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REVIEW 5 major objections 6 minor 29 references

QuadKAN: KAN-Enhanced Quadruped Motion Control via End-to-End Reinforcement Learning

T0 review · 5 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Replacing the MLP encoders and fusion heads of a vision-guided quadruped policy with spline-parameterized KAN layers yields a policy that earns higher reward, collides less, and generalizes to unseen obstacles in simulation.

desk verdict Plausible and novel architecture, but the headline KAN advantage is not yet secure: the key MLP comparison may be confounded, and the collision reduction is under-powered. read the letter →

arxiv 2508.19153 v2 pith:PKGG3W6W submitted 2025-08-26 cs.RO cs.AIcs.CVcs.SYeess.IVeess.SY

Yinuo Wang , Gavin Tao This is my paper
classification cs.ROcs.AIcs.CVcs.SYeess.IVeess.SY
keywords QuadrupedalRobotsVision-drivenLocomotionReinforcementLearningMulti-modalFusionEnd-to-endPolicyKolmogorov-ArnoldNetworksSplineParameterizationDomainRandomization
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 the function class of a locomotion policy matters: replacing the unstructured multilayer perceptron regressors used in current vision-guided quadruped pipelines with spline-parameterized Kolmogorov-Arnold Network (KAN) layers gives the policy an inductive bias that matches the piecewise-smooth structure of gait. QuadKAN uses a KAN spline encoder for proprioception and a KAN spline fusion head for proprioception-plus-depth inputs, trained end-to-end with PPO under multi-modal delay randomization. On the trained thin-obstacle terrain it reaches an episode return of 874.37 with 15.23 collisions, versus 794.30 and 63.27 for the best MLP fusion baseline, and it generalizes better to unseen static- and dynamic-obstacle terrains. If the claim holds, spline-structured policies are a simple, interpretable alternative to unstructured regressors for reliable, foresighted legged control.

What carries the argument

The key machinery is the B-spline-parameterized KAN layer: each unit projects the input to a scalar with a learnable vector and bias, expands that scalar on a fixed bank of B-spline basis functions, and combines the basis coefficients with learnable weights before a smooth nonlinearity. Because the bases have local support, the resulting function is piecewise-smooth and locally controlled, matching the phase structure of gait; curvature and Jacobian/Lipschitz regularizers keep the policy smooth and low-jitter. The same spline construction serves as the proprioceptive encoder and as an attention-free fusion head that pools proprioceptive and vision tokens, keeping complexity linear in token c

What would settle it

On the Thin Obstacle terrain, run the MLP fusion head with a width sweep (for example hidden widths 64, 256, 1024, 2048) under the same PPO budget and record return and collisions; if any MLP width reaches or beats QuadKAN's 874.37 return with 15.23 collisions, the spline inductive bias is not the deciding factor.

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Extended reading notes

Core claim

The paper's central claim is that the spline parameterization itself, not merely additional parameters or training effort, is what lifts performance. KAN layers implement learnable one-dimensional functions as B-spline basis expansions with local support; using them in the proprioceptive encoder and the cross-modal fusion head aligns the state-to-action mapping with the piecewise-smooth nature of gait—smooth within a contact phase, sharp at foot-strike and lift-off. Trained end-to-end with PPO and with multi-modal delay randomization to mimic real sensor asynchrony, QuadKAN beats unstructured MLP fusion on return and collision avoidance across all three simulated terrains. On the trained thi

Load-bearing premise

The load-bearing premise is that the MLP baselines get parameter counts and training budgets comparable to QuadKAN's; Section 5.1 promises this, but no parameter counts or runtimes are reported, so if the MLPs are smaller or under-trained the gap could be capacity rather than spline structure.

Editorial extensions

If this is right

  • On the trained Thin Obstacle terrain, replacing MLP fusion heads with the KAN spline head increases episode return by about 10% (874.37 vs 794.30) and cuts obstacle collisions by about 76% (15.23 vs 63.27) at comparable distance.
  • Zero-shot on the unseen static rugged-obstacle terrain, the spline policy keeps its advantage: higher return, about 44% fewer collisions, and nearly equal distance against the MLP fusion baseline.
  • On the unseen dynamic-obstacle terrain, the gap widens: QuadKAN's return rises from 105.70 to 261.52 and distance from 12.60 m to 17.77 m relative to the MLP fusion baseline.
  • Unimodal depth-only policies, whether MLP or KAN, nearly collapse in these environments, confirming that proprioception and vision carry complementary information.
  • KAN policies converge faster and show lower cross-seed variance (coefficient of variation 0.094 vs 0.105 for the MLP fusion policy), which the paper reads as training stability under PPO.

