbolization the discovered solution matches the analytical one to errors on the order of 1e-11; the same procedure recovers power attenuation, GVD, and TOD laws. For the self-steepening effect, the network identifies the implicit relation I(z,t)=f(t-3sIz) by using I itself as an input feature. For intrapulse Raman scattering, which lacks an analytical pulse-like solution, the KAN reaches a mean maximum error of 0.0303 against 0.0561 for an MLP of 618 parameters, and in supercontinuum generation it learns high-frequency components that the equivalent-scale MLP essentially misses.","pith_inferences":["Beyond the paper, the same pretrain-prune-train-symbolize pipeline could be applied to other envelope equations (coupled-mode, Gross-Pitaevskii, or Lugiato-Lefever) whenever the target dynamics admit decompositions into a few univariate splines; the main obstacle will be the absence of known symbolic targets to validate against.","The self-steepening identity-path failure is a general caution for implicit-law discovery: when an output variable is also an input, one should penalize or forbid the copy map either architecturally or in the loss, otherwise a low test loss can reflect the trivial mapping rather than a discovered law.","If the KAN advantage at equal parameter count persists outside these benchmarks, the framework offers a practical route to data-efficient optical channel modeling, because the symbolic edge functions can be reused and lightly retrained when fiber type or wavelength changes."],"forward_implications":["FiberKAN can turn a few thousand sampled pulse-propagation points into closed-form symbolic laws (e.g., the soliton solution) without a candidate library, because each spline is individually symbolized and fine-tuned.","For effects with no analytic solution, such as intrapulse Raman scattering, KAN offers an interpretable black-box model with lower error and lower variance than an MLP of comparable parameter count.","Trained KAN structures transfer between similar dispersion regimes: the GVD model for u(z,ω) is adapted to TOD dynamics in about 100 iterations with only one activation function changing.","In supercontinuum generation, KANs preserve high-frequency spectral components that MLPs of similar size fail to reproduce, implying better suitability for broadband nonlinear dynamics."],"supporting_citations":[{"why":"This reference supplies the nonlinear Schrödinger equation and the physical effects (attenuation, GVD, TOD, SPM, SS, IRS) that define the target dynamics.","marker":"[11]"},{"why":"This reference introduces the KAN architecture with learnable spline activations on edges, the structure FiberKAN builds upon.","marker":"[29]"},{"why":"This reference introduces MultKAN and its multiplication nodes, which FiberKAN uses to represent separable products in the discovered solutions.","marker":"[42]"},{"why":"This reference provides the PINN-based fiber-optic results that FiberKAN compares against in accuracy and parameter efficiency.","marker":"[19]"},{"why":"This reference states the Kolmogorov-Arnold theorem that justifies representing multivariate dynamics as superpositions of univariate functions.","marker":"[30]"},{"why":"This reference supports the claim that intrapulse Raman scattering produces a non-Hamiltonian perturbation without an analytical pulse-like solution.","marker":"[46]"},{"why":"This reference defines supercontinuum generation, the high-frequency benchmark where KAN's learning advantage over MLP is demonstrated.","marker":"[47]"},{"why":"This reference gives error bounds for deep networks using Kolmogorov-Arnold superposition, cited as theoretical grounding for KAN approximation.","marker":"[39]"}],"fun_headline_variants":["KAN rediscovers optical soliton with 608 parameters","Transparent KAN beats MLPs on fiber-optic dynamics","KAN finds soliton, self-steepening, Raman scattering","Soliton discovery: KAN outperforms larger MLPs"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The self-steepening discovery assumes that when the output intensity is also given as input, the network genuinely learns the nonlinear relation I(z,t)=sech(t-3sIz) rather than the simpler route I_out=I_in, because the training intentionally removes the regularization that would push the network away from that trivial copy; if the low held-out error actually comes from the identity mapping plus a small correction, the implicit-discovery claim collapses.","fun_headline_variants_meta":{"raw":{"variants":["KAN rediscovers optical soliton with 608 parameters","Transparent KAN beats MLPs on fiber-optic dynamics","KAN finds soliton, self-steepening, Raman scattering","Soliton discovery: KAN outperforms larger MLPs"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000597,"raw_usage":{"total_tokens":2843,"prompt_tokens":1045,"completion_tokens":1798,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":661,"completion_tokens_details":{"reasoning_tokens":1726}},"tokens_in":661,"tokens_out":1798,"duration_ms":13626,"temperature":1.0,"reasoning_tokens":1726,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:08:27.699076+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the Section III-D self-steepening experiment and inspect the post-pruning network: if the edge from the input I to the output I survives with a weight near 1 and the other edges account for only a small correction, or if predictions outside the training range match the identity mapping rather than sech(t-3sIz), then the implicit-discovery claim is falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference supplies the nonlinear Schrödinger equation and the physical effects (attenuation, GVD, TOD, SPM, SS, IRS) that define the target dynamics."},{"cited_title":"Physics- Informed Neural Network for Nonlinear Dynamics in Fiber Optics,","cited_arxiv_id":null,"evidence_quote":"This reference provides the PINN-based fiber-optic results that FiberKAN compares against in accuracy and parameter efficiency."},{"cited_title":"On the representation of continuous functions of several variables as superpositions of continuous functions of a smaller number of variables,","cited_arxiv_id":null,"evidence_quote":"This reference states the Kolmogorov-Arnold theorem that justifies representing multivariate dynamics as superpositions of univariate functions."},{"cited_title":"Soliton robustness in optical fibers,","cited_arxiv_id":null,"evidence_quote":"This reference supports the claim that intrapulse Raman scattering produces a non-Hamiltonian perturbation without an analytical pulse-like solution."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference defines supercontinuum generation, the high-frequency benchmark where KAN's learning advantage over MLP is demonstrated."},{"cited_title":"Error bounds for deep ReLU networks using the Kolmogorov –Arnold superposition theorem,","cited_arxiv_id":null,"evidence_quote":"This reference gives error bounds for deep networks using Kolmogorov-Arnold superposition, cited as theoretical grounding for KAN approximation."}],"review_version":1}