Dynamic neural manifolds for flexible closed-loop control on neuromorphic hardware

Andrew Lehr; Christian Tetzlaff; Oskar von Seeler

REVIEW 3 major objections 7 minor 29 references

Dynamic neural manifolds for flexible closed-loop control on neuromorphic hardware

T0 review · 3 major / 7 minor · reviewed 2026-07-09 · glm-5.2

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Steering neural manifold geometry on neuromorphic hardware

desk verdict Solid neuromorphic implementation of known framework; maze demo needs quantification read the letter →

arxiv 2607.07373 v1 pith:TJBXTAKS submitted 2026-07-08 cs.NE

Oskar von Seeler , Christian Tetzlaff , Andrew Lehr This is my paper · ORCID

classification cs.NE

keywords neuromorphiccomputingneuralmanifoldsSpiNNaker2ringnetworksubspacerotationclosed-loopcontrolspikingnetworksdynamic

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 implements a ring-network circuit on the SpiNNaker 2 neuromorphic chip where three biologically inspired control mechanisms — multiplicative gain, additive current, and random silencing of neuron subsets — act as interpretable knobs that steer the geometry of low-dimensional neural activity trajectories. Gain controls trajectory speed, additive current controls trajectory radius (bump width), and heterogeneous inhibition rotates the subspace in which the trajectory unfolds, with the rotation angle scaling as arccos(1 − p_inh) where p_inh is the fraction of silenced neurons. The authors show that a spiking, sparsified, circulant-weight implementation on chip faithfully reproduces the analytical predictions of the original rate-based model across all three control dimensions, operates within the 1 ms real-time threshold, and can drive closed-loop motor control: a simulated two-wheeled robot navigates a maze by using sensory feedback to modulate the three control parameters in real time, with a linear readout trained on random exploration decoding motor commands from the ring network's spike output.

What carries the argument

A ring network of 500 spiking neurons with asymmetric circulant recurrent connectivity (20% sparse, stored as a single weight row plus a bitmask) deployed on SpiNNaker 2. Three control inputs — multiplicative gain S, additive current I, and inhibitory ensemble selection p — modulate trajectory speed, radius, and subspace orientation respectively. A spike-based communication layer with deterministic spike generation replaces stochastic sampling. A linear readout trained via regression on smoothed spike signals decodes motor commands. Closed-loop operation streams spikes off-chip to a host that computes control parameters and streams them back, achieving a full control loop latency of ~3 time步

What would settle it

If the subspace rotation angle on SpiNNaker 2 deviates from the arccos(1 − p_inh) prediction across the full range of p_inh, or if the closed-loop maze navigation fails when the maze structure demands motor commands outside the distribution explored during readout training.

Watch

Extended reading notes

Core claim

The central discovery is that the geometric properties of neural population activity on a spiking neuromorphic chip can be steered by three simple circuit-level mechanisms in a way that is both analytically predictable and functionally sufficient for closed-loop control. The subspace rotation angle follows the arccos(1 − p_inh) scaling law precisely on chip, trajectory speed and bump width respond to gain and additive current as predicted by the rate-based model, and these three controls can be combined and modulated by sensory feedback in real time to produce flexible, explainable motor behavior in a maze navigation task.

Load-bearing premise

The maze navigation demonstration relies on a linear readout trained on 200 random actions (250 timesteps each) generalizing to the structured, sequential demands of actual maze traversal, but the paper does not report readout error or generalization metrics during navigation itself.

Editorial extensions

If this is right

If the subspace-rotation scaling law generalizes, neuromorphic engineers could design multi-behavior controllers by pre-computing inhibitory ensembles whose pairwise angles are analytically determined, eliminating the need for training-based subspace discovery.
The circulant-plus-bitmask weight storage scheme could allow substantially larger ring networks on-chip than naive dense storage, potentially scaling to thousands of neurons per chip for multi-network architectures.
Extending the framework to 2D cortical-sheet topologies with spatially heterogeneous inhibition could yield traveling-wave controllers with region-specific modulation, expanding the behavioral repertoire beyond what a 1D ring can express.
If sensory feedback can modulate manifold geometry at 3 ms latency, the approach could be viable for real-time prosthetic control where neural population activity must be rapidly reconfigured in response to changing task demands.

