In this talk, we propose to decipher the activity of neural networks via a “multiply and conquer” approach. This approach considers limit networks made of infinitely many replicas with the same basic neural structure. The key point is that these so-called replica-mean-field networks are in fact simplified, tractable versions of neural networks that retain important features of the finite network structure of interest. The finite size of neuronal populations and synaptic interactions is a core determinant of neural dynamics, being responsible for non-zero correlation in the spiking activity and for finite transition rates between metastable neural states. Theoretically, we develop our replica framework by expanding on ideas from the theory of communication networks rather than from statistical physics to establish Poissonian mean-field limits for spiking networks. Computationally, we leverage our original replica approach to characterize the stationary spiking activity of various network models via reduction to tractable functional equations. We conclude by discussing perspectives about how to use our replica framework to probe nontrivial regimes of spiking correlations and transition rates between metastable neural states.

Individuals vary widely in how they categorize novel phenomena. This individual variation has led canonical theories in cognitive and social science to suggest that communication in large social networks leads populations to construct divergent category systems. Yet, anthropological data indicates that large, independent societies consistently arrive at similar categories across a range of topics. How is it possible for diverse populations, consisting of individuals with significant variation in how they view the world, to independently construct similar categories? Through a series of online experiments, I show how large communication networks within cultures can promote the formation of similar categories across cultures. For this investigation, I designed an online “Grouping Game” to observe how people construct categories in both small and large populations when tasked with grouping together the same novel and ambiguous images. I replicated this design for English-speaking subjects in the U.S. and Mandarin-speaking subjects in China. In both cultures, solitary individuals and small social groups produced highly divergent category systems. Yet, large social groups separately and consistently arrived at highly similar categories both within and across cultures. These findings are accurately predicted by a simple mathematical model of critical mass dynamics. Altogether, I show how large communication networks can filter lexical diversity among individuals to produce replicable society-level patterns, yielding unexpected implications for cultural evolution. In particular, I discuss how participants in both cultures readily harnessed analogies when categorizing novel stimuli, and I examine the role of communication networks in promoting cross-cultural similarities in analogy-making as the key engine of category formation.

The talk will detail work drawing on behavioural results, formal analysis, and computational modelling with agent-based simulations to unpack the scale of the challenge humans face when trying to work out and factor in the reliability of their sources. In particular, it is shown how and why this task admits of no easy solution in the context of wider communication networks, and how this will affect the accuracy of our beliefs. The implications of this for the shift in the size and topology of our communication networks through the uncontrolled rise of social media are discussed.