Skip to main content

Ideas Worth Spreading: A Free Energy Proposal for Cumulative Cultural Dynamics

  • Conference paper
  • First Online:
Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1524))


While there is a fast growing body of theoretical work on characterizing cumulative culture, quantifiable models underlining its dynamics remain scarce. This paper provides an active-inference formalization and accompanying simulations of cumulative culture in two steps: Firstly, we cast cultural transmission as a bi-directional process of communication that induces a generalized synchrony (operationalized as a particular convergence) between the internal states of interlocutors. Secondly, we cast cumulative culture as the emergence of accumulated modifications to cultural beliefs from the local efforts of agents to converge on a shared narrative.

N. Kastel and C. Hesp--Private authors.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others


  • Aunger, R.: Darwinizing Culture: The Status of Memetics as a Science. Oxford University Press, Oxford (2001)

    Book  Google Scholar 

  • Buskell, A., Enquist, M., Jansson, F.: A systems approach to cultural evolution. Palgrave Commun. 5(1), 1–15 (2019)

    Article  Google Scholar 

  • Bettencourt, L.M., Cintrón-Arias, A., Kaiser, D.I., Castillo-Chávez, C.: The power of a good idea: quantitative modeling of the spread of ideas from epidemiological models. Physica A Stat. Mech. Appl. 364, 513–536 (2006)

    Article  Google Scholar 

  • Clark, H.H., Brennan, S.E.: Grounding in Communication. American Psychological Association, Washington DC (1991)

    Book  Google Scholar 

  • Constant, A., Ramstead, M.J., Veissière, S.P., Friston, K.: Regimes of expectations: an active inference model of social conformity and human decision making. Front. Psychol. 10, 679 (2019)

    Article  Google Scholar 

  • Constant, A., Ramstead, M.J., Veissiere, S.P., Campbell, J.O., Friston, K.J.: A variational approach to niche construction. J. R. Soc. Interface 15(141), 20170685 (2018)

    Article  Google Scholar 

  • Creanza, N., Kolodny, O., Feldman, M.W.: Cultural evolutionary theory: how culture evolves and why it matters. Proc. Natl. Acad. Sci. 114(30), 7782–7789 (2017)

    Article  Google Scholar 

  • Dawkins, R.: Viruses of The Mind. Dennett and his Critics: Demystifying Mind, vol. 13, p. e27 (1993)

    Google Scholar 

  • Dean, L.G., Vale, G.L., Laland, K.N., Flynn, E., Kendal, R.L.: Human cumulative culture: a comparative perspective. Biol. Rev. 89(2), 284–301 (2014)

    Article  Google Scholar 

  • Dunstone, J., Caldwell, C.A.: Cumulative culture and explicit metacognition: a review of theories, evidence and key predictions. Palgrave Commun. 4(1), 1–11 (2018)

    Article  Google Scholar 

  • Echterhoff, G., Higgins, E.T., Levine, J.M.: Shared reality: experiencing commonality with others’ inner states about the world. Perspect. Psychol. Sci. 4(5), 496–521 (2009)

    Article  Google Scholar 

  • Enquist, M., Ghirlanda, S., Eriksson, K.: Modelling the evolution and diversity of cumulative culture. Philos. Trans. Royal Soc. B Biol. Sci. 366(1563), 412–423 (2011)

    Article  Google Scholar 

  • Friston, K., Frith, C.: A duet for one. Conscious. Cogn. 36, 390–405 (2015)

    Article  Google Scholar 

  • Friston, K.J., Frith, C.D.: Active inference, communication and hermeneutics. Cortex 68, 129–143 (2015)

    Article  Google Scholar 

  • Gabora, L.: Meme and variations: a computational model of cultural evolution. In: 1993 Lectures in Complex Systems, pp. 471–485. Addison Wesley, Boston (1995)

    Google Scholar 

  • Hesp, C., Ramstead, M., Constant, A., Badcock, P., Kirchhoff, M., Friston, K.: A multi-scale view of the emergent complexity of life: a free-energy proposal. In: Evolution, Development and Complexity, pp. 195–227. Springer, Cham (2019).

