A neural network that finds a naturalistic solution for the production of muscle activity
Open accessAbstract
It remains an open question how neural responses in motor cortex relate to movement. We explored the hypothesis that motor cortex reflects dynamics appropriate for generating temporally patterned outgoing commands. To formalize this hypothesis, we trained recurrent neural networks to reproduce the muscle activity of reaching monkeys. Models had to infer dynamics that could transform simple inputs into temporally and spatially complex patterns of muscle activity. Analysis of trained models revealed that the natural dynamical solution was a low-dimensional oscillator that generated the necessary multiphasic commands. This solution closely resembled, at both the single-neuron and population levels, what was observed in neural recordings from the same monkeys. Notably, data and simulations agreed only when models were optimized to find simple solutions. An appealing interpretation is that the empirically observed dynamics of motor cortex may reflect a simple solution to the problem of generating temporally patterned descending commands.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
A shortcoming of the DNN approach is that it does not predict how an individual neuron causally contributes to behaviour.
“A shortcoming of this approach is that the DNN does not predict how an individual neuron causally contributes to behaviour, making it difficult to interpret the role of the neuron in the sensorimotor transformation.”
From Mapping model units to visual neurons reveals population code for social behaviour (2024) · cites this paper as [2]
The Discussion (page unavailable) says individual-neuron responses rarely resemble muscle activity and warns against interpreting each response as a representation of a meaningful variable. That supports the difficulty of interpreting a neuron's role, but the paper does not say the network cannot predict an individual neuron's causal contribution to behaviour. (LLM, conf=0.84)
Experimental — accuracy not yet measuredSome have gone on to suggest a direct correspondence between cortical circuits and optimized, appropriately regularized, recurrent neural networks.
“Some have gone on to suggest a direct correspondence between cortical circuits and optimized, appropriately regularized (Sussillo et al., 2015), recurrent neural networks (Liao and Poggio, 2016).”
From Toward an integration of deep learning and neuroscience (2016) · cites this paper as Sussillo et al., 2015
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Emergence of simple-cell receptive field properties by learning a sparse code for natural images
Olshausen, B. A., & Field, D. J. (1996) · Nature · doi:10.1038/381607a0 · Cited by 5,694 · see citing works
Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication
Jaeger, H., & Haas, H. (2004) · Science · doi:10.1126/science.1091277 · Cited by 3,811 · see citing works
Neuronal Population Coding of Movement Direction
Georgopoulos, A. P., Schwartz, A. B., & Kettner, R. E. (1986) · Science · doi:10.1126/science.3749885 · Cited by 3,187 · see citing works
Optimal feedback control as a theory of motor coordination
Todorov, E., & Jordan, M. I. (2002) · Nature Neuroscience · doi:10.1038/nn963 · Cited by 3,081 · see citing works
Context-dependent computation by recurrent dynamics in prefrontal cortex
Mante, V., Sussillo, D., Shenoy, K. V., & Newsome, W. T. (2013) · Nature · doi:10.1038/nature12742 · Cited by 1,807 · see citing works
Self-citationNeural population dynamics during reaching
Churchland, M. M., Cunningham, J. P., Kaufman, M. T., Foster, J. D., Nuyujukian, P., Ryu, S. I., & Shenoy, K. V. (2012) · Nature · doi:10.1038/nature11129 · Cited by 1,636 · see citing works
Self-citationRelation of pyramidal tract activity to force exerted during voluntary movement.
Evarts, E. V. (1968) · Journal of Neurophysiology · doi:10.1152/jn.1968.31.1.14 · Cited by 1,258 · see citing works
Generating Coherent Patterns of Activity from Chaotic Neural Networks
Sussillo, D., & Abbott, L. F. (2009) · Neuron · doi:10.1016/j.neuron.2009.07.018 · Cited by 1,092 · see citing works
Self-citationOptimal feedback control and the neural basis of volitional motor control
Scott, S. H. (2004) · Nature reviews. Neuroscience · doi:10.1038/nrn1427 · Cited by 1,073 · see citing works
Cortical Control of Arm Movements: A Dynamical Systems Perspective
Shenoy, K. V., Sahani, M., & Churchland, M. M. (2013) · Annual Review of Neuroscience · doi:10.1146/annurev-neuro-062111-150509 · Cited by 835 · see citing works
Self-citationCortical activity in the null space: permitting preparation without movement
Kaufman, M. T., Churchland, M. M., Ryu, S. I., & Shenoy, K. V. (2014) · Nature Neuroscience · doi:10.1038/nn.3643 · Cited by 831 · see citing works
Self-citationPostspike facilitation of forelimb muscle activity by primate corticomotoneuronal cells
Fetz, E. E., & Cheney, P. D. (1980) · Journal of Neurophysiology · doi:10.1152/jn.1980.44.4.751 · Cited by 754 · see citing works
Anticipatory activity of motor cortex neurons in relation to direction of an intended movement.
