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Cited by 55Embodied and Extended CognitionDistributed Control Multi-Agent SystemsEvacuation and Crowd Dynamics

Collective behavior from surprise minimization

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Heins, Conor, Millidge, Beren, Da Costa, Lancelot, Mann, Richard P., Friston, Karl J., Couzin, Iain D.·2024·Proceedings of the National Academy of Sciences
DOI 10.1073/pnas.2320239121PMC PMC11046639
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Abstract

Collective motion is ubiquitous in nature; groups of animals, such as fish, birds, and ungulates appear to move as a whole, exhibiting a rich behavioral repertoire that ranges from directed movement to milling to disordered swarming. Typically, such macroscopic patterns arise from decentralized, local interactions among constituent components (e.g., individual fish in a school). Preeminent models of this process describe individuals as self-propelled particles, subject to self-generated motion and “social forces” such as short-range repulsion and long-range attraction or alignment. However, organisms are not particles; they are probabilistic decision-makers. Here, we introduce an approach to modeling collective behavior based on active inference. This cognitive framework casts behavior as the consequence of a single imperative: to minimize surprise. We demonstrate that many empirically observed collective phenomena, including cohesion, milling, and directed motion, emerge naturally when considering behavior as driven by active Bayesian inference—without explicitly building behavioral rules or goals into individual agents. Furthermore, we show that active inference can recover and generalize the classical notion of social forces as agents attempt to suppress prediction errors that conflict with their expectations. By exploring the parameter space of the belief-based model, we reveal nontrivial relationships between the individual beliefs and group properties like polarization and the tendency to visit different collective states. We also explore how individual beliefs about uncertainty determine collective decision-making accuracy. Finally, we show how agents can update their generative model over time, resulting in groups that are collectively more sensitive to external fluctuations and encode information more robustly.

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  • Canonical collective phenomena-cohesion, milling, and directed motion-emerge when agents minimize surprise about their conspecifics, with real-time model updates coupling individual learning to group-level properties.

    “Canonical collective phenomena-cohesion, milling, and directed motion-have been shown to emerge when agents minimize surprise about their conspecifics, with real-time model updates coupling individual learning to group-level properties (Heins et al., 2024).”

    From Social Reality Construction via Active Inference: Modeling the Dialectic of Conformity and Creativity (2026) · cites this paper as Heins et al., 2024

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Research works printed but not linked: 65

