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Internal representation of task rules by recurrent dynamics: the importance of the diversity of neural responses
Open accessAbstract
Neural activity of behaving animals, especially in the prefrontal cortex, is highly heterogeneous, with selective responses to diverse aspects of the executed task. We propose a general model of recurrent neural networks that perform complex rule-based tasks, and we show that the diversity of neuronal responses plays a fundamental role when the behavioral responses are context-dependent. Specifically, we found that when the inner mental states encoding the task rules are represented by stable patterns of neural activity (attractors of the neural dynamics), the neurons must be selective for combinations of sensory stimuli and inner mental states. Such mixed selectivity is easily obtained by neurons that connect with random synaptic strengths both to the recurrent network and to neurons encoding sensory inputs. The number of randomly connected neurons needed to solve a task is on average only three times as large as the number of neurons needed in a network designed ad hoc. Moreover, the number of needed neurons grows only linearly with the number of task-relevant events and mental states, provided that each neuron responds to a large proportion of events (dense/distributed coding). A biologically realistic implementation of the model captures several aspects of the activity recorded from monkeys performing context-dependent tasks. Our findings explain the importance of the diversity of neural responses and provide us with simple and general principles for designing attractor neural networks that perform complex computation.
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“However, neural responses with combinatorial (mixed) properties are hallmarks of goal-directed cognitive control (Rigotti et al., 2010), and in the context of information selection may embody the bank of knowledge that is necessary for selecting cues.”
From Attention, learning, and the value of information (2012) · cites this paper as Rigotti et al., 2010
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Cites
Cortes, C., & Vapnik, V. (1995) · Machine Learning · doi:10.1007/bf00994018 · Cited by 59,421
Cortes, C., & Vapnik, V. N. (1995) · Machine Learning · doi:10.1023/a:1022627411411 · Cited by 34,565
Reducing the dimensionality of data with neural networks
Hinton, G. E., & Salakhutdinov, R. R. (2006) · Science · doi:10.1126/science.1127647 · Cited by 20,928
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270
An Integrative Theory of Prefrontal Cortex Function
Miller, E. K., & Cohen, J. D. (2001) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.24.1.167 · Cited by 12,803
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
Candès, E. J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.885507 · Cited by 6,809
Introduction to the theory of neural computation
Hertz, J., Krogh, A., & Palmer, R. G. (1994) · Neural Networks · doi:10.1016/0893-6080(94)90014-0 · Cited by 6,410
Maass, W., Natschläger, T., & Markram, H. (2002) · Neural Computation · doi:10.1162/089976602760407955 · Cited by 4,025
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
A learning algorithm for Boltzmann machines
Ackley, D. H., Hinton, G. E., & Sejnowski, T. J. (1985) · Cognitive Science · doi:10.1207/s15516709cog0901_7 · Cited by 3,402
Marr, D. (1969) · The Journal of Physiology · doi:10.1113/jphysiol.1969.sp008820 · Cited by 3,253
Mnemonic coding of visual space in the monkey's dorsolateral prefrontal cortex
Funahashi, S., Bruce, C. J., & Goldman-Rakic, P. S. (1989) · Journal of Neurophysiology · doi:10.1152/jn.1989.61.2.331 · Cited by 2,685
A theory of cerebellar function
Albus, J. S. (1971) · Mathematical Biosciences · doi:10.1016/0025-5564(71)90051-4 · Cited by 2,539
Amit, D. J. (1989) · Cambridge University Press eBooks · doi:10.1017/cbo9780511623257 · Cited by 2,261
Mullin, A., & Rosenblatt, F. F. (1963) · American Mathematical Monthly · doi:10.2307/2312103 · Cited by 2,211
Neuron Activity Related to Short-Term Memory
Fuster, J. M., & Alexander, G. E. (1971) · Science · doi:10.1126/science.173.3997.652 · Cited by 2,085
