Rotation detectors have matured faster than the methods for comparing motifs across stages

Question: How have rotational and other low-dimensional dynamical motifs been identified and compared across neural populations at different processing stages, such as sensory versus motor regions or different cortical layers?

Answer

Across these papers, identification is largely a solved methodological problem while comparison is not. Rotation-sensitive decompositions now extract low-variance rotational modes from single trials and have been applied across spikes, calcium imaging, fMRI and MEG [1], and latent dynamical-system fitting converts trajectories into named motifs — fixed points, limit cycles, sequences — that can be read out of high-dimensional models [6] [7] [29]. Comparison across stages, however, has mostly taken the form of applying one pipeline to one task and reporting whether a motif is present or absent on either side of an anatomical boundary, and where this has been done the answer has repeatedly been that motifs differ: spinal populations lack the rotation seen in motor cortex in the same isometric task [4], M1 and SMA adopt different solutions to the same movement [7], and parietal areas differ in how much their planning and execution subspaces overlap [13]. Coordinate-free alignment machinery capable of making such comparisons principled — topological matching of manifold features [14], diffeomorphic vector-field alignment [28] — exists but has not been applied at scale to sensory-versus-motor or laminar contrasts, and no retrieved paper compares a dynamical motif across cortical layers at all.

Rotation is now extracted by decompositions tuned to rotation rather than to variance

Rotational Component Analysis was built specifically to optimise detection of low-variance rotational modes rather than high-variance axes, and it recovers them even within individual trials [1]. The same method revealed double-rotation modes with two centres of rotation that separate preparatory from task dynamics, and rotational irreversibility that distinguished early psychosis where PCA showed no group difference [1]. Dedicated detection changes what is found in a single region: human motor cortex during rhythmic tapping shows low-dimensional rotational dynamics whose radii scale with tempo and whose axes relate to kinematic properties, while tempo preparation is carried in an orthogonal dimension rather than in the rotation itself [5]. The motif is not confined to cortex — bilateral hindlimb motor-unit populations rotate continuously through all phases of the locomotor cycle within a low-dimensional manifold, and this organisation survives complete spinal cord injury [20].

Fitting latent dynamical systems renames trajectories as motifs and makes cross-stage vocabularies shareable

A compositional account of M1 and PMd during reaching decomposes population dynamics into a posture subspace of fixed points, rotations that transition between those fixed points, and a condition-independent shift dimension [6]. Comparing two motor areas on one task shows the vocabulary can discriminate: M1 converges to the same limit cycle for rhythmic and discrete movements, whereas SMA dynamics diverge according to upcoming movement type before reaching a helical spiral [7]. In lumbar spinal cord, locomotion occupies a limit-cycle-like locomotor manifold while stopping corresponds to a fixed-point attractor, and kicking the state out of that fixed point lands it on a nearby different fixed point, with repeated stoppings forming a postural manifold [3]. On the model side, spectral submanifold reduction supplies mathematically precise definitions of line and ring attractors recovered from RNNs [29], and a library of dynamical archetypes with a trajectory-estimable dissimilarity measure groups systems by effective behaviour while tolerating the structural fragility of continuous attractors [26] [27].

When one task and pipeline cross a stage boundary, the motifs usually differ

The cleanest cross-stage test in this set applies the same analysis to primate cervical spinal cord and motor cortex during an alternating isometric wrist task: spinal activity shows low-dimensional alternating patterns without rotational dynamics, while positive controls confirm rotational structure in motor cortex during the same task [4]. Within parietal cortex, PE occupies nearly orthogonal subspaces for planning and execution whereas V6A and PEc show both shared and exclusive subspaces, indicating area-specific rather than uniform latent organisation [13]. Across cortex and striatum the picture splits by measure: M1 and striatum share the same hierarchical organisation of dynamics across behaviours despite stronger muscle correlation in M1 and greater behaviour specificity in striatum [8], yet decoding shows dorsomedial striatum encoding the preparatory period better and M1 encoding rhythmic limb kinematics better [19]. Timescale analyses place M1 above PMd in the temporal hierarchy, with longer single-unit timescales and smaller LFP aperiodic exponents in M1 [15].

Coordinate-free matching is available but barely used for stage contrasts

The method of analogous cycles matches topological features of neural manifolds across populations using only within- and between-population dissimilarity matrices, correctly identifying shared circular coordinate systems and rejecting matches that are not intrinsic to one system, without dimensionality reduction or optimisation [14]. Diformorphic vector field alignment learns a nonlinear coordinate transformation between two systems' state spaces to assess topological equivalence and to locate motifs such as invariant manifolds and saddle limit sets inside high-dimensional models [28]. Representational-geometry comparisons are less distinctive than they appear, since centering makes RSA and CKA largely equivalent and connects both to canonical correlations analysis [16]. Two cautions apply to any such comparison: subspace relations can be partial rather than all-or-none, as when instantaneous subspaces during action execution and observation remain mostly distinct yet partially align with canonical correlation [21], and inter-regional coupling estimates change when models operate at the population rather than single-neuron level, as with reduced V1-to-higher-visual-area coupling during locomotion detected only by pop-GLM [22].