Reading between the lines

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

The readout generalization gap is the most consequential untested assumption: if the linear readout trained on 200 random actions fails to generalize to structured sequential maze navigation, the closed-loop demonstration may depend on the maze being simple enough that interpolation within the training distribution suffices. Testing readout error during actual maze traversal would clarify this.
The three-parameter control space (speed, shape, subspace) may be too low-dimensional for tasks requiring simultaneous independent control of multiple movement features — for instance, controlling forward speed, turning radius, and postural adjustment concurrently would require either more control parameters or a multi-ring architecture.
The claim of explainability rests on the mapping from control parameters to manifold geometry being one-to-one and invertible; if noise on the chip (particularly the deterministic spike approximation) introduces sufficient distortion to the rate signal, the geometric interpretation may degrade in ways that are hard to detect without continuous monitoring of subspace angles.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This paper ports the authors' dynamic neural manifold framework [12,13] to SpiNNaker 2 and demonstrates it in closed-loop robotic control. The implementation work is the real contribution: spike-based communication, circulant sparse connectivity with bitmask storage, and a deterministic spike rule that approximates stochastic firing without expensive RNG. The parameter sweeps in Figure 4 are thorough — 10 trials per condition, systematic variation of all three control parameters, and clean agreement with analytical predictions (arccos(1−p_inh) scaling, bump size vs. additive current, rotation speed vs. gain). Runtime benchmarks show the system stays well under 1ms per timestep for the relevant parameter ranges. This is reproducible, parameter-free validation against a known analytical result, and it holds up well. The engineering is legitimate and the validation is done right. The soft spot is the maze demonstration. The stress-test concern about readout generalization is valid but somewhat overstated. The readout is a linear regression from smoothed spike rates to motor speeds — this is a simple mapping within a fixed subspace, not a complex policy. The training distribution (random constant actions) and test distribution (sequential plan with local sensory adaptations) differ, but the mapping the readout learns is essentially “which subspace am I in, and what are the gain/shape parameters” → motor speeds. That mapping is fairly stable across contexts. The bigger issue is that the paper reports no quantitative evaluation at all: no success rate, no readout error, no comparison to a direct motor command baseline. A single example trajectory (Figure 5B,D) is not enough to support the claim of closed-loop control. Also, the smoothing parameter α (Eqs. 5-6) is unspecified. These are fixable gaps, not structural flaws. The external hand-coded planner is fine — the paper is explicit that it assumes a world model and focuses on motor execution. That scoping is honest. This paper is for neuromorphic hardware researchers and computational neuroscientists building interpretable control circuits. The implementation and validation sections are solid enough to warrant peer review. The maze section needs quantification before the application claim is fully supported, but the core engineering contribution stands on its own. Recommend accepting for peer review with a request to add quantitative maze metrics and specify α.

Referee Report

3 major / 7 minor

Summary. This manuscript presents an implementation of a dynamic neural manifold framework on the SpiNNaker 2 neuromorphic chip. The architecture uses a ring network with asymmetric recurrent connectivity to generate sequential activity, with three control mechanisms (additive current for shape, multiplicative gain for speed, and heterogeneous inhibition for subspace rotation) that can be modulated in real time. The authors validate their spike-based, sparsified implementation against the original rate-based model and analytical predictions across systematic parameter sweeps (Figure 4), and demonstrate sub-millisecond runtime per timestep. They then apply the system to a closed-loop maze navigation task where sensory feedback modulates control parameters and a linear readout maps ring network activity to motor commands.

