A Novel Model for Novelty: Modeling the Emergence of Innovation from Cumulative Culture

Abstract

While the underlying dynamics of active inference communication and cumulative culture have already been formalized, the emergence of novel cultural information from these dynamics has not yet been understood. In this paper, we apply an active Inference framework, informed by genetic speciation, to the emergence of innovation from a population of communicating agents in a cumulative culture. Our model is premised on the idea that innovation emerges from accumulated cultural information when a collective group of agents agree on the legitimacy of an alternative belief to the existing (or- status quo) belief.

Appendices

Appendix A - Methodology for Simulating the Dynamics of Cumulative Culture

1.1 A.1 Simulating the Local Dynamics of Communication

In our model, cultural transmission is cast as the mutual attunement of actively inferring agents to each other’s internal belief states. This builds on a recent formalization of communication as active inference (Friston and Frith 2015) which resolves the problem of hermeneutics, (i.e., provides a model for the way in which people are able to understand each other rather precisely despite lacking direct access to each other’s internal representations of meaning) by appealing to the notion of generalized synchrony as signaling the emergence of a shared narrative to which both interlocutors refer to. In active inference, this shared narrative is attained through the minimisation of uncertainty, or (variational) free energy when both communicating parties employ sufficiently similar generative models. We build on this to suggest that having sufficiently similar generative models allows communicating agents to recombine distinct representations of a belief (expressed as generative models) into one synchronized, shared model of the world (Fig. 2). When we simulate the belief-updating dynamics between interacting agents, the cultural reproduction of a particular idea takes the form of a specific convergence between their respective generative models.

Under this theory, the elementary unit of heritable information takes the form of an internal belief state, held by an agent with a certain probability. When we simulate the belief-updating dynamics between interacting agents, a reproduced cultural belief is carried by the minds (or generative models) of both interlocutors as a site of cultural selection, where it may be further reproduced through the same process. Our simulations of communication involve two active inference agents with distinct generative models and belief claims that engage in communication over a hundred time steps.

1.2 A.2 Simulating the Global Dynamics of Cumulative Culture

Cultural beliefs and practices spread within a society through communication, a process which we have referred to as the local dynamics of cumulative culture. This description is appropriate because the accumulated outcomes of each (local) dyadic interaction collectively determine the degree to which an idea is prevalent in a culture. Moving from local communication dynamics to a degree to which an idea is prevalent in a cumulative culture is what we refer to as the global dynamics of cumulative culture.

In our simulations of a cumulative culture, 50 active inference agents simultaneously engage in local dyadic communication as shown in our first simulation, such that 25 couples are engaged in conversation at every given time step. At the first time step, all agents have relatively similar belief states- referred to as the status quo. When we introduce an agent holding a divergent belief state to that of the status quo in the population, it propagates through it via pseudo-random engagements of agents in dialogue. In a simulated world of actively inferring agents, their individual mental (generative) models are slightly modified with every interlocutor they encounter, as their distinct representations converge to a shared narrative (Constant et al. 2019). The attunement of interlocutor’s to each other’s generative models on the microscale thus translates over time and with multiple encounters into collective free energy minimisation on the macroscale.

Fig. 2.

Communication Coupling Parameters. Our model defines two groups of parameters that couple the internal states of agents: Learning and inference. Perceptual learning (A2) is the learning of associations between emotional valence and belief states that guide the long term actions of our agents who hold and express beliefs. This learning happens at slow time scales, accumulating across multiple interactions and used to modify models over extended periods of exchange. Perceptual Inference (A1) – namely, sensitivity to model evidence – operates on fast time scales and is direct and explicit to agents during dialogue. Importantly, we hypothesized that without precise evidence accumulation, agents would be insensitive to evidence regarding the belief state of the other, and their internal states would not converge.

Appendix B - Generative Model Architecture, Factors and Parameters

In our simulations, agents attempt to convince each other of a cultural belief by utilizing generative models that operate with local information only. For the establishment of such generative models, we will formulate a partially observed Markov decision process (MDP), where beliefs take the form of discrete probability distributions (for more details on the technical basis for MDP’S under an active inference framework, see Hesp 2019).

Under the formalism of a partially observed Markov decision process, active inference entails a particular structure. Typically, variables such as agent’s hidden states (x, s), observable outcomes (o) and action policies (u) are defined, alongside parameters (representing matrices of categorical probability distributions).

