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.

Theories of how people learn relationships between continuous variables have tended to focus on two possibilities: one, that people are estimating explicit functions, or two that they are performing associative learning supported by similarity. We provide a rational analysis of function learning, drawing on work on regression in machine learning and statistics. Using the equivalence of Bayesian linear regression and Gaussian processes, which provide a probabilistic basis for similarity-based function learning, we show that learning explicit rules and using similarity can be seen as two views of one solution to this problem. We use this insight to define a rational model of human function learning that combines the strengths of both approaches and accounts for a wide variety of experimental results. Keywords A rational model of function learningEvery time we get into a rental car, we have to learn how hard to press the gas pedal for a given amount of acceleration. Solving this problem-which is an important part of driving safely-requires learning a relationship between two continuous variables. Over the past 50 years, several studies of function learning have shed light on how people come to understand continuous relationships (Carroll 1963;Brehmer 1971;1974;Koh and Meyer 1991;Busemeyer et al. 1997;DeLosh et al. 1997;Kalish et al. 2004;McDaniel and Busemeyer 2005). It has become clear that people can learn and recall a wide variety of relationships, but demonstrate certain systematic biases that tell us about the mental representations and implicit assumptions that humans employ when solving function learning problems. For example, people tend to expect that relationships will be linear when extrapolating to novel examples , and find it more difficult to learn relationships that change direction than those that do not (Brehmer 1974;Byun 1995).Several models have been developed to understand the cognitive mechanisms behind function learning. These models tend to fall into two different theoretical camps. The first includes rule-based theories (e.g., Carroll, 1963, Brehmer, 1974, Koh and Meyer, 1991, which suggest that people learn an explicit function from a given family, such as polynomials (Carroll 1963;McDaniel and Busemeyer 2005) or power-law functions (Koh and Meyer 1991). This approach attributes rich representations to human learners, but has traditionally given limited treatment to how such representations could be acquired. A second approach includes similarity-based theories (e.g., DeLosh et al., 1997, which focus on the idea that 1194 Psychon Bull Rev (2015) 22:1193-1215 people learn by forming associations: if x is used to predict y, observations with similar x values should also have similar y values. This approach can be straightforwardly implemented in a connectionist architecture and thus gives an account of the underlying learning mechanisms, but faces challenges in explaining how people generalize so broadly beyond their experience. Most recently, hybrids of these two approaches have ...

All models of self-motion from optical flow assume the instantaneous velocity field as input. We tested this assumption for human observers using random-dot displays that simulated translational and circular paths of movement by manipulating the lifetime and displacement of individual dots. For translational movement, observers were equally accurate in judging direction of heading from a "velocity field" with a two-frame dot life and a "direction field" in which the magnitudes of displacement were randomized while the radial pattern of directions was preserved, but at chance with a "speed field" in which the directions were randomized, preserving only magnitude. Accuracy declined with increasing noise in vector directions, but remained below 2.6 degrees with a 90 degrees noise envelope. Thus, the visual system uses the radial morphology of vector directions to determine translational heading and can tolerate large amounts of noise in this pattern. For circular movement, observers were equally accurate with a 2-frame "velocity field", 3-frame "acceleration" displays, and 2-frame and 3-frame "direction fields", consistent with the use of the pattern of vector directions to locate the center of rotation. The results indicate that successive independent velocity fields are sufficient for perception of translational and circular heading.

Working memory is crucial for many higher level cognitive functions, ranging from mental arithmetic to reasoning and problem solving. Likewise, the ability to learn and categorize novel concepts forms an indispensable part of human cognition. However, very little is known about the relationship between working memory and categorization. This article reports 2 studies that related people's working memory capacity (WMC) to their learning performance on multiple rule-based and information-integration perceptual categorization tasks. In both studies, structural equation modeling revealed a strong relationship between WMC and category learning irrespective of the requirement to integrate information across multiple perceptual dimensions. WMC was also uniformly related to people's ability to focus on the most task-appropriate strategy, regardless of whether or not that strategy involved information integration. Contrary to the predictions of the multiple systems view of categorization, working memory thus appears to underpin performance in both major classes of perceptual category-learning tasks.