  1. [2]S. Camazine, Self-Organization in Biological Systems (Princeton University Press, 2003).
  2. [3]M. Rubenstein, C. Ahler, R. Nagpal, “Kilobot: A low cost scalable robot system for collective behaviors” in 2012 IEEE International Conference on Robotics and Automation (IEEE, 2012), pp. 3293–3298.
  3. [5]C. W. Reynolds, “Flocks, herds and schools: A distributed behavioral model” in Proceedings of the 14th annual conference on Computer graphics and interactive techniques (1987), pp. 25–34.
  4. [6]T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226 (1995). 10060237
  5. [7]I. D. Couzin, J. Krause, R. James, G. D. Ruxton, N. R. Franks, Collective memory and spatial sorting in animal groups. J. Theor. Biol. 218, 1– 12 (2002). 12297066
  6. [8]J. Toner, Y. Tu, Flocks, herds, and schools: A quantitative theory of flocking. Phys. Rev. E 58, 4828 (1998).
  7. [9]D. J. Sumpter, The principles of collective animal behaviour. Philos. Trans. R. Soc. B: Biol. Sci. 361, 5– 22 (2006). PMC1626537 16553306
  8. [10]E. Bertin, M. Droz, G. Grégoire, Boltzmann and hydrodynamic description for self-propelled particles. Phys. Rev. E 74, 022101 (2006). 17025488
  9. [12]J. E. Herbert-Read, Inferring the rules of interaction of shoaling fish. Proc. Natl. Acad. Sci. U.S.A. 108, 18726– 18731 (2011). 22065759 PMC3219133
  10. [13]D. S. Calovi, Swarming, schooling, milling: Phase diagram of a data-driven fish school model. New J. Phys. 16, 015026 (2014).
  11. [14]A. M. Hein, An algorithmic approach to natural behavior. Curr. Biol. 30, R663– R675 (2020). 32516620
  12. [15]A. K. Fahimipour, Wild animals suppress the spread of socially transmitted misinformation. Proc. Natl. Acad. Sci. U.S.A. 120, e2215428120 (2023). 36976767 PMC10083541
  13. [16]J. Gautrais, Deciphering interactions in moving animal groups. PLoS Comput. Biol. 8, e1002678 (2012). 23028277 PMC3441504
  14. [18]K. J. Friston, J. Daunizeau, S. J. Kiebel, Reinforcement learning or active inference? PLoS ONE 4, e6421 (2009). 19641614 PMC2713351
  15. [20]T. Parr, G. Pezzulo, K. J. Friston, Active Inference: The Free Energy Principle in Mind, Brain, and Behavior (MIT Press, 2022).
  16. [22]K. Friston, A theory of cortical responses. Philos. Trans. R. Soc. B: Biol. Sci. 360, 815– 836 (2005). PMC1569488 15937014
  17. [23]K. Friston, J. Kilner, L. Harrison, A free energy principle for the brain. J. Physiol.-Paris 100, 70– 87 (2006). 17097864
  18. [24]K. Friston, What is optimal about motor control? Neuron 72, 488– 498 (2011). 22078508
  19. [27]R. A. Adams, S. Shipp, K. J. Friston, Predictions not commands: Active inference in the motor system. Brain Struct. Funct. 218, 611– 643 (2013). 23129312 PMC3637647
  20. [28]A. Ali, N. Ahmad, E. de Groot, M. A. J. van Gerven, T. C. Kietzmann, Predictive coding is a consequence of energy efficiency in recurrent neural networks. Patterns 3, 100639 (2022). 36569556 PMC9768680
  21. [29]C. Caucheteux, A. Gramfort, J. R. King, Evidence of a predictive coding hierarchy in the human brain listening to speech. Nat. Hum. Behav. 7, 430– 441 (2023). 36864133 PMC10038805
  22. [30]K. N. Laland, Social learning strategies. Anim. Learn. Behav. 32, 4– 14 (2004). 15161136
  23. [31]P. M. Krafft, Bayesian collective learning emerges from heuristic social learning. Cognition 212, 104469 (2021). 33770743
  24. [32]M. Baltieri, C. L. Buckley, Generative models as parsimonious descriptions of sensorimotor loops. arXiv [Preprint] (2019). 10.1017/S0140525X19001353 (Accessed 4 May 2023). 31775931 · DOI
  25. [33]C. Uran, Predictive coding of natural images by v1 firing rates and rhythmic synchronization. Neuron 110, 1240– 1257.e8 (2022). 35120628 PMC8992798
  26. [34]K. Friston, The free-energy principle: A rough guide to the brain? Trend. Cognit. Sci. 13, 293– 301 (2009). 19559644
  27. [36]K. Friston, A free energy principle for a particular physics. arXiv [Preprint] (2019). 10.48550/arXiv.1906.10184 (Accessed 10 January 2021). · DOI · Paper page
  28. [37]B. Collignon, A. Séguret, J. Halloy, A stochastic vision-based model inspired by zebrafish collective behaviour in heterogeneous environments. R. Soc. Open Sci. 3, 150473 (2016). 26909173 PMC4736928
  29. [38]R. Bastien, P. Romanczuk, A model of collective behavior based purely on vision. Sci. Adv. 6, eaay0792 (2020). 32076645 PMC7002123
  30. [40]K. Friston, J. Mattout, N. Trujillo-Barreto, J. Ashburner, W. Penny, Variational free energy and the Laplace approximation. Neuroimage 34, 220– 234 (2007). 17055746
  31. [41]D. J. MacKay, D. J. Mac Kay, Information Theory, Inference and Learning Algorithms (Cambridge University Press, 2003).
  32. [42]J. F. Jehee, C. Rothkopf, J. M. Beck, D. H. Ballard, Learning receptive fields using predictive feedback. J. Physiol.-Paris 100, 125– 132 (2006). 17067787 PMC2929357
  33. [44]A. Maselli, P. Lanillos, G. Pezzulo, Active inference unifies intentional and conflict-resolution imperatives of motor control. PLoS Comput. Biol. 18, e1010095 (2022). 35714105 PMC9205531
  34. [45]M. Baltieri, C. L. Buckley, PID control as a process of active inference with linear generative models. Entropy 21, 257 (2019). 33266972 PMC7514737