Reading between the lines

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

  • An implication the authors leave implicit: if the spline bias is responsible for the gains, the same KAN encoder/fusion recipe should transfer to other contact-rich or periodic gaits such as biped walking, hopping, or stair climbing; zero-shot transfer on those simulators would test this.
  • A testable extension: vary the curvature and Jacobian regularizer weights to see whether the reported heavier-tailed, more localized spline weights predict lower action jitter and fewer collisions, as the interpretability analysis suggests.
  • The attention-free design opens a scaling path the paper does not benchmark: more vision tokens or higher-resolution depth could be fused at linear cost, exactly where transformer-based fusion becomes costly.
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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

5 major / 6 minor

Summary. The paper proposes QuadKAN, a vision-guided quadruped locomotion policy in which the proprioceptive encoder and the cross-modal fusion head are parameterized by Kolmogorov–Arnold Networks (KANs) with B-spline bases, replacing standard MLPs. The method is trained end-to-end with PPO under Multi-Modal Delay Randomization (MMDR). The authors report evaluations in PyBullet on a trained Thin Obstacle terrain and two unseen terrains (static and dynamic obstacles with rugged ground), comparing QuadKAN against MLP and unimodal baselines on return, collision times, and distance traveled. The central claim is that spline-parameterized KAN policies outperform unstructured MLP policies, with headline numbers such as a 10.1% return gain and 75.9% collision reduction on the trained terrain (Table 4).

Significance. If the reported gains were established, the paper would provide evidence that a structured, spline-based function class improves sample efficiency, safety, and interpretability in vision-guided quadruped control, an area where MLP policies are standard. The idea of using KANs in a cross-modal locomotion policy is timely and the attention-free fusion design is interesting. However, the evidence is not yet convincing: the MLP baseline is not shown to be matched in capacity or runtime; several headline differences are statistically indistinguishable from noise; the ablation does not isolate the KAN encoder from the KAN fusion head; and claimed jitter/energy improvements are not directly measured. The paper also does not currently provide code or a complete set of hyperparameters, limiting reproducibility. With additional careful experiments and reporting, the manuscript could be a useful contribution.

major comments (5)
  1. [§5.1, §5.2, Table 4] RQ2 explicitly requires comparison 'at matched parameter count and runtime,' but no parameter counts, model sizes, or inference runtimes are reported for the MLP Proprio-Vision baseline or any other baseline. Figure 9 gives parameter counts for KAN variants (2.63M vs. 2.22M) but not for the MLP baseline. The observed 10.1% return and 75.9% collision differences could therefore be due to capacity, training dynamics, or runtime differences rather than the spline inductive bias. The central claim is not secure without reporting these statistics and, ideally, a matched-capacity MLP baseline.
  2. [§5.1, Baselines and Variants] The text states that all agents 'share the same proprioceptive and depth encoders with a matched token width,' but QuadKAN is described as having a 'KAN-based proprioceptive encoder.' If the MLP Proprio-Vision baseline uses the same KAN encoder, then Table 4 only tests the KAN fusion head against an MLP fusion head, providing no evidence for the claimed encoder-level benefit. If it uses an MLP encoder, then the encoders are not shared and the statement is false. This inconsistency must be resolved, and ablated variants (e.g., KAN encoder + MLP fusion and MLP encoder + KAN fusion) are needed to separate the two contributions.
  3. [§5.2, Tables 4 and 5] No statistical significance tests or confidence intervals are reported anywhere. For the flagship collision claim on Thin Obstacle, QuadKAN's 15.23±20.69 vs. MLP Proprio-Vision's 63.27±86.91 (n=10) gives Welch t≈1.7, p≈0.12, so the 75.9% collision reduction is not established. In the dynamic-obstacle generalization (Table 5), the return difference (261.52±371.47 vs. 105.70±475.62) has very large overlap and is not significant; the static-obstacle return difference (787.98±191.89 vs. 745.26±205.93) is also far from significant (t≈0.5). The paper's claim of 'consistently higher returns' and 'fewer collisions' across terrains is therefore overstated. Report per-metric paired bootstrap intervals or equivalent tests for every comparison.
  4. [§3.2, Eq. (9), §5.3] The spline curvature and Jacobian regularizers in Eq. (9) are explicitly designed to smooth the policy output, yet the paper claims 'reduced action jitter and energy' without reporting any jitter, torque, or energy metric. The return includes a small energy penalty (Eq. 26), but a −0.005·‖τ‖² term cannot substantiate a general energy claim. Add direct measurements of action smoothness (e.g., action-rate or jerk) and energy consumption for all compared methods, ideally with the regularizers ablated.
  5. [Table 1 and §4.2] Several hyperparameters that are load-bearing for the method are missing. The spline degree q and knot vector Ψ in Eq. (8) are not specified; the table only gives 'b=8' bases per unit. The regularization strengths λ_c, λ_L, and β_spline in Eq. (9)/(20) are not reported, despite being part of the proposed loss. The visual patch size P is also not given. Without these values, the experiments cannot be reproduced and the role of the regularizers in the reported gains cannot be assessed.
minor comments (6)
  1. [§5.3] Typo: 'Albation Studies' should be 'Ablation Studies.'
  2. [§5.5] The text contains malformed percentages '− − 8.4%' and '− − 8.7%' in the Dynamic Obstacle paragraph; these appear to be arithmetic errors or typos and should be corrected.
  3. [§5.1, Collision metric] The collision count is accumulated until 'three evaluation episodes complete or the robot falls,' and episodes with no obstacle interaction are excluded. This metric conflates fall timing with collision rate and may make collision counts non-comparable across methods with different fall rates. Clarify the evaluation protocol and consider reporting per-episode collision counts over a fixed number of episodes.
  4. [§4.1, Repository] The paper states both 'A repository is hosted at https://github.com/allen-quad-robot/quadkan' and 'to be made available upon acceptance.' This is contradictory; code access is important for reproducibility.
  5. [§2 and §5.2] The baselines are internal variants (MLP/Proprio/KAN), not actual published state-of-the-art locomotion policies. The abstract and introduction use 'state-of-the-art (SOTA) baselines,' which is misleading. Either compare against published vision-guided locomotion methods or rephrase.
  6. [§3.2, Eq. (8)] Define the B-spline basis functions B_m, the degree q, and the number of bases M precisely; the current notation ('b=8' in Table 1) is insufficient to reproduce the architecture.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: QuadKAN's central claim is an empirical KAN-vs-MLP comparison, not a derived prediction; a minor same-author citation and an unverified matched-capacity assertion do not make the derivation circular.

