AI has seen remarkable progress in recent years, due to a switch from hand-designed shallow representations, to learned deep representations. While these methods excel with plentiful training data, they are still far from the human ability to learn concepts from just a few examples by reusing previously learned conceptual knowledge in new contexts. We argue that this gap might come from a fundamental misalignment between human and typical AI representations: while the former are grounded in rich sensorimotor experience, the latter are typically passive and limited to a few modalities such as vision and text. We take a step towards closing this gap by proposing an interactive, behavior-based model that represents concepts using sensorimotor contingencies grounded in an agent's experience. On a novel conceptual learning and benchmark suite, we demonstrate that conceptually meaningful behaviors can be learned, given supervision via training curricula.

Despite the recent successes of probabilistic programming languages (PPLs) in AI applications, PPLs offer only limited support for random variables whose distributions combine discrete and continuous elements. We develop the notion of measure-theoretic Bayesian networks (MTBNs) and use it to provide more general semantics for PPLs with arbitrarily many random variables defined over arbitrary measure spaces. We develop two new general sampling algorithms that are provably correct under the MTBN framework: the lexicographic likelihood weighting (LLW) for general MTBNs and the lexicographic particle filter (LPF), a specialized algorithm for state-space models. We further integrate MTBNs into a widely used PPL system, BLOG, and verify the effectiveness of the new inference algorithms through representative examples.