Circuitry of Primate Prefrontal Cortex and Regulation of Behavior by Representational Memory
Goldman‐Rakic, P. S. (1987) · Comprehensive Physiology · doi:10.1002/cphy.cp010509 · Cited by 1,960
Introduction to the Theory of Neural Computation
Hertz, J., Krogh, A., & Palmer, R. G. (2018) · CRC Press eBooks · doi:10.1201/9780429499661 · Cited by 1,812
Uncertainty, Neuromodulation, and Attention
Yu, A. J., & Dayan, P. (2005) · Neuron · doi:10.1016/j.neuron.2005.04.026 · Cited by 1,774
Neural Mechanisms of Visual Working Memory in Prefrontal Cortex of the Macaque
Miller, E. K., Erickson, C. A., & Desimone, R. (1996) · Journal of Neuroscience · doi:10.1523/jneurosci.16-16-05154.1996 · Cited by 1,474
Synaptic theory of working memory
Mongillo, G., Barak, O., & Tsodyks, M. (2008) · Science · doi:10.1126/science.1150769 · Cited by 1,253
Probabilistic decision making by slow reverberation in cortical circuits
Wang, X.-J. (2002) · Neuron · doi:10.1016/s0896-6273(02)01092-9 · Cited by 1,242
Variability, compensation and homeostasis in neuron and network function
Marder, E., & Goaillard, J.-M. (2006) · Nature Reviews Neuroscience · doi:10.1038/nrn1949 · Cited by 1,212
Zipser, D., & Andersen, R. A. (1988) · Nature · doi:10.1038/331679a0 · Cited by 1,172
Parallel models of associative memory
Heath, R. A. (1982) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(82)90036-0 · Cited by 1,111
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
Single neurons in prefrontal cortex encode abstract rules
Wallis, J. D., Anderson, K. C., & Miller, E. K. (2001) · Nature · doi:10.1038/35082081 · Cited by 1,075
Synaptic reverberation underlying mnemonic persistent activity
Wang, X.-J. (2001) · Trends in Neurosciences · doi:10.1016/s0166-2236(00)01868-3 · Cited by 1,059
The Frontal Lobes and Voluntary Action
Passingham, R. (1993) · doi:10.1093/oso/9780198521853.001.0001 · Cited by 970
Parallel models of associative memory
Hinton, G. E., & Anderson, J. A. (1981) · CERN Document Server (European Organization for Nuclear Research) · Cited by 927
Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates
Brunel, N., & Hakim, V. (1999) · Neural Computation · doi:10.1162/089976699300016179 · Cited by 907
The Complexity of Boolean Functions
Wegener, I. (1987) · Cited by 882
Synaptic basis of cortical persistent activity: the importance of NMDA receptors to working memory
Wang, X.-J. (1999) · The Journal of Neuroscience · doi:10.1523/jneurosci.19-21-09587.1999 · Cited by 859
Neurocomputing: Foundations of Research
Anderson, J. A., & Rosenfeld, E. (1988) · Cited by 851
Neuronal correlates of parametric working memory in the prefrontal cortex
Romo, R., Brody, C. D., Hernández, A., & Lemus, L. (1999) · Nature · doi:10.1038/20939 · Cited by 822
Decision Making in Recurrent Neuronal Circuits
Wang, X.-J. (2008) · Neuron · doi:10.1016/j.neuron.2008.09.034 · Cited by 679
Prefrontal cortex and decision making in a mixed-strategy game
Barraclough, D. J., Conroy, M. L., & Lee, D. (2004) · Nature Neuroscience · doi:10.1038/nn1209 · Cited by 678
Brunel, N., & Wang, X.-J. (2001) · Journal of Computational Neuroscience · doi:10.1023/a:1011204814320 · Cited by 620
Neural Activity in the Primate Prefrontal Cortex during Associative Learning
Asaad, W. F., Rainer, G., & Miller, E. K. (1998) · Neuron · doi:10.1016/s0896-6273(00)80658-3 · Cited by 593
Cascade Models of Synaptically Stored Memories
Fusi, S., Drew, P. J., & Abbott, L. F. (2005) · Neuron · doi:10.1016/j.neuron.2005.02.001 · Cited by 569
Computational Explorations in Cognitive Neuroscience
O’Reilly, R. C., & Munakata, Y. (2000) · The MIT Press eBooks · doi:10.7551/mitpress/2014.001.0001 · Cited by 564
Temporal Association in Asymmetric Neural Networks
Sompolinsky, H., & Kanter, I. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.2861 · Cited by 546
Brunel, N., & Wang, X. (2014) · Journal of Computational Neuroscience · doi:10.1007/s10827-014-0506-8 · Cited by 538
Nieder, A., & Miller, E. K. (2003) · Neuron · doi:10.1016/s0896-6273(02)01144-3 · Cited by 531
Motor conditional associative-learning after selective prefrontal lesions in the monkey
Petrides, M. (1982) · Behavioural Brain Research · doi:10.1016/0166-4328(82)90044-4 · Cited by 499