Significance. The implementation and validation work is the strongest part of this paper. The systematic parameter sweeps in Figure 4 cleanly demonstrate that the SpiNNaker 2 implementation reproduces analytical predictions, including the parameter-free arccos(1-p_inh) scaling for subspace angles. The runtime benchmarks are thorough and show the system operates well within real-time constraints. The engineering contributions — including the deterministic spike rule (Eq. 3), circulant weight storage with bitmasks, and streaming control parameters for arbitrary-duration simulations — are well-motivated and clearly described. The paper provides a useful proof of principle that dynamic manifold control mechanisms are readily portable to neuromorphic hardware.

major comments (3)

§'Navigating a virtual maze', Figure 5B,D: The maze navigation claim — that the architecture 'can drive closed-loop motor control in a maze navigation task' — is supported only by a single example trajectory with no quantitative evaluation. No success rate, readout test error, or generalization metric is reported. This is load-bearing because the paper's abstract and introduction explicitly claim closed-loop motor control as a key contribution. At minimum, the authors should report readout accuracy (e.g., mean squared error between predicted and target motor speeds) during actual maze traversal, and ideally report success rates across multiple maze instances or random seeds. Without any such metric, the reader cannot assess whether the readout generalizes from the training distribution (200 random actions with constant parameters per episode, Methods/Readout) to the structured, context-
§'Navigating a virtual maze', Methods/Readout: The linear readout (Eq. 7) is trained via linear regression on smoothed spike signals from 200 random actions lasting 250 timesteps each. At test time, the agent executes a structured sequential plan with rapid subspace transitions, continuous parameter modulation, and local sensory adaptations (e.g., curved motion for wall avoidance). This is a substantial distribution shift from the training regime of isolated random actions with constant control parameters. The paper does not discuss this gap or provide evidence that the readout is robust to it. The authors should either (a) report test-time readout performance during maze traversal, or (b) explicitly acknowledge this limitation and reframe the maze result as a qualitative demonstration rather than a validation of closed-loop control capability.
§'Navigating a virtual maze': The division of labor between the external program and the ring network is unclear and affects the strength of the application claim. The external program handles sensory processing, planning, action selection, and translation of actions to control parameters. The ring network's functional role is limited to mapping control parameters to motor speeds via the learned readout. The paper should explicitly state what computational role the ring network plays that could not be achieved by a simpler lookup table from control parameters to motor speeds. If the network's contribution is primarily as a proof-of-concept substrate rather than a functionally necessary component, this should be stated clearly.

minor comments (7)

Figure 2 caption: The panel labels in the caption (A-F) do not clearly map to the sub-panels in the figure. Panel E is mentioned in the caption but the figure layout makes it hard to identify. Please clarify.
§'Implementation of dynamic neural manifolds on SpiNNaker 2', Eq. (3): The deterministic spike rule uses a floor function notation that is slightly ambiguous. A brief note clarifying that ⌊2/r⌋ is the floor of 2/r (and that the neuron spikes when t+i is divisible by this value) would improve readability.
Figure 4C: The y-axis label reads '180 arccos(1 pinh)' which appears to be a rendering issue for '180/π · arccos(1-p_inh)'. Please fix the label.
§'Closed-loop applications', Environment: The motor noise is described as k_left, k_right ~ N(1, σ) with σ=0.01 on normal ground and σ=0.1 on gravel. It would help to clarify whether σ is the standard deviation (as the notation suggests) and whether the noise is applied per timestep.
§'Discussion': The phrase 'neuromophic' appears to be a typo for 'neuromorphic'.
Supplementary Figure 1: The red boxes highlighting control parameter ranges used in the closed-loop application are mentioned but hard to see in the figure. Please increase their visibility.
References [10], [26], [27], [28] are dated 2026. If these are forthcoming/in-press, please confirm publication status.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The referee correctly identifies that the maze navigation results are the weakest part of the manuscript. We agree with the substance of all three major comments and will revise accordingly.

read point-by-point responses

Referee: §'Navigating a virtual maze', Figure 5B,D: The maze navigation claim — that the architecture 'can drive closed-loop motor control in a maze navigation task' — is supported only by a single example trajectory with no quantitative evaluation. No success rate, readout test error, or generalization metric is reported.