full rationale

Walking the derivation chain: Section 3 defines the spline-KAN encoder and fusion head; Section 4 fixes PPO and MMDR; Section 5 compares against MLP baselines. No equation uses the target result as an input. The spline curvature/Jacobian penalties (Eq. 9a-9c, folded into Eq. 20) explicitly target smooth, low-jitter actuation, so any jitter reduction would be partly by construction; however, the paper reports no direct jitter metric and the central claims about return and collisions are not derived from these penalties. Reference [5] (Locomamba) is by the same authors but only supports a general statement about vision, and is not load-bearing; MMDR is adopted from prior work [6] rather than justified by self-citation. The more serious issue is that RQ2's 'matched parameter count and runtime' condition is asserted but parameter counts and runtimes for the MLP baseline are not reported (Section 5.1/Table 4), and the baseline description is ambiguous about whether it shares the KAN proprioceptive encoder. This is a missing-support/confound issue for the empirical comparison, not a circularity. Score 2 reflects only the minor same-author citation; the derivation itself is self-contained.

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

The central comparison rests on hand-tuned reward weights, unreported regularization coefficients, unspecified visual tokenization and delay distributions, plus assumed simulation fidelity and MMDR effectiveness.

free parameters (6)
  • Reward weights (alive, energy) = 0.1, 0.005
    Hand-chosen coefficients in Eq. (26); directly shape policy behavior and are not tuned in the paper.
  • Spline regularization strengths (lambda_c, lambda_L, beta_spline) = not reported
    Eq. (9) and (20) claim curvature and Jacobian penalties reduce jitter and stabilize training, but the coefficients are never given and jitter is not measured.
  • CNN patch size P = unspecified
    Table 1 defines visual token count N=(64/P)^2 but never specifies P; the visual tokenization is load-bearing for fusion.
  • Visual delay sampling distribution = unspecified
    Section 4.5 gives proprioception latency range in Table 3 but does not specify the visual delay distribution or buffer length, despite MMDR being central to training robustness.
  • Obstacle density curriculum schedule = unspecified
    Section 4.4 says density is annealed linearly to a target distribution but neither the schedule nor the target is reported.
  • Spline degree and knot vector = unspecified
    The B-spline basis in Eq. (8) requires degree q and knot vector, never stated; these affect the inductive bias.
assumptions (5)
  • domain assumption PyBullet simulation with randomized dynamics approximates physical quadruped behavior
    All results are simulation-only; no hardware experiments, so central claims about robust locomotion depend on simulation fidelity (Section 4.1, Section 6).
  • domain assumption Gait is piecewise smooth and B-spline bases with local support capture this structure
    This is the core motivation for KAN (Section 3.2); it is asserted rather than empirically validated against other basis choices.
  • domain assumption Multi-Modal Delay Randomization from Imai et al. [6] is effective in this PPO setting
    MMDR is adopted from prior work (Section 3.5) without ablation; its benefit to QuadKAN is assumed.
  • standard math KAN implementation from Liu et al. [8] is mathematically correct and trainable with PPO
    The architecture follows the published KAN construction; the paper assumes correctness of B-spline parameterization (Eq. 8).
  • standard math PPO with GAE, Tanh-Gaussian policy, and the given hyperparameters optimizes the MDP reliably
    Standard RL assumptions; training stability is claimed but not proven.

