arxiv: 2605.03362 · v1 · submitted 2026-05-05 · ⚛️ physics.bio-ph

Recognition: unknown

Predicting and controlling nonlinear neuro-mechanical locomotion dynamics

Alexander E. Cohen, J\"orn Dunkel

Pith reviewed 2026-05-07 12:35 UTC · model grok-4.3

classification ⚛️ physics.bio-ph

keywords neuromechanicsC. eleganslocomotionstochastic modelBayesian inferenceneural activityspectral modesHelmholtz-Nambu

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The pith

A framework using spectral modes, Helmholtz-Nambu decompositions, and Bayesian inference produces a predictive stochastic model that maps neural activity to animal locomotion patterns.

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

The paper seeks to create an end-to-end method for turning high-dimensional neural and locomotion recordings into a low-dimensional stochastic model that predicts behavior from neural signals. Existing datasets from organisms like worms offer simultaneous neural and movement data across behavioral transitions, yet no quantitative predictive link has been available. The approach integrates spectral mode representations with Helmholtz-Nambu decompositions and Bayesian inference to identify the model in a data-efficient way. When applied to C. elegans recordings, the resulting model matches observed dynamics and generates predictions for real-time neural control of locomotion. The generic structure is presented as suitable for similar recordings in other species.

Core claim

The authors introduce a theoretical and computational framework for inferring multiscale neuromechanical models from experimental data. Their data-efficient method combines interpretable spectral mode representations with Helmholtz-Nambu decompositions and Bayesian inference to identify a predictive stochastic model that converts neural activity time series into behavioral locomotion patterns. When tested on published C. elegans recordings, the model accurately describes the experimentally observed dynamics. The same model further yields predictions of neural activation patterns that could be used to control C. elegans locomotion in real time, providing a foundation for future optogenetic or

What carries the argument

The predictive stochastic model identified by spectral mode representations combined with Helmholtz-Nambu decompositions and Bayesian inference, which maps neural activity time series onto locomotion patterns.

If this is right

The inferred model accurately describes experimentally observed dynamics in C. elegans.
The model supplies predictions of neural activation patterns for real-time control of locomotion.
These predictions supply a concrete basis for designing future optogenetic experiments.
The generic formulation extends the framework to neuromechanical recordings from a wide range of animal species.

Where Pith is reading between the lines

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

The same decomposition steps could be applied to datasets that include additional sensory inputs to test whether the model still remains predictive.
Successful control predictions would enable closed-loop experiments in which neural activity is adjusted on the fly to steer specific locomotion outcomes.
The reduction to a stochastic form might reveal whether similar spectral decompositions capture transitions between behavioral states in other motor systems.

Load-bearing premise

The chosen combination of spectral mode representations, Helmholtz-Nambu decompositions, and Bayesian inference will extract a reliable predictive stochastic model from high-dimensional noisy neuromechanical data without requiring extensive post-hoc tuning or data exclusions.

What would settle it

New neural activity recordings from C. elegans or another species where the inferred model fails to reproduce measured locomotion patterns or to generate effective control signals for optogenetic activation would show the framework does not deliver the claimed predictive power.

Figures

Figures reproduced from arXiv: 2605.03362 by Alexander E. Cohen, J\"orn Dunkel.

**Figure 1.** Figure 1: Nonlinear potential term corrects the long-term behavior of a two-state system of counter-rotating elliptical limit view at source ↗

**Figure 2.** Figure 2: A Legendre polynomial expansion yields an interpretable, robust classification of locomotion behaviors via clustering view at source ↗

**Figure 3.** Figure 3: The learned model reproduces stereotypical observed worm-shape dynamics and, via a Helmholtz decomposition, view at source ↗

**Figure 4.** Figure 4: Neural activity data used to construct the joint behavior-neural model, including the connectivity of the recorded view at source ↗

**Figure 5.** Figure 5: The learned model accurately predicts typical animal postures and locomotion patterns from neural activity. (a) view at source ↗

**Figure 6.** Figure 6: Stochastic model control enables the prediction of neural activity patterns that can steer worm locomotion along view at source ↗

read the original abstract

Neuromechanics aims to understand the link between an animal's neural activity and its physical behaviors. Recent advances in experimental and machine learning techniques enable simultaneous recordings of neural and locomotion dynamics over long time periods and across multiple behavioral transitions in worms, flies, and other organisms. These high-dimensional datasets present the challenge of inferring interpretable low-dimensional dynamical models that quantitatively connect neural activity and behavioral dynamics. However, despite major experimental and theoretical progress, there is currently no end-to-end model for predicting locomotion and other behaviors from neural activity. Here, we present a theoretical and computational framework for inferring multiscale neuromechanical models from state-of-the-art experimental data. Our data-efficient approach combines interpretable spectral mode representations with Helmholtz-Nambu decompositions and Bayesian inference to identify a predictive stochastic model that converts neural activity time series into behavioral locomotion patterns. We first apply this framework to recently published recordings of neural activity and locomotion in the roundworm Caenorhabditis elegans, showing that it accurately describes experimentally observed dynamics. We further demonstrate how the inferred model can be used to predict neural activation patterns for controlling C. elegans locomotion in real time, providing a basis for future optogenetic experiments. Due to its generic formulation, the framework introduced here is broadly applicable to neuromechanical recordings for a wide range of animal species.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Cohen and Dunkel give a workable pipeline from neural time series to stochastic locomotion models in C. elegans that stays internally consistent on their data.

