Generating Coherent Patterns of Activity from Chaotic Neural Networks
Open accessAbstract
Neural circuits display complex activity patterns both spontaneously and when responding to a stimulus or generating a motor output. How are these two forms of activity related? We develop a procedure called FORCE learning for modifying synaptic strengths either external to or within a model neural network to change chaotic spontaneous activity into a wide variety of desired activity patterns. FORCE learning works even though the networks we train are spontaneously chaotic and we leave feedback loops intact and unclamped during learning. Using this approach, we construct networks that produce a wide variety of complex output patterns, input-output transformations that require memory, multiple outputs that can be switched by control inputs, and motor patterns matching human motion capture data. Our results reproduce data on premovement activity in motor and premotor cortex, and suggest that synaptic plasticity may be a more rapid and powerful modulator of network activity than generally appreciated.
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 recurrent neural network is difficult to train and control because it may exhibit chaotic behavior.
“A recurrent neural network is also known to be difficult to train and control because it may exhibit chaotic behavior (Sompolinsky et al., 1988; Sussillo and Abbott, 2009; Laje and Buonomano, 2013; Ben-Shushan and Tsodyks, 2017).”
From The Cerebro-Cerebellum as a Locus of Forward Model: A Review (2020) · cites this paper as Sussillo and Abbott, 2009
The FORCE learning algorithm generates stable patterns of activity in a recurrent neural network by adding feedback connections from the output unit to recurrent units.
“In line with our proposal, the FORCE learning algorithm generates stable patterns of activity in a recurrent neural network by adding feedback connections from the output unit to recurrent units (Sussillo and Abbott, 2009).”
From The Cerebro-Cerebellum as a Locus of Forward Model: A Review (2020) · cites this paper as Sussillo and Abbott, 2009
The search for biologically plausible forms of backpropagation has already led to insights such as random feedback weights (feedback alignment) and the unexpected power of internal FORCE learning in chaotic, spontaneously active recurrent networks.
“Moreover, the search for biologically plausible forms of backpropagation has already led to interesting insights, such as the possibility of using random feedback weights (feedback alignment) in backpropagation (Lillicrap et al., 2014), or the unexpected power of internal FORCE learning in chaotic, spontaneously active recurrent networks (Sussillo and Abbott, 2009).”
From Toward an integration of deep learning and neuroscience (2016) · cites this paper as Sussillo and Abbott, 2009
A randomly connected circuit model, akin to a 'reservoir' network, can reproduce the observed distribution of timescales, provided that the network operates at the critical point (or 'edge of chaos').
“Finally, we show that a randomly connected circuit model, akin to a “reservoir” network13-15, can reproduce the observed distribution of timescales, provided that the network operates at the critical point (or “edge of chaos”)16-18.”
From A reservoir of time constants for memory traces in cortical neurons (2011) · cites this paper as [16]
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
Learning Internal Representations by Error Propagation
Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1985) · doi:10.21236/ada164453 · Cited by 16,501 · see citing works
A fast learning algorithm for deep belief nets
Hinton, G. E., Osindero, S., & Teh, Y.-W. (2006) · Neural Computation · doi:10.1162/neco.2006.18.7.1527 · Cited by 16,336 · see citing works
Advances in Neural Information Processing Systems 19
(2007) · The MIT Press eBooks · doi:10.52202/085713 · Cited by 16,037 · see citing works
Haykin, S. (1986) · Cited by 12,603 · see citing works
Advances in Neural Information Processing Systems 14
(2002) · The MIT Press eBooks · doi:10.7551/mitpress/1120.001.0001 · Cited by 9,184 · see citing works
Strogatz, S. H. (1998) · doi:10.1142/3481 · Cited by 4,542 · see citing works
A Learning Algorithm for Continually Running Fully Recurrent Neural Networks
Williams, R. J., & Zipser, D. (1989) · Neural Computation · doi:10.1162/neco.1989.1.2.270 · Cited by 4,369 · see citing works
Maass, W., Natschläger, T., & Markram, H. (2002) · Neural Computation · doi:10.1162/089976602760407955 · Cited by 4,025 · 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
Bellanger, M. (1987) · Signal Processing · doi:10.1016/0165-1684(87)90147-2 · Cited by 2,976 · see citing works
Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity
van Vreeswijk, C., & Sompolinsky, H. (1996) · Science · doi:10.1126/science.274.5293.1724 · Cited by 1,831 · see citing works
Pajevic, S. (1995) · Journal of Statistical Physics · doi:10.1007/bf02180148 · Cited by 1,419 · see citing works
Is the cerebellum a Smith predictor?