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Cite this review

Pith. "Pith review of QuadKAN: KAN-Enhanced Quadruped Motion Control via End-to-End Reinforcement Learning." pith.science (2026). https://pith.science/paper/PKGG3W6W

@misc{pith2026250819153,
  author       = {Pith},
  title        = {Pith review of: QuadKAN: KAN-Enhanced Quadruped Motion Control via End-to-End Reinforcement Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PKGG3W6W}},
  note         = {Machine review of arXiv:2508.19153}
}
read the original abstract

We address vision-guided quadruped motion control with reinforcement learning (RL) and highlight the necessity of combining proprioception with vision for robust control. We propose QuadKAN, a spline-parameterized cross-modal policy instantiated with Kolmogorov-Arnold Networks (KANs). The framework incorporates a spline encoder for proprioception and a spline fusion head for proprioception-vision inputs. This structured function class aligns the state-to-action mapping with the piecewise-smooth nature of gait, improving sample efficiency, reducing action jitter and energy consumption, and providing interpretable posture-action sensitivities. We adopt Multi-Modal Delay Randomization (MMDR) and perform end-to-end training with Proximal Policy Optimization (PPO). Evaluations across diverse terrains, including both even and uneven surfaces and scenarios with static or dynamic obstacles, demonstrate that QuadKAN achieves consistently higher returns, greater distances, and fewer collisions than state-of-the-art (SOTA) baselines. These results show that spline-parameterized policies offer a simple, effective, and interpretable alternative for robust vision-guided locomotion. A repository will be made available upon acceptance.

Figures

Figures reproduced from arXiv: 2508.19153 by the authors.

Figure 1
Figure 1. Overall architecture of QuadKAN. Proprioceptive states are mapped by a KAN into a compact token; a lightweight CNN patchifies depth into spatial tokens. Tokens are projected to a common width and fused by a KAN-based spline head without attention. Policy and value heads are trained end-to-end with PPO. 2.4. Asynchrony, Delay, and Domain Randomization Latency varies across sensing, inference, and actuation, with visu… view at source ↗
Figure 2
Figure 2. Spline–KAN encoder. Each unit projects the input to a scalar, expands it over a compact bank of B-spline basis functions, aggregates with learnable coefficients, and applies a smooth nonlinearity. Stacking units produces tokens with localized, phase-aware sensitivities. Optional curvature and Jacobian regularizers promote smooth, low-jitter actuation. (a) (b) (c) [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 5
Figure 5. Training stability measured by the coefficient of variation (CoV) of all episodes return. Lower values indicate more stable optimization. Allen Wang and Gavin Tao: Preprint submitted to Elsevier Page 10 of 9 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figures from the paper (4 more)
Figure 6
Figure 6. Figure 6: Spline weight analysis of QuadKAN (Ours) (Including 2-layer Proprio encoder KAN and 3-layer Fusion head KAN as introduced in [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Spline weight analysis of Vision-Only KAN. Without proprioceptive anchoring, learned spline weights are weaker and less structured. Compared with [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Spline activation functions (10 sampled neurons) vs. ReLU. Left: Vision-only KAN; Right: QuadKAN (Ours). Unlike ReLU, spline activations exhibit rich nonlinearities to modal complex scenarios. Proprioceptive anchoring stabilizes activations, producing more coherent res…
Figure 9
Figure 9. Figure 9: Comparative spline statistics for Vision-only KAN and QuadKAN (Ours). The dashboard summarizes parameter counts, weight distributions, normalized statistics, layer-wise magnitudes, and sample activations. Despite fewer parameters, QuadKAN learns richer and more coheren…

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Reviewed August 5, 2026 · model on record in the stance chip above.