  In this paper we explore the richness of information captured by the latent
space of a vision-based generative model. The model combines unsupervised
generative learning with a task-based performance predictor to learn and to
exploit task-relevant object affordances given visual observations from a
reaching task, involving a scenario and a stick-like tool. While the learned
embedding of the generative model captures factors of variation in 3D tool
geometry (e.g. length, width, and shape), the performance predictor identifies
sub-manifolds of the embedding that correlate with task success. Within a
variety of scenarios, we demonstrate that traversing the latent space via
backpropagation from the performance predictor allows us to imagine tools
appropriate for the task at hand. Our results indicate that affordances-like
the utility for reaching-are encoded along smooth trajectories in latent space.
Accessing these emergent affordances by considering only high-level performance
criteria (such as task success) enables an agent to manipulate tool geometries
in a targeted and deliberate way.