Tanji, J., & Evarts, E. (1976) · Journal of Neurophysiology · doi:10.1152/jn.1976.39.5.1062 · Cited by 740 · see citing works
Opening the black box: low-dimensional dynamics in high-dimensional recurrent neural networks
Sussillo, D., & Barak, O. (2013) · Neural Computation · doi:10.1162/neco_a_00409 · Cited by 575 · see citing works
Self-citationLearning Recurrent Neural Networks with Hessian-Free Optimization
Martens, J., & Sutskever, I. (2011) · Cited by 525 · see citing works
Cortical Preparatory Activity: Representation of Movement or First Cog in a Dynamical Machine?
Churchland, M. M., Cunningham, J. P., Kaufman, M. T., Ryu, S. I., & Shenoy, K. V. (2010) · Neuron · doi:10.1016/j.neuron.2010.09.015 · Cited by 506 · see citing works
Self-citationNeural Variability in Premotor Cortex Provides a Signature of Motor Preparation
Churchland, M. M., Yu, B. M., Ryu, S. I., Santhanam, G., & Shenoy, K. V. (2006) · Journal of Neuroscience · doi:10.1523/jneurosci.3762-05.2006 · Cited by 484 · see citing works
Self-citationRobust timing and motor patterns by taming chaos in recurrent neural networks
Laje, R., & Buonomano, D. V. (2013) · Nature Neuroscience · doi:10.1038/nn.3405 · Cited by 454 · see citing works
Direct cortical control of muscle activation in voluntary arm movements: a model
Todorov, E. (2000) · Nature Neuroscience · doi:10.1038/73964 · Cited by 439 · see citing works
Muscle representation in the macaque motor cortex: An anatomical perspective
Rathelot, J.-A., & Strick, P. L. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0602933103 · Cited by 433 · see citing works
Buys, E., LEMON, R. N., Mantel, G. W. H., et al. (1986) · The Journal of Physiology · doi:10.1113/jphysiol.1986.sp016342 · Cited by 418 · see citing works
A central source of movement variability
Churchland, M. M., Afshar, A., & Shenoy, K. V. (2006) · Neuron · doi:10.1016/j.neuron.2006.10.034 · Cited by 393 · see citing works
A NEUROPHYSIOLOGICAL STUDY OF THE PREMOTOR CORTEX IN THE RHESUS MONKEY
Weinrich, M., Wise, S. P., & Mauritz, K.-H. (1984) · Brain · doi:10.1093/brain/107.2.385 · Cited by 373 · see citing works
Direct Cortical Representation of Drawing
Schwartz, A. B. (1994) · Science · doi:10.1126/science.8036499 · Cited by 371 · see citing works
Temporal Complexity and Heterogeneity of Single-Neuron Activity in Premotor and Motor Cortex
Churchland, M. M., & Shenoy, K. V. (2007) · Journal of Neurophysiology · doi:10.1152/jn.00095.2007 · Cited by 356 · see citing works
Self-citationOptimal Control of Transient Dynamics in Balanced Networks Supports Generation of Complex Movements
Hennequin, G., Vogels, T. P., & Gerstner, W. (2014) · Neuron · doi:10.1016/j.neuron.2014.04.045 · Cited by 348 · see citing works
Are movement parameters recognizably coded in the activity of single neurons
Fetz, E. E. (1992) · Behavioral and Brain Sciences · doi:10.1017/s0140525x00072599 · Cited by 312 · see citing works
Computational Aspects of Feedback in Neural Circuits
Maass, W., Joshi, P., & Sontag, E. D. (2005) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0020165 · Cited by 241 · see citing works
Laje, R., & Buonomano, D. V. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1210.2104 · Cited by 226 · see citing works
Do neurons in the motor cortex encode movement direction? An alternative hypothesis
Mussa-Ivaldi, F. A. (1988) · Neuroscience Letters · doi:10.1016/0304-3940(88)90257-1 · Cited by 211 · see citing works
Training Deep and Recurrent Networks with Hessian-Free Optimization
Martens, J., & Sutskever, I. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-35289-8_27 · Cited by 207 · see citing works
From Intention to Action: Motor Cortex and the Control of Reaching Movements
Kalaska, J. F. (2008) · Advances in experimental medicine and biology · doi:10.1007/978-0-387-77064-2_8 · Cited by 195 · see citing works
Inconvenient Truths about neural processing in primary motor cortex
Scott, S. H. (2008) · The Journal of Physiology · doi:10.1113/jphysiol.2007.146068 · Cited by 190 · see citing works
Prediction of Muscle Activity by Populations of Sequentially Recorded Primary Motor Cortex Neurons
Morrow, M. M., & Miller, L. E. (2003) · Journal of Neurophysiology · doi:10.1152/jn.00632.2002 · Cited by 167 · see citing works
