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REVIEW 2 major objections 4 minor 41 references

This paper argues that swapping fixed-activation MLP token mixers for Taylor-polynomial KAN token mixers improves spatial and temporal traffic forecasting, with the strongest gains on traffic-flow benchmarks.

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2026-08-02 06:24 UTC pith:CZWHAHBJ

load-bearing objection A competently built, honestly scoped KAN-for-traffic architecture paper whose central 'approximator choice matters' claim is weaker than the abstract suggests because the key ablation is not parameter-matched. the 2 major comments →

arxiv 2607.13108 v1 pith:CZWHAHBJ submitted 2026-07-14 cs.LG cs.AI

STKAN: Kolmogorov-Arnold Networks for Spatio-Temporal Forecasting

Sicong Lai , Yuehong Hu , Siru Zhong , Si Qiao , Yuxuan Liang , Guangyin Jin This is my paper
classification cs.LG cs.AI
keywords spatio-temporal forecastingtraffic forecastingKolmogorov-Arnold networksTaylorKANtoken mixingsoft node groupingattentionfunction approximators
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper asks whether the choice of nonlinear function approximator, not just the architectural skeleton, determines forecasting quality. It introduces STKAN, which uses Taylor-polynomial Kolmogorov-Arnold layers for spatial and temporal token mixing, a learnable soft node-group assignment, and attention for long-range interactions. Across five traffic benchmarks, STKAN achieves best average MAE and RMSE on three datasets, ties the strongest baseline on a fourth, and remains competitive on a fifth. An ablation replacing the TaylorKAN mixers with MLPs raises errors on the tested datasets, which the authors take as evidence that approximator design is a useful complement to architectural design.

Core claim

The central claim is that TaylorKAN token mixing—learnable univariate polynomial functions, not fixed activations—carries a performance benefit in spatio-temporal forecasting when embedded in spatial and temporal mixers. The authors construct STKAN with a soft assignment matrix that aggregates sensors into macro-level spatial groups, a spatial TaylorKAN mixer over groups, a temporal TaylorKAN mixer over the compressed time axis, and spatial-temporal attention on top. On the evaluated traffic-flow benchmarks, STKAN posts the best average MAE and RMSE on PEMS04, PEMS07, and PEMS08, ties the top baseline in average MAE on PEMS-BAY, and is competitive but not best on METR-LA. The ablation replac

What carries the argument

The load-bearing object is the TaylorKAN layer: a Taylor-inspired polynomial basis where each connection learns its own univariate function phi(x)=sum_{p,r} theta_{q,p,r} x^r + b (eq. 7), with coefficients optimized directly rather than set as analytic derivatives. This replaces the fixed activation of an MLP with dataset-tuned nonlinearities. It is embedded in residual token-mixing blocks along spatial and temporal dimensions, with soft node-group assignment (eqs. 3–4) compressing the N nodes into G groups and permutation operators P_s and P_t aligning the mixed dimension. The learnable group matrix lets the network discover macro-level spatial units, while the TaylorKAN mixers provide the

Load-bearing premise

The central claim rests on the assumption that the MLP variant in the ablation is a fair control; if the MLP token mixers differ in parameter count, capacity, or tuning, the observed gain cannot be attributed to the KAN parameterization.

What would settle it

Run a parameter-matched and hyperparameter-tuned comparison: replace the TaylorKAN layers with MLPs of equal parameter count and train both under the same budget. If the MLP variant matches or beats STKAN on the same benchmarks, the central claim that approximator choice matters would be falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Function-approximator design becomes a third axis, alongside spatial and temporal architecture, in spatio-temporal modeling.
  • TaylorKAN mixers can be dropped into existing mixer-style forecasting architectures without relying on a predefined graph.
  • On traffic-flow benchmarks, soft grouping plus KAN mixing yields best average errors among the compared baselines on three datasets.
  • Ablations show spatial KAN mixing and temporal KAN mixing provide complementary contributions; removing either hurts performance.
  • Attention components further refine the KAN-based results, but do not dominate them, on the tested datasets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper's own caveat that no parameter-matched comparison was run means the most direct interpretation—KAN parameterization, not capacity—is not yet established; a parameter-matched ablation would settle it.
  • If TaylorKAN's benefit survives parameter-matching, the polynomial-basis idea could transfer to other sequence-mixing tasks such as weather or energy forecasting where nonlinear interactions are important.
  • The learned soft grouping appears to capture spatially contiguous corridors on one benchmark, which could become a cheap graph-learning alternative, but the paper only presents it as qualitative evidence.
  • The non-monotonic sensitivity to the number of groups suggests group width is a dataset-dependent hyperparameter; a principled prior relating group count to sensor network topology could be worth testing.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper proposes STKAN, a spatio-temporal forecasting architecture that replaces MLP token mixers with Taylor-polynomial KAN layers in both spatial and temporal dimensions. The model also introduces a learnable soft node-group assignment mechanism, applies group-wise spatial mixing, and augments the KAN mixers with spatial/temporal self-attention. Experiments on five traffic benchmarks (PEMS04/07/08, PEMS-BAY, METR-LA) report competitive or best average MAE/RMSE/MAPE on the three PEMS datasets, a tie with STAEformer on PEMS-BAY, and a loss on METR-LA. The authors claim that the choice of nonlinear function approximator can complement architectural design, based primarily on an ablation that replaces TaylorKAN token mixers with MLP layers. The paper explicitly limits its conclusions to the evaluated configurations and lists parameter-matched comparisons as future work.