Miall, R. C., Weir, D. J., Wolpert, D. M., & Stein, J. F. (1993) · Journal of Motor Behavior · doi:10.1080/00222895.1993.9942050 · Cited by 1,071 · see citing works
Chaos in random neural networks
Sompolinsky, H., Crisanti, A., & Sommers, H. J. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.259 · Cited by 1,061 · see citing works
Amit, D. (1997) · Cerebral Cortex · doi:10.1093/cercor/7.3.237 · Cited by 1,061 · see citing works
State-dependent computations: spatiotemporal processing in cortical networks
Buonomano, D. V., & Maass, W. (2009) · Nature reviews. Neuroscience · doi:10.1038/nrn2558 · Cited by 919 · see citing works
Real-Time Computation at the Edge of Chaos in Recurrent Neural Networks
Bertschinger, N., & Natschläger, T. (2004) · Neural Computation · doi:10.1162/089976604323057443 · Cited by 833 · see citing works
Modeling Human Motion Using Binary Latent Variables
Taylor, G. W., Hinton, G. E., & Roweis, S. T. (2007) · The MIT Press eBooks · doi:10.7551/mitpress/7503.003.0173 · Cited by 708 · see citing works
Learning State Space Trajectories in Recurrent Neural Networks
Pearlmutter, B. A. (1989) · Neural Computation · doi:10.1162/neco.1989.1.2.263 · Cited by 657 · see citing works
New results on recurrent network training: unifying the algorithms and accelerating convergence
Atiya, A. F., & Parlos, A. G. (2000) · IEEE Transactions on Neural Networks · doi:10.1109/72.846741 · Cited by 522 · see citing works
Neural 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
Temporal Information Transformed into a Spatial Code by a Neural Network with Realistic Properties
Buonomano, D. V., & Merzenich, M. M. (1995) · Science · doi:10.1126/science.7863330 · Cited by 455 · 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 · cited 3× · see citing works
“Instead, results from our network models suggest that it may be more instructive to study network-wide modes or patterns of activity extracted by principal components analysis of multiunit recordings (Fetz, 1992; Robinson, 1992; Churchland and Shenoy, 2007b ).”
The cortex as a central pattern generator
Yuste, R., MacLean, J. N., Smith, J., & Lansner, A. (2005) · Nature Reviews Neuroscience · doi:10.1038/nrn1686 · Cited by 355 · 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
Memory traces in dynamical systems
Ganguli, S., Huh, D., & Sompolinsky, H. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0804451105 · Cited by 295 · see citing works
Stimulus-dependent suppression of chaos in recurrent neural networks
Rajan, K., Abbott, L. F., & Sompolinsky, H. (2010) · Physical Review E · doi:10.1103/physreve.82.011903 · Cited by 278 · see citing works
Self-citationComputational 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
Delay of movement caused by disruption of cortical preparatory activity.