Authors: The referee is correct. The maze navigation result is currently supported by a single example trajectory with no quantitative evaluation. We will address this by (1) reporting readout mean squared error between predicted and target motor speeds during actual maze traversal, computed across multiple time steps and behavioral conditions, and (2) running the maze navigation across multiple maze instances and random seeds, reporting success rates. We will add these quantitative results to a revised Figure 5 and the corresponding text. We agree that without such metrics, the closed-loop control claim is not adequately supported. revision: yes
Referee: §'Navigating a virtual maze', Methods/Readout: The linear readout is trained via linear regression on smoothed spike signals from 200 random actions lasting 250 timesteps each. At test time, the agent executes a structured sequential plan with rapid subspace transitions, continuous parameter modulation, and local sensory adaptations. This is a substantial distribution shift from the training regime. The paper does not discuss this gap or provide evidence that the readout is robust to it.

Authors: This is a fair point. There is indeed a distribution shift between the training regime (isolated random actions with constant control parameters per 250-timestep episode) and the test regime (structured sequential plan with rapid subspace transitions, continuous parameter modulation, and local sensory adaptations such as curved wall-avoidance motion). We did not previously discuss this gap. In the revision, we will (a) report test-time readout performance (MSE) during actual maze traversal to provide direct evidence of robustness, and (b) explicitly acknowledge the distribution shift in the text, discussing why the readout may generalize despite it — namely, that the control parameters at test time remain within the ranges sampled during training, and the linear readout operates on the same smoothed spike representations regardless of how control parameters were generated. If the quantitative results reveal degradation under distribution shift, we will report that honestly and reframe the maze result as a qualitative demonstration rather than a validation of closed-loop control capability, as the referee suggests as option (b). revision: yes
Referee: §'Navigating a virtual maze': The division of labor between the external program and the ring network is unclear and affects the strength of the application claim. The external program handles sensory processing, planning, action selection, and translation of actions to control parameters. The ring network's functional role is limited to mapping control parameters to motor speeds via the learned readout. The paper should explicitly state what computational role the ring network plays that could not be achieved by a simpler lookup table from control parameters to motor speeds.

Authors: We agree that the current presentation does not clearly articulate the ring network's functional role beyond serving as a substrate for mapping control parameters to motor outputs. In the specific maze application as implemented, the external program does handle sensory processing, planning, and action selection, and the ring network's contribution is indeed limited to generating the activity patterns from which motor commands are read out. We will revise the text to state this division of labor explicitly and transparently. Regarding the lookup-table comparison: in the current application, the mapping from control parameters to motor speeds is approximately linear and could in principle be replaced by a simpler mechanism. The ring network's value in this context is primarily as a proof-of-concept substrate demonstrating that dynamic manifold control mechanisms are portable to neuromorphic hardware and can support closed-loop operation — not that the ring network is functionally necessary for this particular maze task. We will state this clearly. The broader motivation for using the ring network rather than a lookup table is that the framework is designed to scale to more complex motor systems (e.g., multi-degree-of-freedom robots) where the sequential structure of ring activity would provide a richer basis for coordinating complex muscle activation sequences, and where the manifold geometry supports interpretable, compositional control. We will add this discussion while being careful not to overclaim the current demonstration's scope. revision: yes

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; self-citations are to parameter-free analytical results independently confirmed on new hardware.

full rationale

The paper's central derivation chain is self-contained against external benchmarks. The key analytical prediction — arccos(1-p_inh) scaling for subspace angles — is cited from the authors' prior work [12, 13] but is a parameter-free formula that the present paper independently validates on SpiNNaker 2 hardware (Figure 4C), comparing against both the analytical solution and a rate-based CPU baseline. This is not circular: the prior result is a mathematical derivation with stated assumptions that do not include the target hardware, and the present paper provides new empirical confirmation on a different computational substrate. The closed-loop maze application uses a linear readout (Eq. 7) trained via linear regression on random exploration data, which is a standard fitting procedure — the readout is not claimed to be a first-principles prediction but a learned mapping. While the reader and skeptic correctly flag generalization concerns (training on random actions, testing on structured navigation), this is a correctness/robustness risk, not circularity. The self-citations to [12, 13] throughout are used to reference the source of the circuit architecture and analytical predictions being implemented, which is normal attribution of prior work, not a load-bearing circular chain where the present result reduces to the cited premise by construction.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities or postulated mechanisms. All circuit mechanisms (heterogeneous inhibition, gain modulation, transient currents) are from prior work [12, 13]. The deterministic spike rule is an engineering approximation, not a new entity. Free parameters are standard for the model class; the readout weights are fitted to data.