Laminar comparisons exist for timescales, drift and manifold topology, but not for dynamical motifs

Depth-resolved work in motor cortex finds LFP autocorrelation timescales systematically longer in deep layers of M1 with smaller spectral exponents in deep layers of both areas, while single-unit timescales show no significant laminar differences — a divergence attributed to spikes reflecting output and LFPs reflecting synaptic population activity [15]. Cortex-wide drift follows distinct laminar motifs, with L5 responses decreasing monotonically across most areas and L2/3 responses changing locally and heterogeneously, and L5 showing more prolonged temporal engagement [23]. At the macroscale, depth-resolved functional gradients dissociate: a superficial-layer dissimilarity index follows the sensory-to-association axis while the deep-layer index aligns with the visual-to-somatomotor axis and peaks in receive-dominant regions [9]. Encoding manifolds spanning V1 and five higher visual areas are topologically continuous with smooth coordinates organised by layer and cell type, and grating preference concentrates in L6 while natural-scene preference is higher in L2/3 and L4 [24]. The closest thing to a spatially resolved cross-area motif comparison is the finding that traveling spiral waves centre on somatosensory cortex, are mirrored between sensory and motor cortex, and match a circular local axonal architecture [25].

Dimensionality itself is not commensurable across stages, which undermines "low-dimensional" as a comparative claim

Applying different retention criteria to the same macaque parietal recordings yields different trends in estimated dimensionality, with parallel analysis conservative and cross-validation better in low-noise regimes [11]. Spectral theory shows the covariance eigenspectrum cannot recover latent dimensionality when neurons are nonlinear, and nonlinear latent modelling reduces visual cortex responses to drifting gratings and spontaneous activity to low-dimensional latents but fails to do so for natural images [10]. Behaviour-anchored supervised latents spanning only two dimensions and 3-7% of variance outperform common alternatives at decoding and remain stable over years while the encoding map drifts [17], and motor cortex encoding patterns switch quickly and drift slowly, with electrical perturbation evoking both timescales [2].

Conflicts and gaps

The spinal cord is the sharpest disagreement: rotation is absent during an alternating isometric wrist task with cortical positive controls [4] but present during locomotion and after spinal injury [20] [3], leaving unresolved whether rotation is a property of the region, of the behavioural timescale, or of the task's rhythmicity. Sensory and motor literatures are not comparable as practised: sensory papers characterise encoding manifolds and representational geometry [24] while motor papers characterise attractor structure, and no retrieved study applies one motif vocabulary across that boundary. Reciprocal inhibition between regions is rarely modelled, so a motif measured in a downstream area may be inherited input rather than local computation, a confound only recently addressable [12]. Human non-invasive stage comparisons inherit the limits of PCA-based trajectory analysis under spatial mixing and linearity assumptions [18].

What would change the answer

A single experiment would settle most of this: simultaneous laminar-resolved Neuropixels recordings along one sensory-to-motor axis during one task, including both isometric and rhythmic variants of the same movement, analysed with one rotation-optimised decomposition [1] and then compared with coordinate-free matching rather than a shared PCA space [14] [28]. Detector calibration on synthetic populations with known mixtures of fixed points, limit cycles and rotations — the use case for which archetype libraries and vector-field alignment were built [26] [28] — would convert present-versus-absent reports into false-negative rates. Perturbation-based motif validation, already used to probe spinal fixed points and motor cortical drift [3] [2], would establish that a motif is causally load-bearing at each stage, and multi-region latent models that separate inter-regional communication from local dynamics [12] would identify which motifs are intrinsic to a stage.