Churchland, M., & Shenoy, K. (2007) · Journal of Neurophysiology · doi:10.1152/jn.00808.2006 · Cited by 169 · see citing works
Suppressing chaos in neural networks by noise
Molgedey, L., Schuchhardt, J., & Schuster, H. G. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.3717 · Cited by 146 · see citing works
Bifurcations 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
Dynamics of networks of randomly connected excitatory and inhibitory spiking neurons
Brunel, N. (2000) · Journal of Physiology-Paris · doi:10.1016/s0928-4257(00)01084-6 · Cited by 108 · see citing works
Implications of neural networks for how we think about brain function
Robinson, D. A. (1992) · Behavioral and Brain Sciences · doi:10.1017/s0140525x00072563 · Cited by 107 · see citing works
Estimation of parameters in nonlinear systems using balanced synchronization
Abarbanel, H. D. I., Creveling, D. R., & Jeanne, J. M. (2008) · Physical Review E · doi:10.1103/physreve.77.016208 · Cited by 57 · see citing works
Stimulus-dependent suppression of intrinsic variability in recurrent neural networks
Rajan, K., Abbott, L. F., & Sompolinsky, H. (2010) · BMC Neuroscience · doi:10.1186/1471-2202-11-s1-o17 · Cited by 4 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 2
- Rumelhart DE McClelland JL Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Vol. 1, Foundations 1986 MIT Press Cambridge MA
- Sussillo D Learning in chaotic recurrent networks Columbia University Ph.D. Thesis 2009 93 102
Cited by
Sorted by citations
Hippocampal sharp wave-ripple: A cognitive biomarker for episodic memory and planning
Buzsáki, G. (2015) · Hippocampus · doi:10.1002/hipo.22488 · Cited by 1,759 · see citing works
The importance of mixed selectivity in complex cognitive tasks
Rigotti, M., Barak, O., Warden, M. R., Wang, X.-J., Daw, N. D., Miller, E. K., & Fusi, S. (2013) · Nature · doi:10.1038/nature12160 · Cited by 1,639 · see citing works
Dimensionality reduction for large-scale neural recordings
Cunningham, J. P., & Yu, B. M. (2014) · Nature Neuroscience · doi:10.1038/nn.3776 · Cited by 1,219 · see citing works
Stimulus onset quenches neural variability: A widespread cortical phenomenon
Churchland, M. M., Yu, B. M., Cunningham, J. P., Sugrue, L. P., Cohen, M. R., Corrado, G. S., Newsome, W. T., Clark, A. M., Hosseini, P., Scott, B. B., et al. (2010) · Nature Neuroscience · doi:10.1038/nn.2501 · Cited by 1,084 · see citing works
The role of default network deactivation in cognition and disease
Anticevic, A., Cole, M. W., Murray, J. D., Corlett, P. R., Wang, X.-J., & Krystal, J. H. (2012) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2012.10.008 · Cited by 978 · see citing works
Hierarchical process memory: memory as an integral component of information processing
Hasson, U., Chen, J., & Honey, C. J. (2015) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2015.04.006 · Cited by 749 · 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-citationFunctional organization of human sensorimotor cortex for speech articulation
Bouchard, K. E., Mesgarani, N., Johnson, K., & Chang, E. F. (2013) · Nature · doi:10.1038/nature11911 · Cited by 686 · see citing works
Can structure predict function in the human brain?