Lillicrap, T. P., & Scott, S. H. (2013) · Neuron · doi:10.1016/j.neuron.2012.10.041 · Cited by 157 · see citing works
Roles of Monkey Premotor Neuron Classes in Movement Preparation and Execution
Kaufman, M. T., Churchland, M. M., Santhanam, G., Yu, B. M., Afshar, A., Ryu, S. I., & Shenoy, K. V. (2010) · Journal of Neurophysiology · doi:10.1152/jn.00231.2009 · Cited by 145 · see citing works
Self-citationBifurcations in the learning of recurrent neural networks
Doya, K. (2003) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.1992.230622 · Cited by 139 · see citing works
Goal-Dependent Modulation of Fast Feedback Responses in Primary Motor Cortex
Pruszynski, J. A., Omrani, M., & Scott, S. H. (2014) · Journal of Neuroscience · doi:10.1523/jneurosci.4520-13.2014 · Cited by 133 · see citing works
Cosine Tuning Minimizes Motor Errors
Todorov, E. V. (2002) · Neural Computation · doi:10.1162/089976602753712918 · Cited by 109 · see citing works
Theoretical Considerations for the Analysis of Population Coding in Motor Cortex
Sanger, T. D. (1994) · Neural Computation · doi:10.1162/neco.1994.6.1.29 · Cited by 100 · see citing works
The roles of monkey M1 neuron classes in movement preparation and execution
Kaufman, M. T., Churchland, M. M., & Shenoy, K. V. (2013) · Journal of Neurophysiology · doi:10.1152/jn.00892.2011 · Cited by 87 · see citing works
Self-citationStrategy-Dependent Encoding of Planned Arm Movements in the Dorsal Premotor Cortex
Pearce, T. M., & Moran, D. W. (2012) · Science · doi:10.1126/science.1220642 · Cited by 68 · see citing works
Aflalo, T., & Graziano, M. S. A. (2007) · Journal of Neuroscience · doi:10.1523/jneurosci.3147-06.2007 · Cited by 60 · see citing works
Partial Reconstruction of Muscle Activity From a Pruned Network of Diverse Motor Cortex Neurons
Schieber, M. H., & Rivlis, G. (2006) · Journal of Neurophysiology · doi:10.1152/jn.00544.2006 · Cited by 54 · see citing works
Ajemian, R., Green, A. M., Bullock, D. H., Sergio, L. E., Kalaska, J. F., & Grossberg, S. (2008) · Neuron · doi:10.1016/j.neuron.2008.02.033 · Cited by 48 · see citing works
A Dynamical Basis Set for Generating ReachesPreprint
Churchland, M. M., & Cunningham, J. P. (2014) · Cold Spring Harbor Symposia on Quantitative Biology · doi:10.1101/sqb.2014.79.024703 · Cited by 44 · see citing works
Self-citationHow the Brain Generates Movement
Rokni, U., & Sompolinsky, H. (2011) · Neural Computation · doi:10.1162/neco_a_00223 · Cited by 34 · see citing works
Cortical mechanisms controlling limb movement
Fetz, E. E. (1993) · Current Opinion in Neurobiology · doi:10.1016/0959-4388(93)90165-u · Cited by 28 · see citing works
Hatsopoulos, N. G. (2005) · Journal of Neurophysiology · doi:10.1152/jn.00533.2005 · Cited by 22 · see citing works
Computing reaching dynamics in motor cortex with Cartesian spatial coordinates
Tanaka, H., & B, T. J. S. A. (2012) · Journal of Neurophysiology · doi:10.1152/jn.00279.2012 · Cited by 22 · see citing works
Maier, M. A., Shupe, L., & Fetz, E. E. (2005) · Journal of Computational Neuroscience · doi:10.1007/s10827-005-0899-5 · Cited by 18 · see citing works
Learning invariant features through local space contractionPreprint
Rifai, S., Muller, X., Glorot, X., et al. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1104.4153 · Cited by 16 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
What Is a Cognitive Map? Organizing Knowledge for Flexible Behavior
Behrens, T. E. J., Muller, T. H., Whittington, J. C. R., Mark, S., Baram, A. B., Stachenfeld, K. L., & Kurth-Nelson, Z. (2018) · Neuron · doi:10.1016/j.neuron.2018.10.002 · Cited by 1,055 · see citing works
Computation Through Neural Population Dynamics
Vyas, S., Golub, M. D., Sussillo, D., & Shenoy, K. V. (2020) · Annual Review of Neuroscience · doi:10.1146/annurev-neuro-092619-094115 · Cited by 671 · see citing works
Self-citationReinforcement learning, fast and slow
Botvinick, M., Ritter, S., Wang, J. X., Kurth-Nelson, Z., Blundell, C., & Hassabis, D. (2019) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2019.02.006 · Cited by 667 · see citing works
Song, H. F., Yang, G. R., & Wang, X.-J. (2016) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1004792 · Cited by 281 · see citing works