Role of the Lateral Prefrontal Cortex in Executive Behavioral Control
Tanji, J., & Hoshi, E. (2008) · Physiological Reviews · doi:10.1152/physrev.00014.2007 · Cited by 477
Deficits on conditional associative-learning tasks after frontal- and temporal-lobe lesions in man
Petrides, M. (1985) · Neuropsychologia · doi:10.1016/0028-3932(85)90062-4 · Cited by 437
Spatial Transformations in the Parietal Cortex Using Basis Functions
Pouget, A., & B, T. J. S. A. (1997) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.1997.9.2.222 · Cited by 437
Learning algorithms with optimal stability in neural networks
Krauth, W., & Mézard, M. (1987) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/20/11/013 · Cited by 410
The Perceptron: A Model for Brain Functioning. I
Block, H. D. (1962) · Reviews of Modern Physics · doi:10.1103/revmodphys.34.123 · Cited by 401
Active maintenance in prefrontal area 46 creates distractor-resistant memory
Sakai, K., Rowe, J. B., & Passingham, R. E. (2002) · Nature Neuroscience · doi:10.1038/nn846 · Cited by 390
Computational approaches to sensorimotor transformations
Pouget, A., & Snyder, L. H. (2000) · Nature Neuroscience · doi:10.1038/81469 · Cited by 357
Memory without Feedback in a Neural Network
Goldman, M. S. (2009) · Neuron · doi:10.1016/j.neuron.2008.12.012 · Cited by 342
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
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 252
A Theory of How the Brain Might WorkPreprint
Poggio, T. (1990) · Cold Spring Harbor Symposia on Quantitative Biology · doi:10.1101/sqb.1990.055.01.084 · Cited by 252
Multiple Forms of Short-Term Plasticity at Excitatory Synapses in Rat Medial Prefrontal Cortex
Hempel, C. M., Hartman, K. H., Wang, X.-J., Turrigiano, G. G., & Nelson, S. B. (2000) · Journal of Neurophysiology · doi:10.1152/jn.2000.83.5.3031 · Cited by 229
Mnemonic Function of the Dorsolateral Prefrontal Cortex in Conflict-Induced Behavioral Adjustment
Mansouri, F. A., Buckley, M. J., & Tanaka, K. (2007) · Science · doi:10.1126/science.1146384 · Cited by 215
Prefrontal Cortex Activity Related to Abstract Response Strategies
Genovesio, A., Brasted, P. J., Mitz, A. R., & Wise, S. P. (2005) · Neuron · doi:10.1016/j.neuron.2005.06.006 · Cited by 212
Frontal Networks for Learning and Executing Arbitrary Stimulus-Response Associations
Boettiger, C. A., & D’Esposito, M. (2005) · Journal of Neuroscience · doi:10.1523/jneurosci.3697-04.2005 · Cited by 211
Role of prefrontal cortex in a network for arbitrary visuomotor mapping
Murray, E. A., Bussey, T. J., & Wise, S. P. (2000) · Experimental Brain Research · doi:10.1007/s002210000406 · Cited by 209
Vries, D. P. (2002) · University of Groningen research database (University of Groningen / Centre for Information Technology) · Cited by 197
Representation of Multiple, Independent Categories in the Primate Prefrontal Cortex
Cromer, J. A., Roy, J. E., & Miller, E. K. (2010) · Neuron · doi:10.1016/j.neuron.2010.05.005 · Cited by 196
Mansouri, F. A., Matsumoto, K., & Tanaka, K. (2006) · Journal of Neuroscience · doi:10.1523/jneurosci.5238-05.2006 · Cited by 196
Hierarchical coding for sequential task events in the monkey prefrontal cortex
Sigala, N., Kusunoki, M., Nimmo-Smith, I., Gaffan, D., & Duncan, J. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0802569105 · Cited by 140
Botvinick, M., & Watanabe, T. (2007) · Journal of Neuroscience · doi:10.1523/jneurosci.2110-07.2007 · Cited by 122
Lapish, C. C., Durstewitz, D., Chandler, L. J., & Seamans, J. K. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0804045105 · Cited by 119
Content-addressability and learning in neural networks
Forrest, B. M. (1988) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/21/1/029 · Cited by 113
Frontal latching networks: a possible neural basis for infinite recursion
Treves, A. (2005) · Cognitive Neuropsychology · doi:10.1080/02643290442000329 · Cited by 104
Salinas, E., & Abbott, L. F. (2001) · Progress in brain research · doi:10.1016/s0079-6123(01)30012-2 · Cited by 100
Fast Remapping of Sensory Stimuli onto Motor Actions on the Basis of Contextual Modulation
Salinas, E. (2004) · The Journal of Neuroscience · doi:10.1523/jneurosci.4569-03.2004 · Cited by 77
Neural networks counting chimes.
