Juan Pablo Neirotti | Searcharxiv

arXiv2016

Consensus formation times in fully connected societies

We developed a statistical mechanics approach to the problem of opinion formation in interacting agents, constrained by a set of social rules, $B$. To provide the agents with an adaptive quality, we represented both the social agents and the social rule by perceptrons. For fully connected societies we find that if the agents' interaction is weak, all agents adapt to the social rule $B$, with which they form a consensus; but if the interaction is sufficiently strong a consensus is built against the established $status$ $quo$. This behavior is observed for all temperatures $T$ and for all values of the agents' interaction parameter $H_{0}$, except in the limit $T\to\infty$ or when the interaction reaches the critical value $H_{0}=1,$ where no consensus is formed. The agents follow a path where, after a time $α_{c},$ they disregard their peers' opinions on socially neutral issues and reach a full consensus at time $α_{d}>α_{c}.$ The measure of time $α$ is proportional to the volume of information provided to the agents.

physics.soc-ph↗

arXiv2002

Dynamical transitions in the evolution of learning algorithms by selection

We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that generates examples. In opposition to concentrating on final results, which would be the natural aim while designing good learning algorithms, we study the evolution process and pay particular attention to the temporal order of appearance of functional structures responsible for the improvements in the learning process, as measured by the generalization capabilities of the resulting algorithms. The effect of such appearances can be described as dynamical phase transitions. The concepts of phenotypic and genotypic entropies, which serve to describe the distribution of fitness in the population and the distribution of symbols respectively, are used to monitor the dynamics. In different runs the phase transitions might be present or not, with the system finding out good solutions, or staying in poor regions of algorithm space. Whenever phase transitions occur, the sequence of appearances are the same. We identify combinations of variables and operators which are useful in measuring experience or performance in rule extraction and can thus implement useful annealing of the learning schedule.

physics.bio-ph↗