Significance. If the results are reliable, STKAN would be a modest but useful addition to spatio-temporal forecasting, showing that token-mixing parameterization (KAN-style polynomial functions) can improve over standard MLP mixers within a fixed architecture. The paper's strengths are its unified evaluation through the BasicTS framework, the inclusion of eleven baselines, the honest caveats about single-run results and non-parameter-matched ablations, and the study of the grouping hyperparameter. The novelty is incremental: the architecture is a combination of known components (soft grouping, KAN layers, attention). The broader scientific claim about function-approximator design is suggestive but not established by the current evidence, because the KAN-versus-MLP ablation is not parameter-matched and no statistical significance is reported.

major comments (2)
  1. [§5.3, Eq. (7)] The KAN-vs-MLP ablation is not parameter-matched. As written in Eq. (7), a TaylorKAN layer with C inputs, K+1 polynomial terms, and one bias has C(K+1)+1 parameters per output, whereas a single linear layer has C+1. For K≥2 this is a factor of at least three in the token-mixing parameters. The observed MAE/RMSE gap on PEMS04 and PEMS08 may therefore be a capacity effect, not evidence that the Taylor-polynomial form itself helps. Since this ablation is the only direct support for the abstract's suggestion that 'the design of nonlinear function approximators can serve as a useful complement,' the paper should either add a parameter-matched MLP baseline (e.g., increasing the MLP width/depth to match parameter count) or explicitly restrict the abstract and conclusion claims to the tested configuration. The manuscript already acknowledges this in Sections 5.3 and 6, but the abstract's wording
  2. [§5.2, Table 2 and Table 3] All reported metrics are single-run without error bars or significance tests. The differences against strong baselines are small (e.g., PEMS04 average MAE 18.09 vs. 18.19 for STAEformer; PEMS-BAY ties at 1.54; METR-LA loses). Without multiple seeds or a statistical test, claims of 'best' and 'better' are not robust. The authors' textual caution is appropriate, but the tables and abstract still make comparative claims. Please provide mean±std over at least three independent runs, or explicitly state that no statistical significance is claimed and remove bolding where differences are within expected noise. This is load-bearing for the empirical conclusions of the paper.
minor comments (4)
  1. [§4.3, Eq. (5)] The wording 'The transmission from the j-th neuron in layer ℓ+1 to all neurons in layer ℓ' is reversed: Eq. (5) transmits from all neurons in layer ℓ to the j-th neuron of layer ℓ+1. Please correct.
  2. [§5.1] The text says 'we use the traffic flow of the last 12 time steps,' but METR-LA is a traffic speed dataset. Rephrase to 'traffic measurements' or specify the variable per dataset.
  3. [§5.3, Figure 3] Figure 3 is described qualitatively ('increases the forecasting errors') without reporting numeric values. Include a small table or numeric annotations for the KAN ablation so readers can judge the magnitude of the differences.
  4. [General] No code availability statement is provided. Given the competitive results and the need for reproducibility in this area, a public implementation (or at least a detailed configuration file) should be supplied.

