Structural Drift: The Population Dynamics of Sequential Learning

We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream “teacher” and then pass samples from the model to their downstream “student”. It extends the population dynamics of genetic drift, recasting Kimura's selectively neutral theory as a special case of a generalized drift process using structured populations with memory. We examine the diffusion and fixation properties of several drift processes and propose applications to learning, inference, and evolution. We also demonstrate how the organization of drift process space controls fidelity, facilitates innovations, and leads to information loss in sequential learning with and without memory. Author Summary: Human knowledge is often transmitted orally within a group via a sequence of communications between individuals. The children's game of Telephone is a familiar, simplified version. A phrase is uttered, understood, and then transmitted to another. Genetic information is communicated in an analogous sequential communication chain via replication. We show that the evolutionary dynamics of both problems is a form of genetic drift which accounts for memory in the communication chain. Using this, one can predict the mechanisms that lead to variations in fidelity and to structural innovation.