Deep reinforcement learning and its neuroscientific implications
Botvinick, M., Wang, J. X., Dabney, W., Miller, K. J., & Kurth-Nelson, Z. (2020) · Neuron · doi:10.1016/j.neuron.2020.06.014 · Cited by 269 · see citing works
The neuroconnectionist research programme
Doerig, A., Sommers, R. P., Seeliger, K., Richards, B., Ismael, J., Lindsay, G. W., Kording, K. P., Konkle, T., van Gerven, M. A. J., Kriegeskorte, N., et al. (2023) · Nature Reviews Neuroscience · doi:10.1038/s41583-023-00705-w · Cited by 233 · see citing works
Flexible multitask computation in recurrent networks utilizes shared dynamical motifs
Driscoll, L., Shenoy, K., & Sussillo, D. (2022) · doi:10.1101/2022.08.15.503870 · Cited by 217 · see citing works
Self-citationMotor learning in neurological rehabilitation
Levin, M. F., & Demers, M. (2021) · Disability and Rehabilitation · doi:10.1080/09638288.2020.1752317 · Cited by 198 · see citing works
Motor primitives in space and time via targeted gain modulation in cortical networks
Stroud, J. P., Porter, M. A., Hennequin, G., & Vogels, T. P. (2018) · Nature Neuroscience · doi:10.1038/s41593-018-0276-0 · Cited by 119 · see citing works
Toward an integration of deep learning and neuroscience
Marblestone, A. H., Wayne, G., & Kording, K. P. (2016) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2016.00094 · Cited by 119 · see citing works
Latent Factors and Dynamics in Motor Cortex and Their Application to Brain–Machine Interfaces
Pandarinath, C., Ames, K. C., Russo, A. A., Farshchian, A., Miller, L. E., Dyer, E. L., & Kao, J. C. (2018) · The Journal of Neuroscience · doi:10.1523/jneurosci.1669-18.2018 · Cited by 103 · see citing works
Neural ensemble dynamics in dorsal motor cortex during speech in people with paralysis
Stavisky, S. D., Willett, F. R., Wilson, G. H., Murphy, B. A., Rezaii, P., Avansino, D. T., Memberg, W. D., Miller, J. P., Kirsch, R. F., Hochberg, L. R., et al. (2019) · eLife · doi:10.7554/elife.46015 · Cited by 105 · see citing works
Self-citationAuxiliary Tasks and Exploration Enable ObjectGoal Navigation
Ye, J., Batra, D., Das, A., & Wijmans, E. (2021) · 2021 IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv48922.2021.01581 · Cited by 120 · see citing works
A goal-driven modular neural network predicts parietofrontal neural dynamics during grasping
Michaels, J. A., Schaffelhofer, S., Agudelo-Toro, A., & Scherberger, H. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2005087117 · Cited by 103 · see citing works
Different population dynamics in the supplementary motor area and motor cortex during reaching
Lara, A. H., Cunningham, J. P., & Churchland, M. M. (2018) · Nature Communications · doi:10.1038/s41467-018-05146-z · Cited by 101 · see citing works
Self-citationRotational dynamics in motor cortex are consistent with a feedback controller
Kalidindi, H. T., Cross, K. P., Lillicrap, T. P., Omrani, M., Falotico, E., Sabes, P. N., & Scott, S. H. (2021) · eLife · doi:10.7554/elife.67256 · Cited by 83 · see citing works
Efficient probabilistic inference in generic neural networks trained with non-probabilistic feedback
Orhan, A. E., & Ma, W. J. (2017) · Nature Communications · doi:10.1038/s41467-017-00181-8 · Cited by 77 · see citing works
Neural representational geometry underlies few-shot concept learning
Sorscher, B., Ganguli, S., & Sompolinsky, H. (2022) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2200800119 · Cited by 78 · see citing works
A virtual rodent predicts the structure of neural activity across behaviours
Aldarondo, D., Merel, J., Marshall, J. D., Hasenclever, L., Klibaite, U., Gellis, A., Tassa, Y., Wayne, G., Botvinick, M., & Ölveczky, B. P. (2024) · Nature · doi:10.1038/s41586-024-07633-4 · Cited by 70 · see citing works
Emergent behaviour and neural dynamics in artificial agents tracking odour plumes
Singh, S. H., van Breugel, F., Rao, R. P. N., & Brunton, B. W. (2023) · Nature Machine Intelligence · doi:10.1038/s42256-022-00599-w · Cited by 61 · see citing works
“In recent years, artificial neural networks (ANNs) have gained increasing popularity for modelling and understanding aspects of neural function and animal behaviour including vision 13 , movement 14 and navigation 15,16 .”
