Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)

Lennart Bastian; Mohammad Rashed; Nassir Navab; Tolga Birdal

REVIEW 3 major objections 3 minor 26 references

Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)

T0 review · 3 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper claims that rotational trajectory forecasting on $SO(3)$ can be made resilient to noise and generalizable to non-conservative, non-inertial systems by conditioning a Neural CDE on $SO(3)$-valued Savitzky-Golay smoothed paths.

desk verdict The submission is two different papers: the abstract is a plausible SO(3) forecasting method, but the full text is a CT denoising paper, so there is nothing to peer review. read the letter →

arxiv 2508.07775 v1 pith:EZE7233Y submitted 2025-08-11 cs.CV

Lennart Bastian , Mohammad Rashed , Nassir Navab , Tolga Birdal This is my paper · ORCID

classification cs.CV

keywords SO(3)neuralcontrolleddifferentialequationsSavitzky-Golaysmoothingrotationalmotionforecastingnon-conservativedynamicsnoisyposeestimationextrapolation

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

The paper presents a method for extrapolating the rotational motion of rigid objects in 3D when observations are noisy and the dynamics need not conserve energy or momentum. Existing $SO(3)$ forecasting methods often assume constant velocity or energy conservation; this work drops those assumptions by pairing a neural controlled differential equation with Savitzky-Golay smoothed paths on the rotation manifold. The authors argue that this combination produces forecasts that tolerate input noise and generalize to unknown physical parameters in both simulation and real-world settings. If correct, it would make rotational trajectory forecasting applicable to tumbling, driven, or otherwise non-inertial objects rather than only free-spinning ones.

What carries the argument

The central object is the Neural Controlled Differential Equation (Neural CDE) on the rotation manifold $SO(3)$, driven by an $SO(3)$-valued Savitzky-Golay path. The Savitzky-Golay path is a locally polynomial smoothing of the noisy rotation observations, adapted to the manifold, and it provides a differentiable control signal encoding local rotational dynamics without assuming a global conservation law. The CDE learns to continue this signal, so the extrapolator is agnostic to energy and momentum while remaining grounded in the geometry of rotations.

What would settle it

Generate a rigid body tumbling under a known non-conservative torque, add noise to short observed segments, train the model on those segments only, then extrapolate beyond the training horizon and compare with the ground-truth rotation. If the forecast error matches a constant-velocity baseline once the noise is smoothed away, the claimed advantage of the guided CDE for non-conservative dynamics would be falsified.

Watch

Extended reading notes

Core claim

The central claim is that a Neural Controlled Differential Equation driven by an $SO(3)$-adapted Savitzky-Golay path can extrapolate rigid-body rotations under external torques and non-conservative forces, without relying on energy or momentum conservation. The guided path supplies a stable, differentiable control signal in which noise has been smoothed on the manifold, and the CDE learns the vector field that continues that path. The authors report that the model generalizes to trajectories with unknown physical parameters and is robust to input noise, while being easy to insert into existing pose-estimation and tracking pipelines.

Load-bearing premise

The load-bearing premise is that the $SO(3)$-adapted Savitzky-Golay smoothing removes observation noise without distorting the true underlying rotation, and that a model trained on such smoothed noisy states extrapolates correctly to unseen external torques and unknown inertia.

Editorial extensions

If this is right

Rotational extrapolation pipelines can replace constant-velocity or energy-conserving priors with a learned CDE module, extending forecasts to objects under external forces and torques.
Noisy pose inputs become usable for forecasting because manifold-aware smoothing is built into the driving path before extrapolation begins.
The method transfers to new trajectories with unknown physical parameters, indicating the learned dynamics are not tied to a specific inertia tensor or torque profile.
As a modular component, it can be added to existing pose-estimation and tracking systems without redesigning the rest of the pipeline.
Explicit estimation of physical quantities such as moment of inertia is no longer required for forecasting rotational motion, since the model learns dynamics directly from noisy states.