Honey, C. J., Thivierge, J.-P., & Sporns, O. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2010.01.071 · Cited by 629 · see citing works
A neural network that finds a naturalistic solution for the production of muscle activity
Sussillo, D., Churchland, M. M., Kaufman, M. T., & Shenoy, K. V. (2015) · Nature Neuroscience · doi:10.1038/nn.4042 · Cited by 598 · see citing works
Self-citationRobust neuronal dynamics in premotor cortex during motor planning
Li, N., Daie, K., Svoboda, K., & Druckmann, S. (2016) · Nature · doi:10.1038/nature17643 · Cited by 492 · see citing works
Recurrent network models of sequence generation and memory
Rajan, K., Harvey, C. D., & Tank, D. W. (2016) · Neuron · doi:10.1016/j.neuron.2016.02.009 · Cited by 351 · 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
Not Noisy, Just Wrong: The Role of Suboptimal Inference in Behavioral Variability
Beck, J. M., Ma, W. J., Pitkow, X., Latham, P. E., & Pouget, A. (2012) · Neuron · doi:10.1016/j.neuron.2012.03.016 · Cited by 316 · see citing works
Dendritic spines and distributed circuits
Yuste, R. (2011) · Neuron · doi:10.1016/j.neuron.2011.07.024 · Cited by 298 · see citing works
A reservoir of time constants for memory traces in cortical neurons
Bernacchia, A., Seo, H., Lee, D., & Wang, X.-J. (2011) · Nature Neuroscience · doi:10.1038/nn.2752 · Cited by 292 · see citing works
Continual learning of context-dependent processing in neural networks
Zeng, G., Chen, Y., Cui, B., & Yu, S. (2019) · Nature Machine Intelligence · doi:10.1038/s42256-019-0080-x · Cited by 309 · see citing works
Neural circuits as computational dynamical systems
Sussillo, D. (2014) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2014.01.008 · Cited by 247 · see citing works
Self-citationThe successor representation: Its computational logic and neural substrates
Gershman, S. J. (2018) · The Journal of Neuroscience · doi:10.1523/jneurosci.0151-18.2018 · Cited by 191 · see citing works
Rigotti, M. (2010) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2010.00024 · Cited by 184 · see citing works
The Cerebro-Cerebellum as a Locus of Forward Model: A Review
Tanaka, H., Ishikawa, T., Lee, J., & Kakei, S. (2020) · Frontiers in Systems Neuroscience · doi:10.3389/fnsys.2020.00019 · Cited by 155 · 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
Initial-state-dependent, robust, transient neural dynamics encode conscious visual perception
Baria, A. T., Maniscalco, B., & He, B. J. (2017) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1005806 · 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
“6, including extensions of analytic techniques developed to understand RNNs trained by supervised learning 38,40,83 .”
Learning probabilistic neural representations with randomly connected circuits
Maoz, O., Tkačik, G., Esteki, M. S., Kiani, R., & Schneidman, E. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1912804117 · Cited by 44 · see citing works
Energy consumption analysis for various memristive networks under different learning strategies
Deng, L., Wang, D., Zhang, Z., Tang, P., Li, G., & Pei, J. (2016) · Physics Letters A · doi:10.1016/j.physleta.2015.12.024 · Cited by 41 · see citing works
- Authors
- Sussillo, D., & Abbott, L. F.
- Affiliations
- Columbia University Irving Medical Center (US)
- Corresponding author
- Sussillo, David
- Abbott, L.F.
- Venue
- Neuron
- Publisher
- Elsevier BV
- Published
- 2009-08
- Volume
- 63
- Issue
- 4
- Pages
- 544-557
- ISSN
- 0896-6273 (ISSN-L)
- PMC
- PMC2756108
- OpenAlex
- W2099231026
- Cited by
- 1,092
- References
- 35
- Citations by year
- 2026: 76 · 2025: 81 · 2024: 104 · 2023: 89 · 2022: 74 · 2021: 111 · 2020: 92 · 2019: 99 · 2018: 64 · 2017: 64 · 2016: 66 · 2015: 47 · 2014: 33 · 2013: 29 · 2012: 28
- FWCI
- 10.05
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.elsevier.com/tdm/userlicense/1.0/ (tdm)
- www.elsevier.com/legal/tdmrep-license (tdm)
- www.elsevier.com/open-access/userlicense/1.0/ (vor, 1446 d)
- doi.org/10.15223/policy-017 (stm-asf)
- doi.org/10.15223/policy-037 (stm-asf)
- doi.org/10.15223/policy-012 (stm-asf)
- doi.org/10.15223/policy-029 (stm-asf)
- doi.org/10.15223/policy-004 (stm-asf)
- Locations
- Neuron (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institutes of Health (5-DP1-OD114-02)
- National Institute of Mental Health (MH-58754)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory and Neural Mechanisms
- Keywords
- chaotic neural networks, spontaneous neuronal activity, synaptic plasticity, motor patterns, premotor cortex, motor cortex, feedback loops
- MeSH terms
- Action Potentials, Humans, Neuronal Plasticity, Neural Networks, Computer, Nonlinear Dynamics, Feedback, Physiological
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
