Witnessing dp-rank

We prove that in NTP_2 theories if p is a dependent type with dp-rank >= \kappa, then this can be witnessed by indiscernible sequences of tuples satisfying p. If p has dp-rank infinity, then this can be witnessed by singletons (in any theory)

On the Locus of Hodge Classes

Let $f: X \rightarrow S$ be a family of non singular projective varieties parametrized by a complex algebraic variety $S$. Fix $s \in S$, an integer $p$, and a class $h \in {\rm H}^{2p}(X_s,\Z)$ of Hodge type $(p,p)$. We show that the locus, on $S$, where $h$ remains of type $(p,p)$ is algebraic. This result, which in the geometric case would follow from the rational Hodge conjecture, is obtained in the setting of variations of Hodge structures.Comment: 25 pages, Plain Te

Intrinsic Motivation Systems for Autonomous Mental Development

Exploratory activities seem to be intrinsically rewarding for children and crucial for their cognitive development. Can a machine be endowed with such an intrinsic motivation system? This is the question we study in this paper, presenting a number of computational systems that try to capture this drive towards novel or curious situations. After discussing related research coming from developmental psychology, neuroscience, developmental robotics, and active learning, this paper presents the mechanism of Intelligent Adaptive Curiosity, an intrinsic motivation system which pushes a robot towards situations in which it maximizes its learning progress. This drive makes the robot focus on situations which are neither too predictable nor too unpredictable, thus permitting autonomous mental development.The complexity of the robot’s activities autonomously increases and complex developmental sequences self-organize without being constructed in a supervised manner. Two experiments are presented illustrating the stage-like organization emerging with this mechanism. In one of them, a physical robot is placed on a baby play mat with objects that it can learn to manipulate. Experimental results show that the robot first spends time in situations which are easy to learn, then shifts its attention progressively to situations of increasing difficulty, avoiding situations in which nothing can be learned. Finally, these various results are discussed in relation to more complex forms of behavioral organization and data coming from developmental psychology. Key words: Active learning, autonomy, behavior, complexity, curiosity, development, developmental trajectory, epigenetic robotics, intrinsic motivation, learning, reinforcement learning, values

Motivational principles for visual know-how development

What dynamics can enable a robot to continuously develop new visual know-how? We present a first experimental investigation where an AIBO robot develops visual competences from scratch driven only by internal motivations. The motivational principles used by the robot are independent of any particular task. As a consequence, they can constitute the basis for a general approach to sensory-motor development

In Search of the Neural Circuits of Intrinsic Motivation

Children seem to acquire new know-how in a continuous and open-ended manner. In this paper, we hypothesize that an intrinsic motivation to progress in learning is at the origins of the remarkable structure of children's developmental trajectories. In this view, children engage in exploratory and playful activities for their own sake, not as steps toward other extrinsic goals. The central hypothesis of this paper is that intrinsically motivating activities correspond to expected decrease in prediction error. This motivation system pushes the infant to avoid both predictable and unpredictable situations in order to focus on the ones that are expected to maximize progress in learning. Based on a computational model and a series of robotic experiments, we show how this principle can lead to organized sequences of behavior of increasing complexity characteristic of several behavioral and developmental patterns observed in humans. We then discuss the putative circuitry underlying such an intrinsic motivation system in the brain and formulate two novel hypotheses. The first one is that tonic dopamine acts as a learning progress signal. The second is that this progress signal is directly computed through a hierarchy of microcortical circuits that act both as prediction and metaprediction systems