Reading between the lines

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

If the noise-robustness claim holds, a natural extension is 6-DOF forecasting by coupling this $SO(3)$ rotation forecast with a separate translation model; the product-manifold structure would require a joint smoothing scheme rather than treating rotation alone.
The Savitzky-Golay window size and polynomial order become hyperparameters that likely interact with noise level and rotational speed; an adaptive or learned smoothing scale would be a testable improvement.
The same guided-CDE design should apply to other Lie-group trajectories such as $SE(3)$ or unit quaternions whenever a manifold-adapted smoothing exists, not only to pure rotations.
Because the method avoids conservation-law assumptions, it may also extend to human motion or articulated rotation, where internal muscle torques make dynamics strongly non-conservative.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The thing to know: the submitted PDF is a different paper. The abstract describes forecasting non-conservative dynamics in SO(3) with Neural CDEs and Savitzky-Golay paths; the full text is an anatomy-aware low-dose CT denoising paper (arXiv:2508.07788). Nothing in the attached text describes the SO(3) method, its equations, experiments, or comparisons. This is not a fixable weakness in the science; it is a missing manuscript, and that is the dominant fact of this submission.

Credit where it is due: the abstract names a real gap. Extrapolating noisy pose trajectories on SO(3) without assuming constant velocity or energy conservation matters for vision and robotics, and using SO(3) Savitzky-Golay smoothing as a guiding signal for a Neural CDE is a plausible combination. The authors also point to public code. If the actual paper delivers what the abstract promises, it could be a useful module for non-inertial object tracking.

The soft spots are large. The abstract contains no citations to prior manifold forecasting work, no quantitative results, and no derivations—so even on its own it would be hard to evaluate. But the full-text mismatch makes everything unverifiable: the definition of the SO(3) Savitzky-Golay path, the handling of non-conservative torques, the claimed generalization to unknown physical parameters, and the empirical claims in simulation and real-world settings. The reader's take and the stress-test note are both right: this is an evidentiary gap, not a demonstration of a flaw in the approach.

Recommendation: desk reject this submission. Send it back for a corrected PDF if this was a file mix-up; the idea is worth a look. But no referee can review the SO(3) claims on the basis of an abstract alone with a CT paper attached. If the correct manuscript shows up, I would then send it to someone who works on Riemannian manifold learning or trajectory forecasting.

Referee Report

3 major / 3 minor

Summary. The manuscript, as identified by its arXiv number and abstract, claims a method for forecasting continuous non-conservative dynamical systems on SO(3). The proposed approach is said to combine Neural Controlled Differential Equations with SO(3) Savitzky-Golay smoothed paths, to be agnostic to energy and momentum conservation, robust to input noise, and capable of generalizing to unknown physical parameters. However, the supplied full text is a completely different paper on low-dose CT denoising (ALDEN), with no equations, derivations, experiments, or algorithmic details related to SO(3) forecasting. Consequently, the technical content needed to assess the central claims is absent from the submitted manuscript.

Significance. If the claims in the abstract were substantiated, the work could be significant for computer vision and robotics: robust SO(3) extrapolation without conservation-law assumptions would address a real gap in current methods, and the proposed module-level integration would be practically attractive. The stated code availability is a positive sign, though the code is not part of the submitted text. However, significance cannot be evaluated without the actual method and experiments. As submitted, the manuscript provides no derivations, no architectural details, no training procedure, no evaluation protocol, and no results. Therefore the potential significance is real but entirely unverified.

major comments (3)

[Full Text (entire manuscript)] The submitted full text is a different paper: 'Anatomy-Aware Low-Dose CT Denoising via Pretrained Vision Models and Semantic-Guided Contrastive Learning' (arXiv:2508.07788), concerning CT denoising. None of the claimed SO(3) forecasting content appears. There is no description of Neural CDEs, no definition or analysis of SO(3) Savitzky-Golay paths, no derivation of the dynamics model, no training procedure, and no experiments on rotational motion. Every load-bearing element of the abstract's central claim is therefore unsupported by the manuscript as submitted. This is not a presentation issue; it is a fundamental evidentiary gap that prevents any verification of correctness, novelty, or robustness.
[Abstract (lines 1-6)] The abstract asserts that the approach is 'agnostic to energy and momentum conservation' and 'generalizes well to trajectories with unknown physical parameters.' These are strong claims that require a formal model of non-conservative forces, a definition of what 'agnostic' means mathematically, and an experimental protocol that varies inertial parameters and external torques. None of this is present. Without the method section or experiments, these claims are unverifiable and cannot be checked for internal consistency or circularity.
[Full Text (no experiments section)] The abstract mentions 'simulation and various real-world settings,' yet the supplied full text contains no experimental section, no datasets, no baselines, no metrics (e.g., geodesic error on SO(3)), and no comparisons to existing extrapolation methods. The claimed robustness to input noise and generalization to unknown physical parameters is not demonstrated anywhere. Even if the correct full text were supplied, the abstract alone would be insufficient; the current submission provides no empirical evidence whatsoever.