Amit, D. J. (1988) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.85.7.2141 · Cited by 72
Diversity in the Neuronal Machine
Soltesz, I. (2006) · doi:10.1093/acprof:oso/9780195177015.001.1 · Cited by 68 · cited 2×
“INTRODUCTION Neurons in the mammalian brain are highly heterogeneous (Soltesz, 2005; Marder and Goaillard, 2006) and show diverse responses to sensory stimuli and other events.”
BackgroundBilinearity, rules, and prefrontal cortex
Dayan, P. (2007) · Frontiers in Computational Neuroscience · doi:10.3389/neuro.10.001.2007 · Cited by 67
Memory Activity of LIP Neurons for Sequential Eye Movements Simulated With Neural Networks
Xing, J., & Andersen, R. A. (2000) · Journal of Neurophysiology · doi:10.1152/jn.2000.84.2.651 · Cited by 60
How Informative Are Spatial CA3 Representations Established by the Dentate Gyrus?
Cerasti, E., & Treves, A. (2010) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000759 · Cited by 56
Attractor concretion as a mechanism for the formation of context representations
Rigotti, M., Rubin, D. B. D., Morrison, S. E., Salzman, C. D., & Fusi, S. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2010.01.047 · Cited by 48
Context-dependent selection of visuomotor maps
Salinas, E. (2004) · BMC Neuroscience · doi:10.1186/1471-2202-5-47 · Cited by 37
The storage capacity of Potts models for semantic memory retrieval
Kropff, E., & Treves, A. (2005) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2005/08/p08010 · Cited by 28
Cognitive flexibility and decision‐making in a model of conditional visuomotor associations
Loh, M., & Deco, G. (2005) · European Journal of Neuroscience · doi:10.1111/j.1460-9568.2005.04505.x · Cited by 26
Role of prefrontal cortex in a network for arbitrary visuomotor mapping
Murray, E. A., Bussey, T. J., & Wise, S. P. (2000) · Springer eBooks · doi:10.1007/978-3-642-59794-7_13 · Cited by 12
Maximal Margin Estimation with Perceptron-Like Algorithm
Korzeń, M., & Klęsk, P. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-69731-2_58 · Cited by 6
Superimposed random coding of stimulus-response connections
Greene, P. H. (1965) · Bulletin of Mathematical Biology · doi:10.1007/bf02477276 · Cited by 5
Flagged first, then by citations
2 of the 85 references couldn’t be matched to a known paper.
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- Minsky M. Papert S. (1969). Perceptrons. Cambridge: MIT Press.
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Why neurons mix: high dimensionality for higher cognition
Fusi, S., Miller, E. K., & Rigotti, M. (2016) · Current Opinion in Neurobiology · doi:10.1016/j.conb.2016.01.010 · Cited by 766
Reworking the language network
Fedorenko, E., & Thompson-Schill, S. L. (2014) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2013.12.006 · Cited by 615
Emotion, Cognition, and Mental State Representation in Amygdala and Prefrontal Cortex
Salzman, C. D., & Fusi, S. (2010) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.051508.135256 · Cited by 628
Metadata
- Authors
- Rigotti, M.
- Affiliations
- University of Zurich (CH)
- Corresponding author
- Rigotti, Mattia
- ORCID
- Rigotti, Mattia
- Venue
- Frontiers in Computational Neuroscience
- Publisher
- Frontiers Media SA
- Published
- 2010
- Volume
- 4
- Pages
- 24-24
- ISSN
- 1662-5188 (ISSN-L)
- PMC
- PMC2967380
- OpenAlex
- W2153719229
- Cited by
- 184
- References
- 85
- Citations by year
- 2026: 8 · 2025: 13 · 2024: 19 · 2023: 10 · 2022: 7 · 2021: 17 · 2020: 13 · 2019: 11 · 2018: 6 · 2017: 8 · 2016: 9 · 2015: 8 · 2014: 12 · 2013: 20 · 2012: 8
- FWCI
- 8.12
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- other-oa
- Locations
- Frontiers in Computational Neuroscience (publishedVersion, other-oa)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- Funders
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (106556)
- National Institute of Mental Health (R01MH062349)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory and Neural Mechanisms
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- recurrent neural networks, attractor dynamics, mixed selectivity, prefrontal cortex, context-dependent behavior, random connectivity, distributed coding, dense coding
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