Radial patterns of optical flow produced by observer translation could be used to perceive the direction of self-movement during locomotion, and a number of formal analyses of such patterns have recently appeared. However, there is comparatively little empirical research on the perception of heading from optical flow, and what data there are indicate surprisingly poor performance, with heading errors on the order of 5 degrees-10 degrees. We examined heading judgments during translation parallel, perpendicular, and at oblique angles to a random-dot plane, varying observer speed and dot density. Using a discrimination task, we found that heading accuracy improved by an order of magnitude, with 75%-correct thresholds of 0.66 degrees in the highest speed and density condition and 1.2 degrees generally. Performance remained high with displays of 63-10 dots, but it dropped significantly with only 2 dots; there was no consistent speed effect and no effect of angle of approach to the surface. The results are inconsistent with theories based on the local focus of outflow, local motion parallax, multiple fixations, differential motion parallax, and the local maximum of divergence. But they are consistent with Gibson's (1950) original global radial outflow hypothesis for perception of heading during translation.

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute a posterior distribution over languages by combining a prior (representing their inductive biases) with the evidence provided by linguistic data. We show that when learners sample languages from this posterior distribution, iterated learning converges to a distribution over languages that is determined entirely by the prior. Under these conditions, iterated learning is a form of Gibbs sampling, a widely-used Markov chain Monte Carlo algorithm. The consequences of iterated learning are more complicated when learners choose the language with maximum posterior probability, being affected by both the prior of the learners and the amount of information transmitted between generations. We show that in this case, iterated learning corresponds to another statistical inference algorithm, a variant of the expectation-maximization (EM) algorithm. These results clarify the role of iterated learning in explanations of linguistic universals and provide a formal connection between constraints on language acquisition and the languages that come to be spoken, suggesting that information transmitted via iterated learning will ultimately come to mirror the minds of the learners.

Knowledge partitioning is a theoretical construct holding that knowledge is not always integrated and homogeneous but may be separated into independent parcels containing mutually contradictory information. Knowledge partitioning has been observed in research on expertise, categorization, and function learning. This article presents a theory of function learning (the population of linear experts model-POLE) that assumes people partition their knowledge whenever they are presented with a complex task. The authors show that POLE is a general model of function learning that accommodates both benchmark results and recent data on knowledge partitioning. POLE also makes the counterintuitive prediction that a person's distribution of responses to repeated test stimuli should be multimodal. The authors report 3 experiments that support this prediction.The learning of concepts by induction from examples is fundamental to cognition and ". . .basic to all of our intellectual activities" (Estes, 1994, p. 4). Many concepts are categorical: for example, when a paleontologist learns to classify dinosaurs as birdhipped or lizard-hipped, when an infant learns to label furry four-legged animals as cats or dogs, or when a physician learns to categorize a nevus as benign or potentially cancerous. In these cases, responses are limited to a nominal scale, often consisting of binary response options such as "Category A" or "Category B."However, people often also learn function concepts, in which a continuous stimulus variable is associated with a continuous response variable. For example, one may learn how long to water the lawn as a function of the day's temperature, how driving speed affects stopping distance, what his or her blood alcohol level will be depending on the number of cocktails consumed, and so on. Function concepts thus subsume category concepts as the small subset of cases in which the response scale is nominal rather than continuous. Remarkably, cognitive psychology to date has devoted far more empirical and theoretical attention to categorization than to function concepts as a whole.The purpose of this article is twofold. First, we seek to raise the profile of function concepts by presenting a computational theory of function learning that is based on the idea that people simplify a complex learning task by partitioning it into multiple independent modules. The theory, known as POLE-for population of linear experts-is shown to handle most existing data on function learning. Three new experiments explore some of POLE's counterintuitive predictions and provide additional support for the theory. We show that when people are confronted with uncertainty about which of several competing functions applies to a test stimulus, responding alternates between different learned functions rather than relying on a blend of existing knowledge, thus giving rise to multimodal response distributions.The second purpose of this article is to evaluate an overarching framework for learning and knowledge acquisition, known as knowledge part...

Cultural transmission of information plays a central role in shaping human knowledge. Some of the most complex knowledge that people acquire, such as languages or cultural norms, can only be learned from other people, who themselves learned from previous generations. The prevalence of this process of "iterated learning" as a mode of cultural transmission raises the question of how it affects the information being transmitted. Analyses of iterated learning utilizing the assumption that the learners are Bayesian agents predict that this process should converge to an equilibrium that reflects the inductive biases of the learners. An experiment in iterated function learning with human participants confirmed this prediction, providing insight into the consequences of intergenerational knowledge transmission and a method for discovering the inductive biases that guide human inferences.

The authors explored the phenomenon that knowledge is not always integrated and consistent but may be partitioned into independent parcels that may contain mutually contradictory information. In 4 experiments, using a function learning paradigm, a binary context variable was paired with the continuous stimulus variable of a to-be-learned function. In the first 2 experiments, when context predicted the slope of a quadratic function, generalization was context specific. Because context did not predict function values, it is suggested that people use context to gate separate learning of simpler partial functions. The 3rd experiment showed that partitioning also occurs with a decreasing linear function, whereas the 4th study showed that partitioning is absent for a linearly increasing function. The results support the notion that people simplify complex learning tasks by acquiring independent parcels of knowledge.