free parameters (4)

Connection sparsity p = 0.2 (closed loop) or 0.5 (validation)
Chosen for SpiNNaker 2 performance; weights scaled by 1/p to compensate.
Weight scaling exponent = Derived from max |W|
Shared 8-bit integer scaling; depends on sparsity and spike frequency compensation.
Readout weights w_left, w_right, w_jump = Trained via linear regression
Fitted to 200 random actions to map smoothed spike signals to motor controls.
Exponential smoothing alpha = Not specified
Used in Eq. 5-6 for spike smoothing; value not stated in the paper.

assumptions (4)

domain assumption The original rate-based ring network model from [12, 13] faithfully captures the relevant circuit mechanisms for manifold control.
The SpiNNaker 2 implementation is validated against this baseline; the framework's correctness depends on the prior model being appropriate.
domain assumption A linear readout from smoothed spike rates is sufficient to decode motor commands.
Eq. 7 assumes motor speeds are linear combinations of smoothed spike signals; no nonlinear decoder is considered.
ad hoc to paper The deterministic spike rule (Eq. 3) approximates stochastic Bernoulli spiking well enough to preserve manifold dynamics.
Introduced for computational efficiency on SpiNNaker 2; validated empirically but no formal bound on approximation error is provided.
domain assumption The world model and high-level plan are assumed given and external to the neuromorphic chip.
Stated in Results: 'we assume that the agent has already learned a world model and focus on translating this world model into motor control.'

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Cite this review

Pith. "Pith review of Dynamic neural manifolds for flexible closed-loop control on neuromorphic hardware." pith.science (2026). https://pith.science/paper/TJBXTAKS

@misc{pith2026260707373,
  author       = {Pith},
  title        = {Pith review of: Dynamic neural manifolds for flexible closed-loop control on neuromorphic hardware},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TJBXTAKS}},
  note         = {Machine review of arXiv:2607.07373}
}

read the original abstract

In biological circuits, sequential neural activity evolves along dynamic, low-dimensional manifolds to enable flexible behavior. Spiking network models link aspects of this sequential activity to features of manifold geometry through specific circuit mechanisms, making dynamic neural manifolds parameterizable, and thereby offering an explainable framework for neural computation. Extending this framework to neuromorphic engineering, we present an implementation on the SpiNNaker 2 chip for real-time, closed-loop control. By allowing sensory inputs to modulate heterogeneous inhibition, gain, and transient currents, our architecture drives rapid subspace rotations to switch between behaviors, as well as fine-grained trajectory control within them. We validate this via a robotic simulation where an agent uses sensory feedback to dynamically reconfigure its manifold geometry to navigate through a maze. Our results establish dynamic manifolds as a feasible approach for explainable neuromorphic architectures and a substrate for investigating biological neural dynamics.

Figures

Figures reproduced from arXiv: 2607.07373 by the authors.

**Figure 1.** Oscillatory sequences on low dimensional manifolds across the brain and spinal cord. Left panels show schematic of experimental setting, middle panels show sequences, right panels show cyclic behavior in state space (A,C,D) or as traces (B). A Rat spinal cord. B Drosophila larvae ganglia. C Turtle spinal cord. D Mouse medial entorhinal cortex. Reproduced under CC BY license from [10, 18, 14, 6]. they undergo dynamic… view at source ↗

**Figure 2.** Implementation overview. A Network architecture. Control neurons (speed, shape, selection) change the activity within a ring network, which can be decoded by downstream readout neurons. B Circulant weight matrix with 50% connection sparsity (weights scaled 2× to compensate). C Sketch of typical activity pattern under varying inputs from control neurons. Control neurons determine the speed of propagation around the r… view at source ↗