  • Kaplan, R., Friston, K.J.: Planning and navigation as active inference. Biol. Cybern. 112(4), 323–343 (2018)

    Article  MathSciNet  Google Scholar 

  • Kashima, Y., Bain, P.G., Perfors, A.: The psychology of cultural dynamics: What is it, what do we know, and what is yet to be known? Annu. Rev. Psychol. 70, 499–529 (2019)

    Article  Google Scholar 

  • Pikovsky, A., Kurths, J., Rosenblum, M., Kurths, J.: Synchronization: A Universal Concept in Nonlinear Sciences (No. 12). Cambridge University Press, Cambridge (2003)

    Google Scholar 

  • Richerson, P.J., Boyd, R., Henrich, J.: Gene-culture coevolution in the age of genomics. Proc. Natl. Acad. Sci. 107(Supplement 2), 8985–8992 (2010)

    Article  Google Scholar 

  • Stout, D., Hecht, E.E.: Evolutionary neuroscience of cumulative culture. Proc. Natl. Acad. Sci. 114(30), 7861–7868 (2017)

    Article  Google Scholar 

  • Weisbuch, M., Pauker, K., Ambady, N.: The subtle transmission of race bias via televised nonverbal behavior. Science 326(5960), 1711–1714 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Appendix A Generative Model Architecture, Factors and Parameters

Appendix A Generative Model Architecture, Factors and Parameters

1.1 A.1 Higher Level Hidden State Factors

1.2 A.2 Lower Level Hidden State Factors (Specify Events on a Given ‘Day’)

A.3 Higher level generative model

1.3 A.4 Lower Level Generative Model For Action

Action model for meeting selection

In our simulations, we have incorporated psychological biases in agents’ preferences for meeting similar (i.e., belief compatible) or unknown agents. Note that while agents biased toward confirming beliefs would tend toward individuals with similar beliefs to their own, novelty seekers would not look for the opposite of this (i.e. look for individuals of divergent beliefs to their own), but rather have a preference for individuals of yet unknown beliefs.

In active inference, action selection is guided by the expected free energy [G], which entails maximising the expected benefit or utility of an action (known as pragmatic value), while also maximising the potential information gain of future actions by reducing uncertainty about the causes of valuable outcomes (known as epistemic value). These constraints to action selection could be interpreted as formalising the exploration–exploitation trade-off in learning systems. Epistemic value (exploration) refers to the benefit related to searching over a sample space in order to get a better estimation of promising areas that will maximise pragmatic value (exploitation). Active-inference agents would therefore maximise epistemic value until information gain is low, after which the maximisation of pragmatic value and exploitation are assured (Friston et al. 2015).

In our model, agents’ choice in meeting interlocutors with known and similar beliefs versus those with unknown beliefs can be cast in terms of a tradeoff between pragmatic and epistemic value. On the one hand, a confirmation bias emerges from the maximisation of expected utility, increasing synchronisation between interlocutors’ internal models, thus allowing for the emergence of shared expectations (Hesp et al. 2019). On the other hand, novelty seeking emerges from the maximisation of information gain, allowing for the exploration of the sample space. Also understood as intrinsically motivated curious behaviour (Friston et al. 2017), maximisation of epistemic value allows individuals to better predict the consequences of their actions (e.g., which agent to meet) through greater certainty about the hidden states of their environment (e.g., the beliefs of other agents).

From the point of view of agents in our simulations, increasing pragmatic value translates into selecting to meet interlocutors with similar beliefs, while increasing epistemic value translates into selecting agents whose beliefs are unknown or highly uncertain (This way, a meeting increases information gain). From this point of view, it is clear the two values constrain each other and maximizing both simultaneously is partially (but not entirely) paradoxical. While maximising pragmatic value requires agents to choose to meet with an interlocutor they know is similar to them, maximising epistemic value necessitates they meet with one they do not know at all.

$$ \begin{gathered} \,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;P\left( {u_{loc} } \right) =\upsigma \left( { -\upgamma _{G,loc} G_{loc} +\upgamma _{E,loc} E_{loc} } \right) \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;G_{loc} = o_{u,belief} \cdot \left( {{\text{ln}}\,o_{u,belief} - C_{belief} } \right) + H \cdot x_{u,2,visit} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x_{u,2}^{\left( 1 \right)} = B_{u}^{\left( 1 \right)} x_{1}^{\left( 1 \right)} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,o_{u,belief} = A_{belief}^{\left( 1 \right)} x_{u,2}^{\left( 1 \right)} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;c_{beleif} = {\text{In}}\left( {A_{C}^{\left( 2 \right)} x_{core}^{\left( 2 \right)} } \right) \hfill \\ \end{gathered} $$
$$ \begin{gathered} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;if\,x_{visit,j} = 1; \hfill \\ {\text{[equal}}\,{1}\,{\text{if}}\,{\text{agent}}\,{\text{visited}}\,{\text{a}}\,{\text{particular}}\,{\text{agent}}\,j{]} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\,\;\;\;\;\;\;\;\;H_{j} = 0 \hfill \\ {\text{[ambiguity}}\,{\text{is}}\,{\text{zero}}\,{\text{if}}\,{\text{agent}}\,{\text{visited}}\,{\text{this}}\,{\text{agent}}\,j\,{\text{already]}}\;else: \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;H_{j} = 0.1 \hfill \\ {\text{[ambiguity}}\,{\text{is}}\,{\text{non - zero}}\,{\text{if}}\,{\text{agent}}\,{\text{has}}\,{\text{not}}\,{\text{visited}}\,{\text{agent}}\,j\,{\text{yet]}} \hfill \\ \end{gathered} $$