BackgroundMapping model units to visual neurons reveals population code for social behaviour
Cowley, B. R., Calhoun, A. J., Rangarajan, N., Ireland, E., Turner, M. H., Pillow, J. W., & Murthy, M. (2024) · Nature · doi:10.1038/s41586-024-07451-8 · Cited by 45 · see citing works
Adversarial Domain Adaptation for Stable Brain-Machine Interfaces
Farshchian, A., Gallego, J. A., Cohen, J. P., Bengio, Y., Miller, L. E., & Solla, S. A. (2018) · arXiv · doi:10.48550/arxiv.1810.00045 · Cited by 48 · see citing works
Lattice physics approaches for neural networks
Bardella, G., Franchini, S., Pani, P., & Ferraina, S. (2024) · iScience · doi:10.1016/j.isci.2024.111390 · Cited by 17 · see citing works
Universality of representation in biological and artificial neural networks
Hosseini, E., Casto, C., Zaslavsky, N., Conwell, C., Richardson, M., & Fedorenko, E. (2024) · doi:10.1101/2024.12.26.629294 · Cited by 10 · see citing works
Subspace communication in the hippocampal–retrosplenial axis
Gonzalez, J., Vöröslakos, M., Aykan, D., Soto, N., Nitzan, N., Swanson, R., Karadas, M., Chen, Z. S., & Buzsáki, G. (2026) · Nature · doi:10.1038/s41586-026-10481-z · Cited by 7 · see citing works
State and capacity in neural models of cognition and consciousness
Wang, P., Liu, H., Ilievski, F., Ganushchak, L., Zou, L., Laureys, S., & Paas, F. (2026) · Trends Open · doi:10.1016/j.treopn.2026.04.004 · Cited by 8 · see citing works
- Authors
- Sussillo, D., Churchland, M. M., Kaufman, M. T., & Shenoy, K. V.
- Affiliations
- Stanford University (US)
- Columbia University Irving Medical Center (US)
- Corresponding author
- Sussillo, David
- Venue
- Nature Neuroscience
- Published
- 2015-06-15
- Volume
- 18
- Issue
- 7
- Pages
- 1025-1033
- ISSN
- 1097-6256 (ISSN-L)
- 1546-1726
- PMC
- PMC5113297
- OpenAlex
- W2102701721
- Cited by
- 598
- References
- 52
- Citations by year
- 2026: 47 · 2025: 72 · 2024: 74 · 2023: 70 · 2022: 47 · 2021: 66 · 2020: 65 · 2019: 56 · 2018: 39 · 2017: 35 · 2016: 21 · 2015: 6
- FWCI
- 20.02
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature Neuroscience (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Cold Spring Harbor Laboratory Institutional Repository (Cold Spring Harbor Laboratory) (submittedVersion)
- Funders
- National Institute of Mental Health (R01 MH93338-02, R01MH093338)
- National Institute of Neurological Disorders and Stroke (DP2NS083037, R01NS076460)
- National Center for Chronic Disease Prevention and Health Promotion (8DP1HD075623)
- Eunice Kennedy Shriver National Institute of Child Health and Human Development (DP1HD075623)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Motor Control and Adaptation
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Engineering › Biomedical Engineering › Muscle activation and electromyography studies
- Keywords
- motor cortex, muscle activity, reaching movements, recurrent neural networks, descending motor commands, motor control, neural dynamics, monkey motor cortex
- MeSH terms
- Animals, Haplorhini, Electromyography, Motor Activity, Motor Cortex, Nerve Net, Neurons, Neural Networks, Computer, Muscle, Skeletal, Electrophysiological Phenomena
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