**Figure 3.** Reproducing control sequences from [12] on SpiNNaker 2. For our implementation on SpiNNaker 2 we show the spikes that are used in neuron-to-neuron communication and PCA projections, which are computed on the recorded internal rates. Network sizes follow the original figures, we use 50% connection sparsity in all cases. A Shape control. Additive current I is temporarily increased, causing a change in bump width, whi… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Comparison of the original model and the SpiNNaker 2 implementation across ranges of three control parameter values. All experiments use 500 neurons with 20% connectivity and are run for 1000 time steps. Each combination of parameters is tested for 10 trials, with each…

**Figure 5.** Figure 5: Dynamic neural manifolds for closed-loop control in a virtual maze. An external agent program observes the current state and the action plan and selects control parameters for the ring network. Given these parameters and its internal state, the ring network produces ou…

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Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages

[1]

DeepMind Lab

C. Beattie, J. Z. Leibo, D. Teplyashin, T. Ward, M. Wainwright, H. K¨ uttler, A. Lefrancq, S. Green, V. Vald´ es, A. Sadik, J. Schrittwieser, K. Anderson, S. York, M. Cant, A. Cain, A. Bolton, S. Gaffney, H. King, D. Hassabis, S. Legg, and S. Petersen. Deepmind lab.ArXiv, abs/1612.03801, 2016

work page Pith review arXiv 2016
[2]

G. F. Elsayed, A. H. Lara, M. T. Kaufman, M. M. Churchland, and J. P. Cunningham. Re- organization between preparatory and move- ment population responses in motor cortex. Nature communications, 7(1):13239, 2016

work page 2016
[3]

P. Gao, E. Trautmann, B. Yu, G. Santhanam, S. Ryu, K. Shenoy, and S. Ganguli. A theory of multineuronal dimensionality, dynamics and measurement.BioRxiv, page 214262, 2017

work page 2017
[4]

George, R

D. George, R. V. Rikhye, N. Gothoskar, J. S. Guntupalli, A. Dedieu, and M. L´ azaro- Gredilla. Clone-structured graph representa- tions enable flexible learning and vicarious eval- uation of cognitive maps.Nature communica- tions, 12(1):1–17, 2021

work page 2021
[5]

H. A. Gonzalez, J. Huang, F. Kelber, K. K. Nazeer, T. Langer, C. Liu, M. Lohrmann, A. Rostami, M. Sch¨ one, B. Vogginger, T. C. Wunderlich, Y. Yan, M. Akl, and C. Mayr. SpiNNaker2: A Large-Scale Neuromorphic Sys- tem for Event-Based and Asynchronous Ma- chine Learning, 2024

work page 2024
[6]

Gonzalo Cogno, H

S. Gonzalo Cogno, H. A. Obenhaus, A. Lautrup, R. I. Jacobsen, C. Clopath, S. O. Andersson, F. Donato, M.-B. Moser, and E. I. Moser. Minute-scale oscillatory sequences in medial entorhinal cortex.Nature, 625(7994):338–344, 2024

work page 2024
[7]

Mastering Diverse Domains through World Models

D. Hafner, J. Pasukonis, J. Ba, and T. Lillicrap. Mastering diverse domains through world mod- els.arXiv preprint arXiv:2301.04104, 2023

work page Pith review arXiv 2023
[8]

H¨ oppner, Y

S. H¨ oppner, Y. Yan, A. Dixius, S. Scholze, J. Partzsch, M. Stolba, F. Kelber, B. Voggin- ger, F. Neum¨ arker, G. Ellguth, S. Hartmann, S. Schiefer, T. Hocker, D. Walter, G. Liu, J. Garside, S. Furber, and C. Mayr. The 14 SpiNNaker 2 Processing Element Architecture for Hybrid Digital Neuromorphic Computing, Aug. 2022

work page 2022

Show all 29 references

[9]

Jazayeri and S

M. Jazayeri and S. Ostojic. Interpreting neural computations by examining intrinsic and em- bedding dimensionality of neural activity.Cur- rent opinion in neurobiology, 70:113–120, 2021

2021
[10]