1.4 A6. Generative Process

Generative process for meeting selection

$$ u_{loc} \sim P\left( {u_{loc} } \right)[actual\,meeting\,u_{loc} \,is\,sampled\,from\,meeting\,selection\,prior\,P\left( {u_{loc} } \right)] $$

Generative process for belief expression and EV (satisfaction) of each agent

At a high level of cognitive control, agents incorporate a series of processes underlying the selection of a particular belief for expression (u2). Other than the partial reliance on a low level habitual factor [E], this action involves multiple higher order considerations.

First, an agent considers their core belief state (x), and the way this state apriori maps on to one of two discrete emotional valence states (s2) via an initial likelihood mapping [A2] Emotional Valence (EV) is defined as the extent to which an emotion is positive or negative (Feldman Barrett and Russell 1999), such that agents’ core beliefs are apriori associated with either positive emotional valence or negative emotional valence (with some probability). As a minimal form of vicarious learning, the initial mapping is further updated based on associations agents observe between their interlocutors’ expressed belief state and EV value The initial mapping therefore involves minimal precision for the expected EV for belief 2, since agents are first introduced to this belief (and associated EV) during the simulations. For this reason, the initial likelihood mapping between states is updated throughout our simulation via a crucial concentration parameter (α).

EV states are generated from core belief states, using a (learnable) likelihood mapping:

$$ x_{sat}^{\left( 1 \right)} = A_{sat}^{\left( 2 \right)} x_{core}^{\left( 2 \right)} $$

Confidence of belief expression is generated using a Gamma distribution, where the rate parameter expris the Bayesian model average of (+, –) values associated with high and low satisfaction:

$$ \begin{gathered} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;P\left( {\upgamma _{expr} } \right) \approx \Gamma \left( {1,\upbeta _{expr} } \right) \hfill \\\upbeta _{expr} =\upbeta ^{{\left( { + , - } \right)}} \cdot x_{sat}^{\left( 1 \right)} ,\;\;\;\;\;\;\;\;\;\;\;\;\;\upbeta ^{{\left( { + , - } \right)}} = [0.25,2.0] \hfill \\ \end{gathered} $$

The expression of beliefs is guided by current core beliefs (scaled with satisfaction-dependent expr) and by habitual belief expression Eexpr (scaled with a fixed parameter E,expr):

$$ P\left( {u_{expr} \left| {\upgamma _{expr} } \right.} \right) = \sigma \left( { -\upgamma _{expr} {\text{ln}}\,x_{core}^{\left( 2 \right)} +\upgamma _{E,expr} E_{expr} } \right) $$

The intrinsically stochastic and itinerant nature of the generative process of communication is modeled by using a two-dimensional Dirichlet distribution to generate observed expressions on the range [0,1], where each agent’s belief expression prior Puexpr|expr is used to specify their concentration parameters (multiplied by 12 to reduce variance):

$$ o_{expr} = Dir\left( {12u_{expr} } \right) $$

Generative process for emotional valence expressed by each agent

$$ \begin{gathered} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;o_{sat} = A_{sat}^{\left( 1 \right)} x_{sat}^{\left( 1 \right)} \hfill \\ [satisfication\,observed\,by\,interaction\,partner\,corresponds\,to\,actual\,satisfaction] \hfill \\ \end{gathered} $$

The EV state predicted is then used to generate an action confidence value (γ) such that positive EV generates high confidence in a certain expression of the belief state (u1) and negative EV generates low confidence values. Higher confidence values produce higher precision on the expected free energy (G) for one’s belief expressed in the current conversation.

1.5 A7. Perception

Updating beliefs about the other agent’s belief based on their expression

$$ Q\left( {x_{belief}^{\left( 1 \right)} } \right) = o_{expr} $$

Updating of core belief based on beliefs expressed by other agents

$$ Q\left( {x_{core}^{\left( 2 \right)} } \right) =\upsigma \left( {{\text{ln}}\,ln\,x_{core}^{\left( 2 \right)} +\upgamma _{A,self}^{\left( 2 \right)} \,{\text{ln}}\,ln\,o_{expr,self} +\upgamma _{A,other}^{\left( 2 \right)} \,{\text{ln}}\,ln\,o_{expr,other} } \right) $$