References

[1] Sihan Chen, Yunlong Xu, Doruk Efe Gökmen, Michel Fruchart, Brent Doiron, Vincenzo Vitelli. "Spontaneous brain-wide rotational dynamics constrain cue-evoked behavior". arxiv. 2026-10-20T00:00:00.000Z. URL: https://arxiv.org/abs/2610.25061

[2] Clarke, S. E., Jun, E. J., Nuyujukian, P.. "Neural modes in motor cortex cycle over fast timescales". bioRxiv. 2026-01-26T00:00:00.000Z. URL: https://doi.org/10.64898/2026.01.26.701671

[3] Komi, S. A., Kaur, J., Winther, A., Bonfils, M. C. A., Houser, G. A., Sorensen, R. J. F., Li, G., Sobriel, K., Berg, R. W.. "Neural manifolds that orchestrate walking and stopping". bioRxiv. 2026-02-12T00:00:00.000Z. URL: https://doi.org/10.1101/2025.11.08.687367

[4] Refy, O., Perlmutter, S. I., Maier, M. A., Smith, W. S., Fetz, E. E., Nielsen, J. B.. "Spinal cord population activity lacks rotational dynamics during an alternating isometric task in macaque". bioRxiv. 2026-07-02T00:00:00.000Z. URL: https://doi.org/10.64898/2026.06.29.735164

[5] Bhatt, R., Sheets, D. E., Jordan, P. M., Downey, J. E., Merchant, H., Greenspon, C. M.. "Finding the groove in neural space". medRxiv. 2026-02-27T00:00:00.000Z. URL: https://doi.org/10.64898/2026.02.26.26347169

[6] Kashefi, M., Michaels, J. A., Kersten, R., Lau, J. C., Diedrichsen, J., Pruszynski, J. A.. "Compositional neural dynamics during reaching". bioRxiv. 2026-01-29T00:00:00.000Z. URL: https://doi.org/10.1101/2025.09.04.674069

[7] Colins Rodriguez, A., Fuentes-Flores, R., Humphries, M. D.. "Primary and Supplementary Motor cortex implement parallel control solutions for rhythmic and discrete arm movements". bioRxiv. 2026-02-17T00:00:00.000Z. URL: https://doi.org/10.64898/2026.02.16.706176

[8] Xing, D. Y., Glaser, J., Miri, A.. "Neural dynamics hierarchy in motor cortex and striatum across naturalistic behaviors". bioRxiv. 2024-12-17T00:00:00.000Z. URL: https://doi.org/10.1101/2024.12.17.629049

[9] Degutis, J. K., Miehlbradt, J., Durand-Ruel, M., Huppi, P., Van De Ville, D.. "Functional gradients dissociate between cortical layers". bioRxiv. 2026-06-23T00:00:00.000Z. URL: https://doi.org/10.64898/2026.02.06.704362

[10] Schmutz, V., Haydaroglu, A., Wang, S., Feng, Y., Carandini, M., Harris, K. D.. "High-dimensional neuronal activity from low-dimensional latent dynamics: a solvable model". bioRxiv. 2026-01-16T00:00:00.000Z. URL: https://doi.org/10.1101/2025.06.03.657632

[11] Vaccari, F. E., Diomedi, S., Bettazzi, E., Filippini, M., De Vitis, M., Hadjidimitrakis, K., Fattori, P.. "More or fewer latent variables in the high-dimensional data space? That is the question". bioRxiv. 2024-12-09T00:00:00.000Z. URL: https://doi.org/10.1101/2024.11.28.625854

[12] Belle Liu, Jacob Sacks, Matthew D. Golub. "Accurate identification of communication between multiple interacting neural populations". arxiv. 2026-06-09T00:00:00.000Z. URL: https://arxiv.org/abs/2506.19094

[13] Diomedi, S., Vaccari, F. E., Hadjidimitrakis, K., Fattori, P., Stoianov, I. P.. "Integration of Motor Planning and Execution through Latent Structure Reorganization in the Posterior Parietal Cortex". bioRxiv. 2025-06-15T00:00:00.000Z. URL: https://doi.org/10.1101/2025.06.10.658832

[14] Iris H. R. Yoon, Gregory Henselman-Petrusek, Yiyi Yu, Robert Ghrist, Spencer LaVere Smith, Chad Giusti. "Tracking the topology of neural manifolds across populations". arxiv. 2025-03-27T00:00:00.000Z. URL: https://doi.org/10.1073/pnas.2407997121

[15] Nandi, N., Lopez-Galdo, L., Nougaret, S., Kilavik, B. E.. "Area- and Layer-Specific Organization of Timescales in Macaque Motor Cortex". bioRxiv. 2026-06-23T00:00:00.000Z. URL: https://doi.org/10.64898/2026.03.21.713374

[16] Williams, A. H.. "Equivalence between representational similarity analysis, centered kernel alignment, and canonical correlations analysis". bioRxiv. 2024-10-24T00:00:00.000Z. URL: https://doi.org/10.1101/2024.10.23.619871

[17] Abdulla, M. U., Clarke, S. E., Jun, E., Nuyujukian, P., Neural Prosthetics Systems Laboratory and Brain Interfacing Laboratory,. "Stability of neural manifolds at minimal dimensionality despite motor representational drift". bioRxiv. 2026-02-02T00:00:00.000Z. URL: https://doi.org/10.64898/2026.01.30.702162