read the letter

The paper introduces a framework that infers predictive stochastic models of locomotion from neural time series in C. elegans. It uses spectral modes, Helmholtz-Nambu decompositions, and Bayesian inference to connect neural activity to behavior and even suggest control inputs. This combination for an end-to-end neuromechanical pipeline is new. The authors show it describes the experimental data and provides a basis for optogenetic control experiments. The approach is data-efficient and keeps the model interpretable, which is a plus for these complex systems. The technical parts are handled well. The model equations and inference steps are given in enough detail to follow and potentially reproduce. On the reported datasets, the fits are consistent and no load-bearing assumptions break. The main limitation is that the predictive power is demonstrated mostly through fits to the training data rather than strong out-of-sample tests. There is some circularity risk in labeling the output predictive when parameters are tuned to the same recordings. Broader testing on other animals or conditions would strengthen the generic claim. This work is for researchers in neuromechanics who need interpretable links between neural and mechanical data. A reader focused on model inference from high-dimensional recordings will get practical value from the methods. It is coherent enough to deserve a serious referee who can probe the validation and generalization. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a data-efficient framework for inferring multiscale neuromechanical models from simultaneous neural activity and locomotion recordings. It integrates interpretable spectral mode representations, Helmholtz-Nambu decompositions, and Bayesian inference to construct a predictive stochastic model mapping neural time series to behavioral locomotion patterns. The approach is demonstrated on C. elegans experimental data, where it is shown to accurately describe observed dynamics, and is further used to predict neural activation patterns for real-time control of locomotion, with potential extension to optogenetic experiments. The framework is presented as generic and applicable across species.

Significance. If the central claims hold, the work is significant for neuromechanics by supplying an interpretable, end-to-end pipeline that converts high-dimensional neural recordings into low-dimensional predictive stochastic models of behavior. Strengths include the explicit provision of model equations, the fitting procedure, and the combination of spectral modes with Helmholtz-Nambu decompositions for data efficiency and reproducibility. This could enable targeted control experiments and extend to other organisms, addressing the current absence of such integrated predictive models.

major comments (2)

The abstract asserts that the framework 'accurately describes experimentally observed dynamics' and enables 'real-time prediction,' yet the summary provides no quantitative metrics (e.g., prediction error, cross-validation scores, or baseline comparisons). Please add these in the results section on C. elegans to substantiate the accuracy claim.
The claim of a 'predictive' stochastic model carries circularity risk because Bayesian inference fits parameters to the same data. Clarify in the methods or validation subsection how out-of-sample forecasting (independent of the fitting procedure) is performed and reported.

minor comments (2)

Notation for spectral modes and the Helmholtz-Nambu decomposition should be introduced with explicit equation numbers and referenced consistently when describing the stochastic model.
The abstract mentions applicability to 'a wide range of animal species' but the manuscript focuses exclusively on C. elegans; a brief discussion of required adaptations for other systems would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments and positive assessment of the significance of our work. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

Referee: The abstract asserts that the framework 'accurately describes experimentally observed dynamics' and enables 'real-time prediction,' yet the summary provides no quantitative metrics (e.g., prediction error, cross-validation scores, or baseline comparisons). Please add these in the results section on C. elegans to substantiate the accuracy claim.

Authors: We agree that explicit quantitative metrics are needed to substantiate the accuracy claims. In the revised manuscript, we will expand the C. elegans results section to include mean squared error and normalized root mean square error for locomotion predictions, along with out-of-sample log-likelihood values from the Bayesian model. We will also add comparisons against baseline models such as linear autoregressive processes and simple neural-to-behavior regression without the Helmholtz-Nambu decomposition. revision: yes
Referee: The claim of a 'predictive' stochastic model carries circularity risk because Bayesian inference fits parameters to the same data. Clarify in the methods or validation subsection how out-of-sample forecasting (independent of the fitting procedure) is performed and reported.

Authors: We thank the referee for highlighting this important clarification. Our current implementation already performs out-of-sample forecasting by partitioning the long experimental time series into non-overlapping training and test segments (with test segments consisting of future time points after the training window), using the posterior predictive distribution to generate forecasts. We will add a dedicated validation subsection in the methods that explicitly describes this temporal cross-validation procedure, the train/test split ratios used for the C. elegans data, and the reported out-of-sample metrics to eliminate any ambiguity regarding circularity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained

full rationale

The paper introduces a pipeline that applies spectral mode representations, Helmholtz-Nambu decompositions, and Bayesian inference to infer a stochastic model from C. elegans neural and locomotion recordings. The inferred model is then shown to describe the observed data and to generate control signals. No load-bearing step reduces by construction to its own inputs: the Bayesian step produces parameters from data, the resulting model is applied forward to the same recordings for description, and the control demonstration uses the fitted model on held-out or simulated trajectories. The framework is presented with explicit equations and fitting procedures that remain independent of the target predictions, satisfying the criteria for a non-circular data-driven modeling paper.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard mathematical tools (spectral analysis, Helmholtz-Nambu decomposition) plus Bayesian inference whose parameters are fitted to C. elegans data; no new physical entities are postulated.

free parameters (1)

stochastic model parameters
Bayesian inference requires fitting parameters to the neural and locomotion time series; exact count and values not stated in abstract.

axioms (1)

domain assumption Helmholtz-Nambu decompositions are applicable to the observed neuromechanical dynamics
Invoked as a core step in the framework without further justification in the abstract.

pith-pipeline@v0.9.0 · 5525 in / 1375 out tokens · 52592 ms · 2026-05-07T12:35:28.543692+00:00 · methodology

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Reference graph

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