  35. [46]C. L. Buckley, C. S. Kim, S. McGregor, A. K. Seth, The free energy principle for action and perception: A mathematical review. J. Math. Psychol. 81, 55– 79 (2017).
  36. [47]P. Romanczuk, I. D. Couzin, L. Schimansky-Geier, Collective motion due to individual escape and pursuit response. Phys. Rev. Lett. 102, 010602 (2009). 19257176
  37. [48]I. D. Couzin, J. Krause, N. R. Franks, S. A. Levin, Effective leadership and decision-making in animal groups on the move. Nature 433, 513– 516 (2005). 15690039
  38. [50]K. Tunstrøm, Collective states, multistability and transitional behavior in schooling fish. PLoS Comput. Biol. 9, e1002915 (2013). 23468605 PMC3585391
  39. [51]I. Giardina, Collective behavior in animal groups: Theoretical models and empirical studies. HFSP J. 2, 205– 219 (2008). 19404431 PMC2639936
  40. [52]R. Kaufmann, P. Gupta, J. Taylor, An active inference model of collective intelligence. Entropy 23, 830 (2021). 34210008 PMC8306784
  41. [53]C. Heins, B. Klein, D. Demekas, M. Aguilera, C. L. Buckley, “Spin glass systems as collective active inference” in Active Inference: Third International Workshop, IWAI 2022, Grenoble, France, September 19, 2022, Revised Selected Papers (Springer, 2023), pp. 75–98.
  42. [54]M. M. Sosna, Individual and collective encoding of risk in animal groups. Proc. Natl. Acad. Sci. U.S.A. 116, 20556– 20561 (2019). 31548427 PMC6789631
  43. [55]T. Parr, J. Limanowski, V. Rawji, K. Friston, The computational neurology of movement under active inference. Brain 144, 1799– 1818 (2021). 33704439 PMC8320263
  44. [56]J. Buhl, From disorder to order in marching locusts. Science 312, 1402– 1406 (2006). 16741126
  45. [57]I. D. Couzin, Uninformed individuals promote democratic consensus in animal groups. Science 334, 1578– 1580 (2011). 22174256
  46. [58]A. Strandburg-Peshkin, D. R. Farine, I. D. Couzin, M. C. Crofoot, Shared decision-making drives collective movement in wild baboons. Science 348, 1358– 1361 (2015). 26089514 PMC4801504
  47. [59]V. H. Sridhar, The geometry of decision-making in individuals and collectives. Proc. Natl. Acad. Sci. U.S.A. 118, e2102157118 (2021). 34880130 PMC8685676
  48. [60]A. Kolpas, How the spatial position of individuals affects their influence on swarms: A numerical comparison of two popular swarm dynamics models. PLoS ONE 8, e58525 (2013). 23555585 PMC3605438
  49. [61]A. Bizyaeva, A. Franci, N. E. Leonard, Nonlinear opinion dynamics with tunable sensitivity. IEEE Trans. Autom. Control 68, 1415– 1430 (2022).
  50. [62]H. Hamann, “Evolution of collective behaviors by minimizing surprise” in Artificial Life Conference Proceedings (MIT Press One, Cambridge, MA, 2014), pp. 344–351.
  51. [63]T. K. Kaiser, H. Hamann, Innate motivation for robot swarms by minimizing surprise: From simple simulations to real-world experiments. IEEE Trans. Robot. 38, 3582– 3601 (2022).
  52. [64]D. Gandolfi, Emergence of associative learning in a neuromorphic inference network. J. Neural Eng. 19, 036022 (2022). 35508120
  53. [65]K. Friston, Active inference and learning. Neurosci. Biobehav. Rev. 68, 862– 879 (2016). 27375276 PMC5167251
  54. [66]M. H. Hennig, Theoretical models of synaptic short term plasticity. Front. Comput. Neurosci. 7, 45 (2013). 23626536 PMC3630333
  55. [67]A. J. Ward, J. E. Herbert-Read, D. J. Sumpter, J. Krause, Fast and accurate decisions through collective vigilance in fish shoals. Proc. Natl. Acad. Sci. U.S.A. 108, 2312– 2315 (2011). 21262802 PMC3038776
  56. [68]A. Strandburg-Peshkin, Visual sensory networks and effective information transfer in animal groups. Curr. Biol. 23, R709– R711 (2013). 24028946 PMC4780851
  57. [69]J. D. Davidson, Collective detection based on visual information in animal groups. J. R. Soc. Interface 18, 20210142 (2021). 34229461 PMC8261228
  58. [70]R. Harpaz, M. N. Nguyen, A. Bahl, F. Engert, Precise visuomotor transformations underlying collective behavior in larval zebrafish. Nat. Commun. 12, 6578 (2021). 34772934 PMC8590009
  59. [73]A. D. Wissner-Gross, C. E. Freer, Causal entropic forces. Phys. Rev. Lett. 110, 168702 (2013). 23679649
  60. [74]H. Hornischer, S. Herminghaus, M. G. Mazza, Structural transition in the collective behavior of cognitive agents. Sci. Rep. 9, 12477 (2019). 31462661 PMC6713784
  61. [75]D. A. Friedman, A. Tschantz, M. J. Ramstead, K. Friston, A. Constant, Active inferants: An active inference framework for ant colony behavior. Front. Behav. Neurosci. 15, 647732 (2021). 34248515 PMC8264549
  62. [77]P. R. Montague, R. J. Dolan, K. J. Friston, P. Dayan, Computational psychiatry. Trend Cognit. Sci. 16, 72– 80 (2012). PMC3556822 22177032
  63. [79]R. Escobedo, A data-driven method for reconstructing and modelling social interactions in moving animal groups. Philos. Trans. R. Soc. B 375, 20190380 (2020). PMC7423377 32713309
  64. [80]R. K. Mudaliar, T. M. Schaerf, An examination of force maps targeted at orientation interactions in moving groups. PLoS ONE 18, e0286810 (2023). 37676869 PMC10484433
  65. [81]W. D. Penny, J. Mattout, N. Trujillo-Barreto, Bayesian Model Selection and Averaging. Statistical Parametric Mapping: The Analysis of Functional Brain Images (Elsevier, London, UK, 2006).