Circularity Check

0 steps flagged

No circularity: the paper's results are empirical benchmark comparisons, its KAN parameters are learned model weights rather than fitted constants of the claim, and the main caveat about non-parameter-matched ablations is explicitly disclosed rather than hidden.

full rationale

The paper contains no derivation chain in which a predicted quantity is equivalent by construction to an input or fitted parameter. The TaylorKAN layer in Eq. (7) uses freely learnable polynomial coefficients: the paper states, 'The coefficients θ_{q,p,r} are optimized directly and are not constrained to equal the analytical derivatives of an underlying function.' The Taylor expansion in Eq. (6) is only motivation for a polynomial basis, not a source of fitted targets. The forecasting outputs in Table 2 are ordinary held-out test-set evaluations of a trained network; no parameter is fitted to the reported metrics and then renamed as a prediction. The central conceptual claim—that nonlinear function-approximator design can complement architectural design—is supported by the ablation in Section 5.3, but the paper explicitly limits that claim: 'These observations are specific to the evaluated model configurations and should not be interpreted as establishing the general advantage of KANs over all parameter-matched MLP alternatives.' Section 6 further defers 'parameter-matched comparisons' to future work. That is an acknowledged control-validity limitation, not a circular step. The only self-citations are background survey references [16,19] and the BasicTS benchmarking framework [27], which is an external codebase used to run baselines; none of these supplies an unverified load-bearing premise. There is no imported uniqueness theorem and no ansatz smuggled in via citation. The paper is self-contained as an empirical architecture study, and its claims are appropriately hedged.

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 0 invented entities

The paper introduces no new theory, entity, or fitted physical constant: the ledger contains only architecture and hyperparameter choices. The honest count is that one of them (G) is explicitly tuned per dataset, while several others (w, s, K, C, d_h, depth) are not reported at all. The axioms are standard: KAT motivation (which the paper itself notes is not a performance guarantee), the standard 12-step traffic setup, and a sequential decomposition that is selected but never compared against alternatives.

free parameters (4)
  • number of spatial groups G = 16 (PEMS04), 20 (PEMS07)
    Selected by grid search per dataset (Table 4); the best value varies with dataset and is not derived. The paper is honest about this, but G is a hand-chosen tuning knob that affects results.
  • PatchConv window w and stride s = not stated
    Patch-extraction hyperparameters in Eq. (2) are never given values in the paper, so re-implementation requires guessing.
  • TaylorKAN polynomial order K and channel count C = not stated
    The core KAN layer in Eq. (7) is defined with K and C but neither is specified anywhere in the manuscript.
  • Embedding and network dimensions (d_f, d_s, d_tod, d_dow, d_h) and number of blocks = not stated
    Architecture sizes are unreported; needed for any faithful re-implementation.
axioms (3)
  • standard math The Kolmogorov-Arnold representation theorem motivates finite KAN layers as a useful parameterization
    Invoked in Section 2.2; the paper correctly notes the theorem does not imply empirical superiority over MLPs, so the axiom is only motivational.
  • domain assumption Traffic flow/speed over the next 12 five-minute steps is predictable from the last 12 steps plus time-of-day and day-of-week embeddings
    Standard setup inherited from the benchmarks (Section 3, Section 4.1); not derived or validated within the paper.
  • domain assumption A sequential spatial-then-temporal decomposition (group mixing, then temporal mixing, then attention) is a sufficient inductive structure
    The architecture in Sections 4.3-4.4 is chosen, not derived; alternative orderings or joint mixing are never compared, so the decomposition is an assumption about the problem structure.

pith-pipeline@v1.3.0-alltime-deepseek · 12379 in / 16062 out tokens · 145478 ms · 2026-08-02T06:24:22.868197+00:00 · methodology

0 comments
read the original abstract

Real-world traffic data exhibit heterogeneous spatial correlations and nonlinear temporal dynamics, posing substantial challenges for accurate spatio-temporal forecasting. Existing approaches have developed increasingly sophisticated graph, attention, and decomposition architectures, while the influence of the underlying nonlinear function approximator has received comparatively less attention. In this work, we propose STKAN, a spatio-temporal forecasting architecture that introduces Taylor-polynomial Kolmogorov--Arnold Network modules into spatial and temporal token mixing. STKAN first constructs high-level spatial representations through a learnable soft node-group assignment mechanism, applies group-wise spatial mixing, and subsequently models temporal dependencies over the compressed sequence. Spatial and temporal self-attention layers are further employed to capture long-range interactions. Experiments on five traffic forecasting benchmarks show that STKAN achieves competitive performance and performs better than the evaluated MLP-based variant in the tested settings. These results suggest that the design of nonlinear function approximators can serve as a useful complement to architectural design in spatio-temporal forecasting.

Figures

Figures reproduced from arXiv: 2607.13108 by Guangyin Jin, Sicong Lai, Si Qiao, Siru Zhong, Yuehong Hu, Yuxuan Liang.

Figure 1
Figure 1. Figure 1: Illustration of different spatio-temporal models. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Overview of our proposed STKAN framework. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: KAN modules ablation on PEMS04 and PEMS08. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Adaptive grouping matrices visualization on PEMS [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

discussion (0)

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Reference graph

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