[18] Vanessa Hadid, Hamza Abdelhedi, Annalisa Pascarella, Sara A. Solla, Paul Cisek, Karim Jerbi. "From Signals to Trajectories: A Primer on Low-Dimensional Dynamics in Human EEG and MEG". arxiv. 2026-09-29T00:00:00.000Z. URL: https://arxiv.org/abs/2609.32315

[19] Singla, D., Yang, L., Weakley, A. S., Davidoff, D., Kao, J. C., Masmanidis, S. C.. "Complementary cortical and striatal encoding of locomotor preparation and performance". bioRxiv. 2025-04-24T00:00:00.000Z. URL: https://doi.org/10.1101/2025.04.24.650464

[20] Colard, J., Harnie, J., Berg, R. W., Frigon, A.. "Spinal rotational dynamics orchestrate locomotor recovery". bioRxiv. 2026-08-21T00:00:00.000Z. URL: https://doi.org/10.64898/2026.07.21.739844

[21] Zhao, Z., Schieber, M.. "Progressively shifting patterns of co-modulation among premotor cortex neurons carry dynamically similar signals during action execution and observation". bioRxiv. 2025-07-10T00:00:00.000Z. URL: https://doi.org/10.1101/2023.11.06.565833

[22] Xin, Q., Urban, K. N., Siegle, J. H., Kass, R. E.. "A Population Coupling Model Identifies Reduced Propagation from V1 to Higher Visual Areas During Locomotion". bioRxiv. 2026-02-06T00:00:00.000Z. URL: https://doi.org/10.64898/2026.02.04.703681

[23] Pollak, Y. E., Sachdev, R., Larkum, M., Gilad, A.. "Cortex-wide representational drift of different layers". bioRxiv. 2026-07-20T00:00:00.000Z. URL: https://doi.org/10.64898/2026.07.15.738614

[24] Dyballa, L., Field, G. D., Stryker, M. P., Zucker, S. W.. "Functional organization and natural scene responses across mouse visual cortical areas revealed with encoding manifolds". bioRxiv. 2026-09-16T00:00:00.000Z. URL: https://doi.org/10.1101/2024.10.24.620089

[25] Ye, Z., Ladd, A., MacKenzie, N., Kolich, L., Li, A., Birman, D., Bull, M. S., Daigle, T. L., Tasic, B., Zeng, H., Steinmetz, N. A.. "Brain-wide topographic coordination of traveling spiral waves". bioRxiv. 2025-03-11T00:00:00.000Z. URL: https://doi.org/10.1101/2023.12.07.570517

[26] Abel Sagodi, Il Memming Park. "Dynamical Archetype Analysis: Autonomous Computation". arxiv. 2026-07-22T00:00:00.000Z. URL: https://arxiv.org/abs/2507.05505

[27] Ábel Ságodi, Guillermo Martín-Sánchez, Piotr Sokół, Il Memming Park. "Back to the Continuous Attractor". arxiv. 2025-03-25T00:00:00.000Z. URL: https://arxiv.org/abs/2408.00109

[28] Ruiqi Chen, Giacomo Vedovati, Todd Braver, ShiNung Ching. "Comparing Dynamical Models Through Diffeomorphic Vector Field Alignment". arxiv. 2026-05-28T00:00:00.000Z. URL: https://doi.org/10.1162/NECO.a.1526

[29] Marraffa, A., Krause, R., Mante, V., Haller, G.. "Data-Driven Reduced Modeling of Recurrent Neural Networks". bioRxiv. 2025-10-14T00:00:00.000Z. URL: https://doi.org/10.1101/2025.10.13.681116

How this survey was made

This survey answers one question: “How have rotational and other low-dimensional dynamical motifs been identified and compared across neural populations at different processing stages, such as sensory versus motor regions or different cortical layers?”

We keep our own collection of recent preprints and refresh it every day from bioRxiv, medRxiv, arXiv, PsyArXiv, SocArXiv and ChemRxiv. For each survey, we search that collection for recent work and keep the strongest matches: papers that use the same terms as the question, and papers on the same topic in different words.

The text was written from the titles and abstracts of those papers; the full texts were not read. Statements that draw on a particular paper are marked with a number in brackets. The reference list just above is the 29 papers whose work this text draws on, chosen from the 177 papers those searches returned; the rest of the shortlist is not printed. It is not a complete review of everything published on the question.

Treat this as a starting point and a reading list, not a peer-reviewed review. The searches behind this survey ran on October 22, 2026 and covered work from the previous two years.