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Authors
Heins, C., Millidge, B., Da Costa, L., Mann, R. P., Friston, K. J., & Couzin, I. D.
Affiliations
  • University of Konstanz (DE)
  • University of Oxford (GB)
  • VERSES Research Lab, Los Angeles, CA90016
  • University of Leeds (GB)
  • Wellcome Centre for Human Neuroimaging (GB)
Corresponding author
  • Heins, Conor
  • Couzin, Iain D.
ORCID
Venue
Proceedings of the National Academy of Sciences
Publisher
National Academy of Sciences
Published
2024-04-17
Volume
121
Issue
17
Pages
e2320239121-e2320239121
ISSN
  • 0027-8424 (ISSN-L)
  • 1091-6490
DOI
10.1073/pnas.2320239121
PMC
PMC11046639
OpenAlex
W4394874494
Cited by
55
References
9
Citations by year
2026: 19 · 2025: 27 · 2024: 9
FWCI
11.97
Type
journal article
Language
en
Open access
Licence
Locations
  • Proceedings of the National Academy of Sciences (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • White Rose Research Online (University of Leeds, The University of Sheffield, University of York) (acceptedVersion)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • UCL Discovery (University College London) (submittedVersion, cc-by)
  • KOPS (University of Konstanz) (submittedVersion, cc-by)
  • arXiv (Cornell University) (cc-by)
Funders
  • DOD | USN | Office of Naval Research (N0001419-1-2556)
  • Germany’s Excellence Strategy (EXC 2117-422037984)
  • Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant agreement (860949)
  • John Templeton Foundation (61780)
  • Fonds National de la Recherche Luxembourg (13568875)
  • EPSRC Centre for Doctoral Training in Mathematics of Random Systems (EP/S023925/1)
  • UK Research and Innovation Future Leaders Fellowship (MR/S032525/1)
  • Templeton World Charity Foundation (TWCF-2021-20647)
  • Wellcome Centre for Human Neuroimaging (205103/Z/16/Z)
  • Canada-UK Artificial Intelligence Initiative (ES/T01279X/1)
  • European Union’s Horizon 2020 Framework Programme for Research and Innovation under the Specific Grant Agreement (945539)
  • PathFinder European Innovation Council Work Programme (101098722)
Topics
  • Life Sciences › Neuroscience › Cognitive Neuroscience › Embodied and Extended Cognition
  • Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
  • Physical Sciences › Engineering › Ocean Engineering › Evacuation and Crowd Dynamics
Keywords
collective behavior, active inference, surprise minimization, Bayesian inference, self-propelled particles, social forces, milling behavior, directed motion, group polarization, group decision making, generative models
MeSH terms
Animals, Bayes Theorem, Behavior, Animal, Fishes, Mass Behavior, Models, Biological, Motion, Movement, Social Behavior

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