minor comments (3)

[Title and Metadata] The title and abstract identify the paper as 'Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)', but the full text has a different title, different authors, and a different subject area. This is a severe mismatch that should be corrected at the source; the arXiv submission appears to have been overwritten or misassociated.
[Abstract] The abstract uses terms such as 'Neural Controlled Differential Equations' and 'SO(3) Savitzky-Golay paths' without definitions or references. In a standalone abstract this may be acceptable, but with no full text these terms cannot be contextualized. If the paper is resubmitted, please include proper references to prior CDE work and Savitzky-Golay filtering on manifolds.
[References] The reference list is entirely from the CT denoising paper and does not include any citations to relevant SO(3) forecasting, Neural CDE, or manifold smoothing literature. This further confirms that the full text does not correspond to the abstract.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: abstract's claims have no derivation chain in the submitted full text, which is an unrelated CT paper.

full rationale

The abstract of arXiv:2508.07775 makes specific claims about SO(3) trajectory forecasting via Neural CDEs guided by SO(3) Savitzky-Golay paths, robustness to non-conservative dynamics, and generalization to unknown physical parameters. However, the provided full text is arXiv:2508.07788, 'Anatomy-Aware Low-Dose CT Denoising via Pretrained Vision Models and Semantic-Guided Contrastive Learning,' a completely different paper by different authors on a different topic. There is no derivation, no equations, no method description, and no experiments in the submitted text that correspond to the abstract's claims. Consequently, none of the circularity patterns (self-definitional, fitted input called prediction, self-citation load-bearing, uniqueness imported from authors, ansatz smuggled via citation, renaming known result) can be instantiated: there is no derivation chain that could reduce to its own inputs because the claimed derivation is absent. This is a fundamental evidentiary gap and a correctness/verifiability problem, not a circularity problem. The absence of circularity finding reflects the lack of any substantive technical content to analyze; it does not positively verify the abstract's claims.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The abstract implies several domain assumptions about the representational power of Neural CDEs on SO(3) and the effectiveness of SO(3) Savitzky-Golay smoothing. No free parameters are specified because the abstract contains no equations or experimental details. No new physical entities are introduced.

assumptions (3)

domain assumption Object dynamics can be represented as a Neural CDE on SO(3).
Implicit in the abstract's proposal; no justification or architecture details are provided.
domain assumption Savitzky-Golay filtering on SO(3) preserves the relevant physical trajectory structure.
Assumed to reduce noise without distorting the dynamics; no proof or analysis is given.
domain assumption Training on noisy pose states suffices to generalize to unknown physical parameters.
Core generalization claim in the abstract; no evidence or theoretical basis is presented.

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Cite this review

Pith. "Pith review of Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)." pith.science (2026). https://pith.science/paper/EZE7233Y

@misc{pith2026250807775,
  author       = {Pith},
  title        = {Pith review of: Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EZE7233Y}},
  note         = {Machine review of arXiv:2508.07775}
}

abstract

Modeling the rotation of moving objects is a fundamental task in computer vision, yet $SO(3)$ extrapolation still presents numerous challenges: (1) unknown quantities such as the moment of inertia complicate dynamics, (2) the presence of external forces and torques can lead to non-conservative kinematics, and (3) estimating evolving state trajectories under sparse, noisy observations requires robustness. We propose modeling trajectories of noisy pose estimates on the manifold of 3D rotations in a physically and geometrically meaningful way by leveraging Neural Controlled Differential Equations guided with $SO(3)$ Savitzky-Golay paths. Existing extrapolation methods often rely on energy conservation or constant velocity assumptions, limiting their applicability in real-world scenarios involving non-conservative forces. In contrast, our approach is agnostic to energy and momentum conservation while being robust to input noise, making it applicable to complex, non-inertial systems. Our approach is easily integrated as a module in existing pipelines and generalizes well to trajectories with unknown physical parameters. By learning to approximate object dynamics from noisy states during training, our model attains robust extrapolation capabilities in simulation and various real-world settings. Code is available at https://github.com/bastianlb/forecasting-rotational-dynamics

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