2.1 B.1 Perceptual Inference

The first level of this generative model aims to capture how agents process belief claims they are introduced to through conversation with other agents. The perception of others’ beliefs (regarded in active inference as evidence) requires prior beliefs(represented as likelihood mapping A1 about how hidden states (s1) generate sensory outcomes (o). Specifically, our agents predict the likelihood of perceiving evidence toward a particular expressed belief, given that this belief is “the actual state of the world”. Parameterizing an agent's perception of an interlocutor's expression of belief in terms of precision values can be simply understood as variability in agents’ general sensitivity to model evidence. High precisions here correspond to high responsiveness to evidence for a hidden state and low precisions to low responsiveness to evidence. Precisions for each agent were generated from a continuous gamma distribution which is skewed in favor of high sensitivity to evidence on a population level (See Fig. 2 & Fig. 3: Perception).

Fig. 3.

A generative model of communication. Variables are visualized as circles, parameters as squares and concentration parameters as dark blue circles. Visualized on a horizontal line from left to right-states evolve in time. Visualized on a vertical line from bottom to top- parameters build to a hierarchical structure that is in alignment with cognitive functions. Parameters are described to the left of the generative model and variables are described on the right.

2.2 B.2 Anticipation

At this level, our generative model specifies agents’ beliefs about how hidden states (detailed in Appendix A2) evolve over time. State transition probabilities [B1] define a particular value for the volatility of an agent’s meeting selection (s2) and belief expression (s1) [B1]. For each agent, this precision parameter is sampled from a gamma distribution, determining the a priori probability of changing state, relative to maintaining a current state. Note that belief states themselves are defined on the continuous range <0, 1> (i.e., as a probability distribution on a binary state), such that multiplication tends to result in a continuous decay of confidence over time in the absence of new evidence (where the rate of decay is inversely proportional to the precision on B) (See Fig. 3: Anticipation).

2.3 B.3 Action

After perceiving and anticipating hidden belief states in the world, our agents carry out deliberate actions biased towards the minimum of the expected free energy given each action (a lower level generative model for action is detailed in Appendix A4 and A5). At each time point, a policy (U) is chosen out of a set of possible sequences for action. In our simulations, two types of actions are allowed: selecting an agent to meet at each given time point (u2) and selecting a specific belief to express in conversation (u1). The first allowable action holds 50 possible outcomes (one for each agent in the simulation) while the second is expressed on the range <0, 1>, where the extremes correspond to complete confidence in denying or supporting the belief claim, respectively. Each policy under the G matrix specifies a particular combination of action outcomes weighted by its expected negative free energy value and a free energy minimizing policy is chosen (See Fig. 3: Action).

Voluntary Meeting Selection.

While the choice of interlocutor is predetermined in a dyad, our multi-agent simulations required some sophistication in formulating the underlying process behind agents’ selection for a conversational partner (s3) at each of the hundred time points. Building on previous work on active inference navigation and planning (Kaplan and Friston 2018), agents’ meeting selection in our model is represented as a preferred location on a grid, where each cell on the grid represents a possible agent to meet.

We demonstrate the feasibility of incorporating empirical cultural data within an active inference model by incorporating (1) confirmation bias through state-dependent preferences [C], biasing meeting selection through the risk component of expected free energy (G) and (2) novelty seeking through the ambiguity component of expected free energy. The first form of bias reflects the widely observed phenomenon in psychology research that people’s choices tend to be biased towards confirming their current beliefs (Nickerson 1998). The second form of bias reflects the extent to which agents are driven by the minimisation of ambiguity about the beliefs of other agents, driving them towards seeking out agents they have not met yet. For a detailed account on the process of meeting selection in these simulations, the reader is referred to Kastel and Hesp 2021.

2.4 B.4 Perceptual Learning

On this level agents anticipate how core belief states (specified in Appendix A1) might change over time [B2] (Fig. 2.3). This is the highest level of cognitive control, where agents experience learning as a high cognitive function (higher level generative model is detailed in Appendix A3). By talking with other simulated agents and observing their emotional and belief states, our agents learn associations between EV and beliefs via a high level likelihood mapping [A2], (updated via concentration parameter α). The Updating of core belief, based on beliefs expressed by other agents, is detailed in Appendix A7. This learning is important because it provides our agents with certainty regarding the emotional value they can expect from holding the alternative belief to the status quo, which has low precision at the beginning of the simulation (before the population is introduced to an agent proclaiming this belief). The prior P(A) for this likelihood mapping is specified in terms of a Dirichlet distribution.