1.6 A8. Learning

Habit learning for meeting selection

$$ \begin{gathered} \;\;\;\;\;P\left( {E_{loc} } \right) = Dir\left( {e_{loc} } \right) \hfill \\ Q\left( {E_{loc} } \right) = Dir\left( {e_{loc} + 0.05u_{loc} } \right) \hfill \\ \end{gathered} $$

Habit learning for belief expression

$$ \begin{gathered} \;\;\;\;P\left( {E_{expr} } \right) = Dir\left( {e_{expr} } \right) \hfill \\ Q\left( {E_{expr} } \right) = Dir\left( {e_{expr} } \right) + 0.1o_{expr} \hfill \\ \end{gathered} $$

Perceptual learning for the mapping between satisfaction and core beliefs, based on the expressions of other agents

$$ \begin{gathered} \,\,\,\;\;\;\;\;P\left( {A_{sat}^{\left( 2 \right)} } \right) = Dir\left( {a_{sat}^{\left( 2 \right)} } \right) \hfill \\ Q\left( {A_{sat}^{\left( 2 \right)} } \right) = Dir\left( {a_{sat}^{\left( 2 \right)} +\upgamma _{A}^{\left( 2 \right)} o_{expr} \,{\text{ln}}\,ln\,x_{sat}^{\left( 1 \right)} } \right) \hfill \\ \end{gathered} $$

1.7 A9. Initialisation of Parameters for Each Agent

$$ \begin{aligned} & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \gamma _{{A,belief}}^{{(2)}} \sim \Gamma (5,6) \\ & [regulates\,the\,integration\,of\,beliefs\,of\,other\,agents\,in\,one's\,own\,core\,belief] \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \gamma _{{A,sat}}^{{(2)}} \sim \Gamma (10,1) \\ & \begin{array}{*{20}l} {\left[ {regulates\,learning\,rate\,of\,mappings\,between\,satisfaction\,and\,core\,belief\,based\,on\,observed} \right.} \hfill \\ {\left. {correspondences\,in\,other\,agents} \right]} \hfill \\ \end{array} \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \gamma _{{G,loc}} \sim \Gamma (1,1) \\ & [regulates\,reliance\,on\,action\,model\,in\,selecting\,agent\,to\,meet] \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \gamma _{{E,loc}} \sim \Gamma (1,1) \\ & [regulates\,reliance\,on\,habitual\,prior\,in\,selecting\,agent\,to\,meet] \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \rm{\gamma }_{{E,expr}} \sim N\left( {\frac{{\rm{\gamma }_{{E.scc}} }}{{10}},\frac{{\rm{\gamma }_{{E.loc}} }}{{200}}} \right) \\ & [regulates\,reliance\,on\,habitual\,prior\,in\,expressing\,action,which\,correlates\,with\,\left. {\gamma _{{E,loc}} } \right] \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \gamma _{{B,core}}^{{(2)}} \sim \Gamma (4,.5) \\ & [regulates\,stability\,of\,core\,beliefs\,across\,days] \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \gamma _{{B,habits}}^{{(2)}} \sim \Gamma (.5,1) \\ & [regulates\,stability\,of\,expression\,habits\,across\,days] \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad B_{0}^{{(2)}} = [[.75,.25],[.25,.75]] \\ & [specifies\,baseline\,transition\,probabilities] \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad B^{{(2)}} = \rm{\sigma }\left( {\rm{\gamma }_{B}^{{(2)}} \ln B_{0}^{{(2)}} } \right) \\ & [corrects\,B_{0}^{{(2)}} \,using\,the\,agent - specific\,\rm{\gamma }_{B}^{{(2)}} \,values] \\ \end{aligned} $$
$$ \begin{aligned} & Agents\,with\,relatively\,weak\,confirmation\,bias: \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad A_{C}^{{(2)}} \sim Dir(6,4) \\ & [induces\,weak\,reliance\,on\,core\,beliefs\,for\,specifying\,lower{\text{-}}level\,preferences] \\ & Agents\,with\,relatively\,strong\,confirmation\,bias: \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad A_{{C,1}}^{{(2)}} \sim Dir(999,1) \\ & [induces\,strong\,reliance\,on\,core\,beliefs\,for\,specifying\,lower{\text{-}}level\,preferences] \\ \end{aligned} $$

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kastel, N., Hesp, C. (2021). Ideas Worth Spreading: A Free Energy Proposal for Cumulative Cultural Dynamics. In: Kamp, M., et al. Machine Learning and Principles and Practice of Knowledge Discovery in Databases. ECML PKDD 2021. Communications in Computer and Information Science, vol 1524. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-93735-5

  • Online ISBN: 978-3-030-93736-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics