Slowness and sparseness lead to place, head-direction, and spatial-view cells.

We present a model for the self-organized formation of place cells, head-direction cells, and spatial-view cells in the hippocampal formation based on unsupervised learning on quasi-natural visual stimuli. The model comprises a hierarchy of Slow Feature Analysis (SFA) nodes, which were recently shown to reproduce many properties of complex cells in the early visual system []. The system extracts a distributed grid-like representation of position and orientation, which is transcoded into a localized place-field, head-direction, or view representation, by sparse coding. The type of cells that develops depends solely on the relevant input statistics, i.e., the movement pattern of the simulated animal. The numerical simulations are complemented by a mathematical analysis that allows us to accurately predict the output of the top SFA layer.

Nash equilibria in multi-agent motor interactions.

Social interactions in classic cognitive games like the ultimatum game or the prisoner's dilemma typically lead to Nash equilibria when multiple competitive decision makers with perfect knowledge select optimal strategies. However, in evolutionary game theory it has been shown that Nash equilibria can also arise as attractors in dynamical systems that can describe, for example, the population dynamics of microorganisms. Similar to such evolutionary dynamics, we find that Nash equilibria arise naturally in motor interactions in which players vie for control and try to minimize effort. When confronted with sensorimotor interaction tasks that correspond to the classical prisoner's dilemma and the rope-pulling game, two-player motor interactions led predominantly to Nash solutions. In contrast, when a single player took both roles, playing the sensorimotor game bimanually, cooperative solutions were found. Our methodology opens up a new avenue for the study of human motor interactions within a game theoretic framework, suggesting that the coupling of motor systems can lead to game theoretic solutions.

Motor coordination: when two have to act as one.

Trying to pass someone walking toward you in a narrow corridor is a familiar example of a two-person motor game that requires coordination. In this study, we investigate coordination in sensorimotor tasks that correspond to classic coordination games with multiple Nash equilibria, such as "choosing sides," "stag hunt," "chicken," and "battle of sexes". In these tasks, subjects made reaching movements reflecting their continuously evolving "decisions" while they received a continuous payoff in the form of a resistive force counteracting their movements. Successful coordination required two subjects to "choose" the same Nash equilibrium in this force-payoff landscape within a single reach. We found that on the majority of trials coordination was achieved. Compared to the proportion of trials in which miscoordination occurred, successful coordination was characterized by several distinct features: an increased mutual information between the players' movement endpoints, an increased joint entropy during the movements, and by differences in the timing of the players' responses. Moreover, we found that the probability of successful coordination depends on the players' initial distance from the Nash equilibria. Our results suggest that two-person coordination arises naturally in motor interactions and is facilitated by favorable initial positions, stereotypical motor pattern, and differences in response times.

Altruistic learning.

The origin of altruism remains one of the most enduring puzzles of human behaviour. Indeed, true altruism is often thought either not to exist, or to arise merely as a miscalculation of otherwise selfish behaviour. In this paper, we argue that altruism emerges directly from the way in which distinct human decision-making systems learn about rewards. Using insights provided by neurobiological accounts of human decision-making, we suggest that reinforcement learning in game-theoretic social interactions (habitisation over either individuals or games) and observational learning (either imitative of inference based) lead to altruistic behaviour. This arises not only as a result of computational efficiency in the face of processing complexity, but as a direct consequence of optimal inference in the face of uncertainty. Critically, we argue that the fact that evolutionary pressure acts not over the object of learning ('what' is learned), but over the learning systems themselves ('how' things are learned), enables the evolution of altruism despite the direct threat posed by free-riders.