S. Komi, J. Kaur, A. Winther, M. C. A. Bonfils, G. A. Houser, R. Sørensen, G. Li, K. Sobriel, and R. W. Berg. Neural manifolds that orches- trate walking and stopping.bioRxiv, 2026

2026
[11]

Langdon, M

C. Langdon, M. Genkin, and T. A. Engel. A unifying perspective on neural manifolds and circuits for cognition.Nature Reviews Neuro- science, pages 1–15, 2023

2023
[12]

A. B. Lehr, A. Kumar, and C. Tetzlaff. Dy- namic control of neural manifolds.bioRxiv, 2024

2024
[13]

A. B. Lehr, A. Kumar, and C. Tetzlaff. Spa- tially heterogeneous inhibition projects sequen- tial activity onto unique neural subspaces. eLife, Nov. 2025

2025
[14]

Lind´ en, P

H. Lind´ en, P. C. Petersen, M. Vestergaard, and R. W. Berg. Movement is governed by ro- tational population dynamics in spinal motor networks.bioRxiv, pages 2021–08, 2021

2021
[15]

Lind´ en, P

H. Lind´ en, P. C. Petersen, M. Vestergaard, and R. W. Berg. Movement is governed by ro- tational neural dynamics in spinal motor net- works.Nature, 610(7932):526–531, 2022

2022
[16]

C. Mayr, S. Hoeppner, and S. Furber. SpiN- Naker 2: A 10 Million Core Processor System for Brain Simulation and Machine Learning. arXiv preprint arXiv:1911.02385, 2019

1911 arXiv
[17]

Pasukonis, T

J. Pasukonis, T. Lillicrap, and D. Hafner. Eval- uating long-term memory in 3d mazes.arXiv preprint arXiv:2210.13383, 2022

2022 arXiv
[18]

S. R. Pulver, T. G. Bayley, A. L. Taylor, J. Berni, M. Bate, and B. Hedwig. Imaging fictive locomotor patterns in larval drosophila. Journal of neurophysiology, 114(5):2564–2577, 2015

2015
[19]

R. V. Raju, J. S. Guntupalli, G. Zhou, C. Wen- delken, M. L´ azaro-Gredilla, and D. George. Space is a latent sequence: A theory of the hippocampus.Science Advances, 10(31):eadm8470, 2024

2024
[20]

A. C. Rodriguez, M. G. Perich, L. E. Miller, and M. D. Humphries. Motor cortex latent dy- namics encode spatial and temporal arm move- ment parameters independently.Journal of Neuroscience, 44(35), 2024

2024
[21]

D. A. Sabatini and M. T. Kaufman. Reach- dependent reorientation of rotational dynam- ics in motor cortex.Nature Communications, 15(1):7007, 2024

2024
[22]

Spreizer, A

S. Spreizer, A. Aertsen, and A. Kumar. From space to time: Spatial inhomogeneities lead to the emergence of spatiotemporal sequences in spiking neuronal networks.PLOS Computa- tional Biology, 15(10):e1007432, Oct. 2019

2019
[23]

T. M. St¨ ober, A. B. Lehr, A. Nikzad, M. Gan- jtabesh, M. Fyhn, and A. Kumar. Competition and cooperation of assembly sequences in re- current neural networks.PLOS Computational Biology, 21(9):e1013403, 2025

2025
[24]

C. Tang, R. Herikstad, A. Parthasarathy, C. Libedinsky, and S.-C. Yen. Minimally de- pendent activity subspaces for working memory and motor preparation in the lateral prefrontal cortex.Elife, 9:e58154, 2020

2020
[25]

J. Wang, D. Narain, E. A. Hosseini, and M. Jazayeri. Flexible timing by temporal scal- ing of cortical responses.Nature neuroscience, 21(1):102–110, 2018

2018
[26]

H. O. Wernecke, A. B. Lehr, and A. Kumar. Controlling spatio-temporal sequences of neu- ral activity by local synaptic changes.J. Neu- roscience, 2026

2026
[27]

Wurgaft, C

D. Wurgaft, C. Rager, M. Kowal, V. Shyam, S. Feucht, U. Bhalla, T. Haklay, E. Bigelow, R. Sarfati, T. McGrath, et al. Manifold steering reveals the shared geometry of neural network representation and behavior.arXiv preprint arXiv:2605.05115, 2026. 15

2026 arXiv
[28]

Z. Ye, A. E. Ladd, N. MacKenzie, L. Kolich, A. J. Li, D. Birman, M. S. Bull, T. L. Daigle, B. Tasic, H. Zeng, et al. Brain-wide topo- graphic coordination of rotating waves.Sci- ence, 392(6804):eadx1369, 2026. 16 Dynamic neural manifolds for flexible closed-loop control on neu...

2026
[29]

Red boxes highlight the control parameter ranges used in the closed loop application.AVarying the number of neurons and the connectivity within the network. Both a larger number of neurons and a higher connectivity lead to an increase in runtime per timestep on the SpiNNaker 2...

Pith tools

Reviewed July 9, 2026 · model on record in the stance chip above.

[1] [1]

DeepMind Lab

C. Beattie, J. Z. Leibo, D. Teplyashin, T. Ward, M. Wainwright, H. K¨ uttler, A. Lefrancq, S. Green, V. Vald´ es, A. Sadik, J. Schrittwieser, K. Anderson, S. York, M. Cant, A. Cain, A. Bolton, S. Gaffney, H. King, D. Hassabis, S. Legg, and S. Petersen. Deepmind lab.ArXiv, abs/1612.03801, 2016

work page Pith review arXiv 2016

[2] [2]

G. F. Elsayed, A. H. Lara, M. T. Kaufman, M. M. Churchland, and J. P. Cunningham. Re- organization between preparatory and move- ment population responses in motor cortex. Nature communications, 7(1):13239, 2016

work page 2016

[3] [3]

P. Gao, E. Trautmann, B. Yu, G. Santhanam, S. Ryu, K. Shenoy, and S. Ganguli. A theory of multineuronal dimensionality, dynamics and measurement.BioRxiv, page 214262, 2017

work page 2017

[4] [4]

George, R

D. George, R. V. Rikhye, N. Gothoskar, J. S. Guntupalli, A. Dedieu, and M. L´ azaro- Gredilla. Clone-structured graph representa- tions enable flexible learning and vicarious eval- uation of cognitive maps.Nature communica- tions, 12(1):1–17, 2021

work page 2021

[5] [5]

H. A. Gonzalez, J. Huang, F. Kelber, K. K. Nazeer, T. Langer, C. Liu, M. Lohrmann, A. Rostami, M. Sch¨ one, B. Vogginger, T. C. Wunderlich, Y. Yan, M. Akl, and C. Mayr. SpiNNaker2: A Large-Scale Neuromorphic Sys- tem for Event-Based and Asynchronous Ma- chine Learning, 2024

work page 2024

[6] [6]

Gonzalo Cogno, H

S. Gonzalo Cogno, H. A. Obenhaus, A. Lautrup, R. I. Jacobsen, C. Clopath, S. O. Andersson, F. Donato, M.-B. Moser, and E. I. Moser. Minute-scale oscillatory sequences in medial entorhinal cortex.Nature, 625(7994):338–344, 2024

work page 2024

[7] [7]

Mastering Diverse Domains through World Models

D. Hafner, J. Pasukonis, J. Ba, and T. Lillicrap. Mastering diverse domains through world mod- els.arXiv preprint arXiv:2301.04104, 2023

work page Pith review arXiv 2023

[8] [8]

H¨ oppner, Y

S. H¨ oppner, Y. Yan, A. Dixius, S. Scholze, J. Partzsch, M. Stolba, F. Kelber, B. Voggin- ger, F. Neum¨ arker, G. Ellguth, S. Hartmann, S. Schiefer, T. Hocker, D. Walter, G. Liu, J. Garside, S. Furber, and C. Mayr. The 14 SpiNNaker 2 Processing Element Architecture for Hybrid Digital Neuromorphic Computing, Aug. 2022

work page 2022